diff --git a/.github/workflows/convergences-probes.yml b/.github/workflows/convergences-probes.yml new file mode 100644 index 0000000..80ef89d --- /dev/null +++ b/.github/workflows/convergences-probes.yml @@ -0,0 +1,26 @@ +name: Convergence research probes +on: + pull_request: + paths: + - 'research/convergences-20261112/**' + - '.github/workflows/convergences-probes.yml' + push: + paths: + - 'research/convergences-20261112/**' + - '.github/workflows/convergences-probes.yml' + workflow_dispatch: +permissions: + contents: read +jobs: + regenerate: + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: '3.14' + cache: pip + cache-dependency-path: research/convergences-20261112/requirements.txt + - run: python -m pip install -r research/convergences-20261112/requirements.txt + - run: python -B -m unittest discover -s research/convergences-20261112 -p test_check.py + - run: python research/convergences-20261112/check.py diff --git a/README.md b/README.md index fc7ee21..51c9426 100644 --- a/README.md +++ b/README.md @@ -16,9 +16,15 @@ This repository is **not** a derivation of a new fundamental theory of gravity, 3. **Phenomenological hypotheses & algebraic re-parameterizations (`CONJECTURE`)**: Wave-6 (`wave6_convergence_unification.py`) evaluates algebraic identities where `hbar`, `m`, and `R_H(z)` cancel by definition of `N_fil = 2*pi*m*c*R_H/hbar` (so `8.9580 kpc` is simply the ordinary MOND radius `r_M` of a `6e10 M_sun` galaxy at `a_dS`) and places a handwritten potential threshold `Phi_crit/c^2 = 8.0e-6` (`sigma_1D = 388.1 km/s`) between logarithmic MOND galaxy potentials and the Bullet Cluster. 4. **Elementary Lean 4 arithmetic checks (`PROVEN (ARITHMETIC-LEMMA)`)**: Stock Lean 4 (`Init`, zero Mathlib dependencies) files in `formal/` check the exact integer/rational exponent equations, interval inequalities, and commutative-ring product rearrangements referenced in `CLAIMS.md`. They do **not** prove physical force laws, Bell's theorem, or Weak Equivalence Principle bounds. +## Cross-repository convergence research + +The [convergence research collection](research/convergences-20261112/README.md) connects this repository with fractals, physics0 and astr0. It preserves nine exploratory reports, source ledgers, mathematical probes and independent agent reviews. + +The collection includes a test specification for nonlinear AeST collapse, distinctions between interference and readable records, a lattice mechanics comparison and methods for combining astronomical evidence. Its scope and next tests are explicit. No nonlinear AeST simulation or new galaxy-data fit is claimed. + ## Repository Layout & Verification Commands -All Python scripts use only the Python 3 standard library. Each certificate file in `results/*.json` embeds a `sha256_canonical` field equal to the `sha256` checksum of `json.dumps(payload_without_sha_field, sort_keys=True, separators=(",", ":"))` computed by the generator script that writes it (this is a deterministic content checksum for reproducibility, not a cryptographic signature). Raw file digests are recorded in `SHA256SUMS`. +The root audit scripts use only the Python 3 standard library. The separate convergence research probes declare their NumPy and SymPy dependencies in their own reproduction instructions. Each certificate file in `results/*.json` embeds a `sha256_canonical` field equal to the `sha256` checksum of `json.dumps(payload_without_sha_field, sort_keys=True, separators=(",", ":"))` computed by the generator script that writes it (this is a deterministic content checksum for reproducibility, not a cryptographic signature). Raw file digests are recorded in `SHA256SUMS`. | Script / Config | Output / Target | Verification Command | |---|---|---| diff --git a/research/convergences-20261112/PROVENANCE.md b/research/convergences-20261112/PROVENANCE.md new file mode 100644 index 0000000..4bfc6f9 --- /dev/null +++ b/research/convergences-20261112/PROVENANCE.md @@ -0,0 +1,40 @@ +# Provenance and claim scope + +This collection preserves a broad research pass across Foundation-0/gravity, fractals, physics0 and astr0, completed on 12 November 2026. Its purpose is to find useful connections and discriminating tests across the projects, while preserving the assumptions of each physical or mathematical model. + +## Authorship and review + +Research coordination and synthesis: gpt-forge, an OpenAI Codex agent working for Ahraz Arifuddin. The nine research agents were explicitly configured as gpt-6-astra with ultra reasoning. Publication preparation used gpt-6.1-sol agents. These are agent-authored exploratory results. Human scientific review remains pending. + +The robustness route independently recalculated selected results from the other routes. The robustness and hidden-dynamics agents separately checked the issue-specific AeST identities and their scope. Their independence concerns implementations and review roles. It is not independent empirical replication or human peer review. + +## Revisions studied + +| Repository | Studied revision | +| --- | --- | +| gravity | [d8c7544](https://github.com/Foundation-0/gravity/tree/d8c7544e89388720fc1c13de816ddb7dd03d2096) | +| fractals | [9669f55](https://github.com/Foundation-0/fractals/tree/9669f5579635c3543f145e8eca86133069ad6f27) | +| physics0 | [76410c3](https://github.com/Foundation-0/physics0/tree/76410c3deebf925f6c51017867dbcef29ff54e8b) | +| astr0 | [607a11e](https://github.com/Foundation-0/astr0/tree/607a11eaa83b2ec7539e0986046c3230406d2b04) | + +Those revisions include the earlier acceleration-evolution drafts. The publication branch starts from gravity's later main revision 1185a438dee8878d7580771b4d412b3860c70061. This collection does not review the later Wave 11 additions. Report links retain the revisions actually studied. + +The neighboring `*-sources.json` files distinguish primary literature, repository statements, the authors' own derivations and untested conjectures. Where a source was only partly inspected, that limitation remains recorded. Published astronomical examples are credited to their original investigators. + +## What the computations establish + +The probes check mathematical consequences of stated models. They include symbolic identities, analytic limits, numerical convergence, independent formulations and synthetic inference examples. Reproduction checks verify the published artifacts under declared tolerances. They do not establish the physical correctness of the selected models. + +The AeST compensated initial pair is a conditional algebraic witness derived from published linear variables. Its complete canonical initial-data map remains unimplemented. The collection also leaves nonlinear collapse, a healthy specified higher-derivative extension, stress lifetime, thermalization and a cosmologically selected pressure scale uncomputed. + +The acceleration-evolution work compares published fitted summaries with a phenomenological model. It supplies no new galaxy-level likelihood or measured evolution exponent. Its source data and covariance requirements remain separate from the synthetic probes in this collection. + +## Publication transformations + +The public edition retains the nine reports, scientific source ledgers, original probe algorithms, generated results, selected derivations and independent review findings. Machine-specific paths become relative paths or immutable public source links. Exact scientific inputs needed for reproduction are bundled with origin and digest records. + +Downloaded copies of third-party papers, temporary renderer output, private operational notes and machine-specific dispatch records are excluded. Their scientific citations and relevant findings remain in the reports. No personal memory store or private instructions are part of this collection. + +Historical review hashes identify the pre-publication text reviewed during the research pass. Path and presentation edits change those bytes without turning the reviews into acceptance of later physical work. The publication validation separately checks the portable edition. + +The repository's Apache-2.0 license applies to code. Documentation and numerical results use its CC-BY-4.0 license. Primary works retain their original authorship and terms. diff --git a/research/convergences-20261112/README.md b/research/convergences-20261112/README.md new file mode 100644 index 0000000..4a502f3 --- /dev/null +++ b/research/convergences-20261112/README.md @@ -0,0 +1,126 @@ +# What becomes visible between the threads? + +This research collection connects gravity, fractals, physics0 and astr0 through nine exploratory reports, primary-source ledgers and reproducible mathematical probes. It asks which patterns become informative when observations, disciplines and descriptions are combined. A shared fundamental theory is not assumed. + +Prepared 12 November 2026. The first research passes are complete. Computational checks do not establish new physical laws or observational discoveries. [Provenance and reviewed revisions](PROVENANCE.md) records authorship, scope and source versions. [Reproduction instructions](VALIDATION.md) cover the executable probes. + +**The most useful emerging distinction is between a thing, its relationships, and the evidence we can obtain about it.** Several examples show why those descriptions must be connected. They also show that joining descriptions is informative only when their differences are preserved. + +## A different view can reveal what the first cannot separate + +The evidence route gives an exact Gaussian example. A reference channel with no information about the target by itself measures a disturbance shared with the target channel. Joining them reduces the target's posterior variance by a factor of 25.75 under the stated model. Repeating the target channel a hundred times with the same shared disturbance barely helps. + +This is an illustration of an established idea used in exoplanet searches, [half-sibling regression](https://proceedings.mlr.press/v37/scholkopf15.pdf). The signal-free reference assumption matters: a contaminated reference can subtract the wanted signal. More agreement among measurements with the same blind spot does not supply the missing view. + +An astronomical example is concrete. DASCH's old observations of ASASSN-24fw support a long period but leave a half-period alternative open. ASAS covers the otherwise missing phase and shows normal brightness, excluding that alternative. [Published analysis, Section III.1](https://arxiv.org/html/2507.05367v3). + +This suggests a practical search strategy across astr0 and physics0: look for the observation that makes the remaining explanations disagree. That may be an old plate, an uneventful exposure, a calibration reference or a spectral line excluded from the original fit. + +## An unchanged local appearance can hide different relationships + +The relations route constructs two quantum examples with the same reduced system state and the same complete dephasing channel. In one, any single environment qubit reveals a classical pointer bit. In the other, information is protected in joint correlations and every one- or two-qubit fragment is uninformative. + +This connects fractals' Witness Map with physics0's quantum-error-correction interests. The example uses an established code, not a newly discovered natural environment. + +A physical limiting case already appears in a paper cited by fractals: perfectly isotropic illumination can cause decoherence without producing redundant readable records. [Riedel and Zurek, Figure 2(b), Eqs. 17-18](https://arxiv.org/html/1001.3419v2). + +The useful question becomes: what disappeared from the system's interference, what remains in correlations, and what can an observer actually read? Those are different quantities. A successful decoherence calculation does not alone determine all three. + +## Geometry, interactions and measured patterns can change separately + +The repetition route follows the existing incentre-lattice fold. Its original five-neighbor bar graph stays fixed as packing density changes. At the fcc endpoint, the full geometric contact graph has twelve neighbors. + +A scalar-spin model with fixed coupling on the original bars is invariant by construction. Adding interactions at new contacts changes it. Even with unchanged graph-indexed spin correlations, a scattering pattern can change because physical positions enter the observation. + +The convergence reviewer independently calculated vibrations of identical central springs on those bars. The spectrum changes as the structure folds, although the sum of squared frequencies stays fixed. A second spectral measure separates the geometries. This gives the spin-model comparison a mechanical counterpart. + +The calculation fixes the periodic cell, uses motions repeated identically in each cell, and omits new contact springs. It does not establish the full mechanical stability or material properties of CaB6. + +The unclaimed-connections route adds a different form of recurrence: a prescribed three-mass shape loop returns to its original internal shape while accumulating 27 degrees of orientation at zero total angular momentum. This is known geometric-phase mechanics. It is not a new free gravitational orbit. It suggests checking shape, orientation, relative phase and full state separately when a pattern appears to repeat. + +## What remains depends on transport, history and the chosen boundary + +The persistence route separates conserved excess, finite reaction exposure, protected configurations and continually rebuilt patterns. Its annihilation calculation shows how a symmetric residual and a conserved asymmetry are different survival mechanisms. Neither explains the origin of an initial asymmetry by itself. + +The physical transport question crosses into gravity. Absence of electromagnetic radiation does not establish absence of energy export: known scalar-field models can eject field energy while leaving a bound object. [Seidel and Suen](https://arxiv.org/abs/gr-qc/9309015). Whether a proposed AeST model does this requires its actual equations, fields and boundary conditions. + +The unclaimed route adds angular momentum as a separate constraint. Cooling energy at fixed angular momentum does not permit arbitrary contraction. Local curl, phase winding, total angular momentum and a rotating figure also describe different things. Its wave examples distinguish them without asserting that the examples model AeST or real dark matter. + +Persistence and visibility separate in observed astronomy too. HS Hya's binary continued to exist while its eclipses ceased as the orbital inclination changed. Historical plates and modern photometry preserve that history. [Davenport et al.](https://arxiv.org/abs/2107.10954). + +## A scale becomes more informative when we can predict how it moves + +The scale route identifies several origins of a boundary: competing rates, accumulated history, an observational threshold or the failure of an approximation. Kibble-Zurek dynamics is an established bridge from finite-rate change to finite correlation length. It does not establish one universality class across galaxies, turbulence and decoherence. + +The proposed galaxy-speed convergence needs further work. Its circular speed and one-dimensional dispersions are different observables, and its cooling calculation selects a gas density and an available time. These assumptions can move the apparent agreement. A useful next test predicts the full response to environment or epoch after definitions and inputs are fixed. + +The independent review makes that test concrete. Under the notebook's fixed-overdensity, Hubble-time cooling assumptions, its cooling speed rises toward earlier epochs. The repository's approximate collapse speed falls. Their present-day proximity need not persist. These are conditional model responses, not new measurements. + +The review also separates a density-profile slope from a stability threshold. The notebook's enclosed-mass formula is smooth through slope two. The proposed trapping onset is an additional assumption. A physical onset needs a growing perturbation or another dynamical criterion in the specified model. + +These velocity scales are separate from the galactic acceleration parameter a₀. + +The earlier [acceleration-evolution study](https://github.com/Foundation-0/gravity/blob/d8c7544e89388720fc1c13de816ddb7dd03d2096/acceleration-evolution/README.md) defines a₀(z)=A[H(z)/H₀]^q and compares its predictions with published observational summaries. It does not supply a new galaxy-data fit or a measured exponent. + +## What we omit can return as a dependence on history + +The hidden-dynamics route found a precise mathematical bridge. Start with two coupled quantities, then eliminate one exactly. Its influence can remain in a weighted history of the retained quantity and a term carrying the hidden initial condition. This is an elementary form of the established [Mori-Zwanzig method](https://math.berkeley.edu/~chorin/CHK02.pdf). + +The probe reproduces the complete trajectory both ways. It also shows how adding a missing present variable can replace the history integral with a larger equation that uses only its present state. Whether a description needs history depends on what it retains. + +A second probe keeps the same steady response while changing the hidden relaxation time. A changing input distinguishes the models. This supplies a concrete question for gravity and turbulence: which omitted variables matter for the timescale and observable we want to predict? + +Readable records and returning influence remain separate. A departing photon can preserve a record without returning to affect its source. A small quantum swap example can return past influence after the system is reset. Neither an information record nor a history integral alone identifies a new fundamental force. + +## The gravity question has a possible collapse experiment + +[A proposed collapse experiment](https://github.com/Foundation-0/gravity/issues/5) asks whether nonlinear collapse in AeST can produce a persistent effective pressure from a dark field. That directly joins scale selection, energy transport, turbulence and the question of which variables suffice to predict a system's evolution. + +In driven atomic-condensate experiments, large-scale shocks resemble those of a dissipative fluid. Conservative three-dimensional wave simulations reproduce the observations. Transverse instabilities feed vortex structures, offering a concrete route from resolved motion into smaller excitations. [Mossman et al.](https://arxiv.org/html/1712.06689). + +That experiment concerns an atomic gas driven by a piston. It does not establish AeST dynamics or a cosmic pressure floor. It does show why a strict one-dimensional calculation could omit the mechanism one wants to test. + +A complementary benchmark exposes a possible blind spot. A known perfect-caustic solution in a related ghost-condensate model has divergent curvature while the fourth spatial derivative vanishes. The proposed type of higher-derivative term supplies no restoring force for that configuration. [Arkani-Hamed et al., Section 3.5](https://arxiv.org/pdf/hep-ph/0507120). + +This is a test case for the regularization, not an AeST impossibility result. The exact action, permitted initial states, boundary fluxes and status of the extra term must be specified. Long-lived velocity dispersion also does not alone establish thermalization or entropy production. + +The route also derives a small diagnostic from the published linear AeST equations. Compensating a changed vector velocity with a changed scalar velocity preserves the initial effective density and velocity, while changing pressure and immediate acceleration. Independent algebra checks agree. + +The complete canonical constraint map remains to be validated, and a restricted cosmological preparation could still permit an accurate fluid approximation. + +The useful next step is to validate that initial-state construction in one specified linear model. Nonlinear tests can then measure retained stress, escaping energy and the response to a further disturbance. This could resolve part of the pressure proposal without claiming to explain a₀, inertia or the origin of the universe. + +## Reports and small probes + +Every report includes primary sources, objections, scope limits and next questions. The neighboring source ledgers record what was read. Probe outputs are calculations under declared assumptions. None is a new astronomical observation. + +| Route | Main report | Research pass | +| --- | --- | --- | +| Scale selection | [scales](reports/scales.md) | Complete | +| Relations and properties | [relations](reports/relations.md) | Complete | +| Repetition and common rules | [repetition](reports/repetition.md) | Complete | +| Persistence through change | [persistence](reports/persistence.md) | Complete | +| Reconnecting evidence | [evidence](reports/evidence.md) | Complete | +| Geometric phase, circulation and support | [unclaimed connections](reports/unclaimed.md) | Complete | +| What survives changes of description? | [robustness](reports/robustness.md) | Complete | +| Hidden variables and effective dynamics | [hidden dynamics](reports/hidden-dynamics.md) | Complete | +| Proposed AeST collapse test | [collapse-test assessment](reports/issue-5.md) | Complete | + +## How the four repositories connect + +| Repository | Connections worth carrying into its own work | +| --- | --- | +| gravity | Predict how candidate scales move. Derive pressure, stability and transport from a specified action. Separate physical memory from missing observations. | +| fractals | Compare repeated shapes with shared equations and their limits. Separate interference loss, accessible records and feedback. Give evolving cutoffs a physical clock. | +| physics0 | Compare a fixed graph with changing geometry and interactions. Reconstruct orientation from shape. Use withheld spectral lines and independent calibration to test inferred structure. | +| astr0 | Join epochs at phases where candidate explanations disagree. Retain informative non-events. Distinguish a surviving source from its changing visibility. | + +## Next small investigations + +- Reproduce one published eclipse-period ambiguity, including the non-event observations and detection completeness that separate its aliases. +- Compare lost interference, wave-spreading competition and accessible environment records for one stated photon-scattering model. +- Compare fixed-bar spin statistics, geometry-sensitive spring modes and distance-dependent interactions along the same lattice fold. +- Reconstruct one existing three-body trajectory's orientation from its reduced shape curve, keeping symmetries and particle labels explicit. +- Before a large dark-field simulation, specify the full action and validate the compensated linear initial-state test. Derive which energy, charge and angular-momentum fluxes must be tracked. No generic scalar-fluid analogy settles those dynamics. + +The original questions about inertia, creation, annihilation and cosmic history remain open. This collection supplies no universe-collision model or common microscopic explanation of every repeated pattern. Its proposed tests identify what evidence would strengthen or weaken each connection. diff --git a/research/convergences-20261112/VALIDATION.md b/research/convergences-20261112/VALIDATION.md new file mode 100644 index 0000000..0d30aef --- /dev/null +++ b/research/convergences-20261112/VALIDATION.md @@ -0,0 +1,49 @@ +# Probe validation + +All nine authored probes reproduced their saved scientific results during publication preparation on 2026-11-12. The check regenerated ten artifacts, including the hidden-dynamics trajectory CSV, in a temporary directory. No scientific values changed. + +From the repository root: + +```sh +python3 -m venv .venv-convergences +.venv-convergences/bin/python -m pip install -r research/convergences-20261112/requirements.txt +.venv-convergences/bin/python research/convergences-20261112/check.py +``` + +A fresh virtual environment installed the pinned requirements and passed the same check. The publication check used Python 3.14.6, NumPy 2.5.4 and SymPy 1.14.0. NumPy is used by relations and robustness. SymPy is used by issue-5. The other probes use the Python standard library, including the historical gravity modules imported by scales. + +The checker compares every generated JSON field and every trajectory CSV cell against the committed artifacts. Strings, structure and Boolean values must match exactly. Except for the six finite-difference residuals described below, numbers must be finite and agree within relative tolerance 1e-9 or absolute tolerance 1e-12. Interpreter and library version labels are excluded from scientific comparisons. + +The five `robustness/results.json` fields `mechanics.rows[i].energy_hessian_discrepancy` measure error in an independent Hessian check. They compare the symmetric finite-displacement spring energy at step 1e-4 with the matrix quadratic form. Both saved and regenerated residuals must be nonnegative, finite and strictly below 3e-8, matching the original probe assertion. + +These residuals include truncation and rounding error, so their final digits are not scientific predictions. Hosted Linux produced 7.631495435589386e-10 where the original Mac run saved 7.645866162420134e-10. The difference slightly exceeds the general absolute tolerance. The field-specific bound preserves the original accuracy requirement. + +The sixth diagnostic is exactly `robustness/results.json.aest_current.maximum_absolute_component_error`. It compares the analytic scalar-action derivative with centered differences at step 1e-5 over sixteen seeded points. Both saved and regenerated errors must be finite, nonnegative and strictly below the native 1e-7 bound. Linux produced 5.862759167030163e-10 versus the saved Mac 5.410445425013677e-10. These are derivative-check errors, not predictions about AeST viability. + +`test_check.py` checks both observed platform differences, rejects every diagnostic at or above its original bound, rejects Boolean or null diagnostic substitutions on either side, and rejects unrelated changed outputs. Boolean outputs also reject integer substitutions. CI runs these negative controls before regeneration. Saved scientific values and probe assertions are unchanged. + +The relations script also offers its original stricter `--check` comparison with absolute tolerance 1e-12. Robustness retains its own `--check` comparison with relative tolerance 1e-9 and a unit absolute floor. + +The saved JSON artifacts retain the original run's version labels. The original absolute interpreter path is replaced by `python3`. Historical input paths are replaced by bundle-relative paths. These are metadata changes. The scales and robustness formulas, constants, seeded inputs, assertions and saved numerical values are unchanged. + +The exact wave10 source, its wave7 import dependency and the wave10 certificate are bundled with digests. Their bytes match gravity commit `d8c7544e89388720fc1c13de816ddb7dd03d2096`. The certificate supplies the robustness collapse-dispersion column, which remains explicitly identified as reused. The manifest prevents a changed historical input from silently passing the check. + +The scoped GitHub Actions workflow runs only for bundle or workflow changes. Hosted CI results are separate evidence from this local check. No downloaded papers, extracted paper text, HTML reading copies, rendered page images, private coordination files or local operations snapshots are included. + +## Audit of all nine numerical outputs + +Only the six exact paths above have special bounds. The full output audit retained the general comparison policy for every other field: + +| Route | Error and residual fields reviewed | Comparison decision | +| --- | --- | --- | +| Evidence | Posterior error variances, seeded Monte Carlo error estimates, graph cycle residuals | Scientific model outputs stay strict, including the deliberately wrong line assignment. | +| Hidden dynamics | RK4 and Volterra error curves, step-halving ratios, closure approximation errors, coordinate and swap defects | Error curves and convergence rates are results. Native finest-step bounds and convergence assertions still run. | +| Issue 5 | Symbolic equation and Burgers residuals | Exact strings remain exact. | +| Persistence | Four RK4 relative errors, about 8e-14 to 1e-12 | General absolute floor suffices. Native errors must remain below 1e-8. | +| Relations | Channel, fragment and emission checks | Scientific matrices and rates stay strict. Native analytic assertions still run. | +| Repetition | Seven maximum squared-bar-length errors, at most 9e-16 | General absolute floor suffices. Native maximum must remain below 1e-12. | +| Robustness | Five Hessian residuals, one derivative error, channel matrix-unit residual | Only the six identified finite differences use native bounds. The channel residual stays strict and must be below 1e-13 natively. | +| Scales | Model curves and sensitivity calculations | Scientific values stay strict. No finite-difference diagnostic exception. | +| Unclaimed | Geometry reconstruction residuals, analytic Hessian, two step-halving trace differences | Values stay strict. Trace differences are about 4e-12 and 2e-13, with a native bound below 1e-9. Floquet traces, multipliers and stability results stay strict. | + +No reference artifact was edited during this audit. A changed error curve, variance, spectrum, stability classification, derivative formula, structure or result status remains a check failure under the existing policy. diff --git a/research/convergences-20261112/check.py b/research/convergences-20261112/check.py new file mode 100644 index 0000000..16df0fd --- /dev/null +++ b/research/convergences-20261112/check.py @@ -0,0 +1,98 @@ +#!/usr/bin/env python3 +"""Regenerate nine probes in a temporary copy and check saved scientific results.""" +from __future__ import annotations +import csv +import hashlib +import json +import math +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile + +HERE = Path(__file__).resolve().parent +PROBES = { + 'evidence': ('evidence_join.py', ['results.json']), + 'hidden-dynamics': ('hidden_dynamics.py', ['results.json', 'trajectories.csv']), + 'issue-5': ('issue5_checks.py', ['results.json']), + 'persistence': ('persistence_probes.py', ['results.json']), + 'relations': ('correlation_probe.py', ['results.json']), + 'repetition': ('graph_vs_geometry.py', ['graph-results.json']), + 'robustness': ('robustness_probes.py', ['results.json']), + 'scales': ('scale_probes.py', ['results.json']), + 'unclaimed': ('constraint_probes.py', ['results.json']), +} +# Environment labels do not describe a scientific result. All other keys count. +ENVIRONMENT_KEYS = {'numpy_version', 'sympy_version', 'python_version', 'python_executable'} +# Only these six finite-difference diagnostics use original native accuracy +# bounds instead of comparing platform-dependent cancellation error digits. +# All other error curves, variances, observables and residuals remain strict. +DIAGNOSTIC_LIMITS = { + **{f'robustness/results.json.mechanics.rows[{index}].energy_hessian_discrepancy': 3e-8 + for index in range(5)}, + 'robustness/results.json.aest_current.maximum_absolute_component_error': 1e-7, +} + + +def compare(actual, expected, location): + if location in DIAGNOSTIC_LIMITS: + limit = DIAGNOSTIC_LIMITS[location] + for value in (actual, expected): + assert isinstance(value, (float, int)) and not isinstance(value, bool), (location, value) + assert math.isfinite(value) and 0 <= value < limit, (location, value) + return + if isinstance(expected, bool): + assert isinstance(actual, bool) and actual == expected, (location, actual, expected) + elif isinstance(expected, dict): + assert isinstance(actual, dict) and actual.keys() == expected.keys(), location + for key in expected: + if key not in ENVIRONMENT_KEYS: + compare(actual[key], expected[key], f'{location}.{key}') + elif isinstance(expected, list): + assert isinstance(actual, list) and len(actual) == len(expected), location + for index, (a, e) in enumerate(zip(actual, expected)): + compare(a, e, f'{location}[{index}]') + elif isinstance(expected, (float, int)) and not isinstance(expected, bool): + assert isinstance(actual, (float, int)) and not isinstance(actual, bool), location + assert math.isfinite(actual) and math.isfinite(expected), location + assert math.isclose(actual, expected, rel_tol=1e-9, abs_tol=1e-12), (location, actual, expected) + else: + assert actual == expected, (location, actual, expected) + + +def main(): + # Refuse changed historical inputs before any probe imports them. + manifest = json.loads((HERE / 'inputs/manifest.json').read_text()) + for item in manifest['files']: + path = HERE / item['bundle_path'] + assert hashlib.sha256(path.read_bytes()).hexdigest() == item['sha256'], path + with tempfile.TemporaryDirectory(prefix='convergences-check-') as directory: + temporary = Path(directory) / 'bundle' + shutil.copytree(HERE, temporary) + for name, (script, outputs) in PROBES.items(): + work = temporary / 'probes' / name + for output in outputs: + (work / output).unlink() + result = subprocess.run([sys.executable, '-B', str(work / script)], capture_output=True, text=True) + if result.returncode: + raise RuntimeError(f'{name}: {result.stdout}\n{result.stderr}') + for output in outputs: + reference = HERE / 'probes' / name / output + generated = work / output + if output.endswith('.json'): + compare(json.loads(generated.read_text()), json.loads(reference.read_text()), f'{name}/{output}') + else: + with generated.open(newline='') as stream: + actual = list(csv.reader(stream)) + with reference.open(newline='') as stream: + expected = list(csv.reader(stream)) + assert actual[0] == expected[0] and len(actual) == len(expected), output + compare([[float(v) for v in row] for row in actual[1:]], + [[float(v) for v in row] for row in expected[1:]], f'{name}/{output}') + print(f'PASS {name}: {", ".join(outputs)}') + print('PASS all nine probes; historical inputs match pinned SHA-256 digests') + + +if __name__ == '__main__': + main() diff --git a/research/convergences-20261112/inputs/README.md b/research/convergences-20261112/inputs/README.md new file mode 100644 index 0000000..92bbf5c --- /dev/null +++ b/research/convergences-20261112/inputs/README.md @@ -0,0 +1,9 @@ +# Historical gravity inputs + +These files preserve the gravity calculations used by the scales and robustness probes. They are exact copies from [Foundation-0/gravity at d8c7544](https://github.com/Foundation-0/gravity/tree/d8c7544e89388720fc1c13de816ddb7dd03d2096). `manifest.json` records each upstream path and SHA-256 digest. + +- `wave10_covariant_jeans_unification.py` supplies the approximate Eisenstein-Hu power spectrum and fixed cosmology used by the scales probe. +- `wave7_group_cluster_threshold_audit.py` is the wave10 module's import dependency. Its catalog fitting routines are not called by these probes. +- `wave10_covariant_jeans_certificates.json` supplies the previously computed collapse-dispersion trajectory used by the robustness probe. That column is a reused calculation, not an independent recomputation. + +The module headers retain their original attribution. The upstream code is Apache-2.0 and the results are CC-BY-4.0, as stated in those headers. The certificate is retained whole so its original digest remains verifiable. The checker verifies every digest before running the probes. It never substitutes current repository data for these historical files. diff --git a/research/convergences-20261112/inputs/manifest.json b/research/convergences-20261112/inputs/manifest.json new file mode 100644 index 0000000..e25e03f --- /dev/null +++ b/research/convergences-20261112/inputs/manifest.json @@ -0,0 +1,21 @@ +{ + "repository": "https://github.com/Foundation-0/gravity", + "commit": "d8c7544e89388720fc1c13de816ddb7dd03d2096", + "files": [ + { + "upstream_path": "wave10_covariant_jeans_unification.py", + "bundle_path": "inputs/wave10_covariant_jeans_unification.py", + "sha256": "af8a2459aa8f5885250ab6b5914c50cc852bcc691982c8ef5cf692603bece927" + }, + { + "upstream_path": "wave7_group_cluster_threshold_audit.py", + "bundle_path": "inputs/wave7_group_cluster_threshold_audit.py", + "sha256": "5de311fa11f22285f62cf82dd5cfc9e2651c2bfbe990fb194e6517171608dc29" + }, + { + "upstream_path": "results/wave10_covariant_jeans_certificates.json", + "bundle_path": "inputs/wave10_covariant_jeans_certificates.json", + "sha256": "dd37a45adcb3c815d1a2d44bbbb58ac0235b9ea30d58d6b5a3438a46d91c874e" + } + ] +} diff --git a/research/convergences-20261112/inputs/wave10_covariant_jeans_certificates.json b/research/convergences-20261112/inputs/wave10_covariant_jeans_certificates.json new file mode 100644 index 0000000..b56b5fa --- /dev/null +++ b/research/convergences-20261112/inputs/wave10_covariant_jeans_certificates.json @@ -0,0 +1,204 @@ +{ + "schema": "FOUNDATION-0/GRAVITY-WAVE10-JEANS-UNIFICATION/1.0", + "claim_c25_linear_sound_speed_nogo": { + "epistemic_status": "COMPUTED (LINEAR PERTURBATION & JEANS SCALING NO-GO BOUND)", + "target_halo_dispersion_kms": 185.0, + "homogeneous_z0_comoving_kJ_Mpc_inv": 0.2504, + "homogeneous_z0_comoving_lambdaJ_Mpc": 25.1, + "recombination_matter_density_over_crit0": 420653209.2, + "recombination_to_virial200_density_ratio": 2103266.0, + "polytrope_gamma2_naive_cs_z1100_over_c": 0.8949, + "scordatura_k4_comoving_kJ_ratio_z1100_over_z0": 0.1736, + "shift_symmetric_K_power_scan": [ + { + "power_p": 2.0, + "eps_z0": 3.808e-07, + "w_z1100": 0.93921, + "cs_z1100_kms": 295055.77, + "k_J_com_z1100_Mpc_inv": 0.0052 + }, + { + "power_p": 4.0, + "eps_z0": 1.1424e-06, + "w_z1100": 0.00031405, + "cs_z1100_kms": 6133.73, + "k_J_com_z1100_Mpc_inv": 0.2506 + }, + { + "power_p": 8.0, + "eps_z0": 2.6656e-06, + "w_z1100": 6.7036e-06, + "cs_z1100_kms": 829.8, + "k_J_com_z1100_Mpc_inv": 1.852 + }, + { + "power_p": 16.0, + "eps_z0": 5.7121e-06, + "w_z1100": 1.4488e-06, + "cs_z1100_kms": 372.69, + "k_J_com_z1100_Mpc_inv": 4.1236 + }, + { + "power_p": 32.0, + "eps_z0": 1.1805e-05, + "w_z1100": 7.2657e-07, + "cs_z1100_kms": 259.63, + "k_J_com_z1100_Mpc_inv": 5.9193 + } + ] + }, + "claim_c26_dark_whim_nonlinear_collapse_scale": { + "epistemic_status": "COMPUTED (ZERO-FREE-PARAMETER PRESS-SCHECHTER SCALE & JEANS SLOPE) & CONJECTURE (NONLINEAR AEST FLUID-SHOCK CLOSURE WITHOUT DARK COOLING)", + "sigma_star_z0_kms": 185.59, + "press_schechter_redshift_trajectory": [ + { + "z": 0.0, + "D_z": 1.0, + "R_star_comoving_Mpc": 3.3483, + "M_star_Msun": 6240000000000.0, + "V_200_kms": 262.46, + "sigma_1D_star_kms": 185.59 + }, + { + "z": 0.3, + "D_z": 0.8528, + "R_star_comoving_Mpc": 2.3822, + "M_star_Msun": 2247000000000.0, + "V_200_kms": 196.97, + "sigma_1D_star_kms": 139.28 + }, + { + "z": 0.5, + "D_z": 0.7689, + "R_star_comoving_Mpc": 1.8798, + "M_star_Msun": 1104000000000.0, + "V_200_kms": 161.74, + "sigma_1D_star_kms": 114.36 + }, + { + "z": 1.0, + "D_z": 0.6067, + "R_star_comoving_Mpc": 1.0388, + "M_star_Msun": 186300000000.0, + "V_200_kms": 98.88, + "sigma_1D_star_kms": 69.92 + }, + { + "z": 2.0, + "D_z": 0.4171, + "R_star_comoving_Mpc": 0.3406, + "M_star_Msun": 6570000000.0, + "V_200_kms": 38.65, + "sigma_1D_star_kms": 27.33 + }, + { + "z": 3.0, + "D_z": 0.3154, + "R_star_comoving_Mpc": 0.1235, + "M_star_Msun": 313400000.0, + "V_200_kms": 16.07, + "sigma_1D_star_kms": 11.36 + }, + { + "z": 5.0, + "D_z": 0.2111, + "R_star_comoving_Mpc": 0.0198, + "M_star_Msun": 1282000.0, + "V_200_kms": 3.13, + "sigma_1D_star_kms": 2.22 + } + ], + "hydrostatic_jeans_slope_suppression": [ + { + "system": "Dwarf_50kms", + "sigma_halo_kms": 35.0, + "hydrostatic_density_slope_gamma_d": 0.0711, + "r_probe_kpc": 5.0, + "R_vir_kpc": 75.0, + "enclosed_dust_fraction_inside_r_probe": 0.000359, + "enclosed_dust_over_Mb_cosmic_cap": 0.00193 + }, + { + "system": "Lstar_spiral_176kms", + "sigma_halo_kms": 125.0, + "hydrostatic_density_slope_gamma_d": 0.9073, + "r_probe_kpc": 10.0, + "R_vir_kpc": 220.0, + "enclosed_dust_fraction_inside_r_probe": 0.001551, + "enclosed_dust_over_Mb_cosmic_cap": 0.00832 + }, + { + "system": "Threshold_halo_185_6kms", + "sigma_halo_kms": 185.59, + "hydrostatic_density_slope_gamma_d": 2.0, + "r_probe_kpc": 15.0, + "R_vir_kpc": 300.0, + "enclosed_dust_fraction_inside_r_probe": 0.05, + "enclosed_dust_over_Mb_cosmic_cap": 0.26822 + } + ], + "zero_fitted_parameter_catalog_benchmarks": { + "clean_60": { + "chi2": 60.2645, + "rms_dex": 0.1283, + "n": 60, + "k_fitted_params": 0, + "bic_k0": 60.2645, + "delta_bic_vs_wave7_3param": -10.01, + "delta_bic_vs_wave9_1param": -3.9 + }, + "primary_77": { + "chi2": 106.5107, + "rms_dex": 0.1461, + "n": 77, + "k_fitted_params": 0, + "bic_k0": 106.5107, + "delta_bic_vs_wave7_3param": -6.6, + "delta_bic_vs_wave9_1param": -4.27 + }, + "full_126": { + "chi2": 148.2134, + "rms_dex": 0.124, + "n": 126, + "k_fitted_params": 0, + "bic_k0": 148.2134, + "delta_bic_vs_wave7_3param": -8.62, + "delta_bic_vs_wave9_1param": -4.75 + } + } + }, + "claim_c27_four_way_scale_convergence_and_forecasts": { + "epistemic_status": "COMPUTED (SCALE COMPARISON & FALSIFIABLE REDSHIFT FORECAST) / CONJECTURE (SINGULAR-ORIGIN COINCIDENCE)", + "four_converging_scales_kms": { + "empirical_wave9_group_onset_clean60_full126": [ + 180.0, + 190.0 + ], + "planck2018_press_schechter_Mstar_z0": 185.59, + "milgrom_btfr_Lstar_vflat": 175.82, + "bremsstrahlung_hubble_cooling_Delta1000": 178.42 + }, + "lorentz_norm_equivalent_Q0_inv_Mpc": 30.052, + "euclid_lsst_200kms_group_redshift_test": [ + { + "redshift_z": 0.0, + "dynamic_dark_whim_sigma_J_kms": 185.59, + "dynamic_f_trap_at_200kms": 0.1389, + "constant_lagrangian_f_trap_at_200kms": 0.1389 + }, + { + "redshift_z": 0.5, + "dynamic_dark_whim_sigma_J_kms": 114.36, + "dynamic_f_trap_at_200kms": 0.673, + "constant_lagrangian_f_trap_at_200kms": 0.1389 + }, + { + "redshift_z": 1.0, + "dynamic_dark_whim_sigma_J_kms": 69.92, + "dynamic_f_trap_at_200kms": 0.8778, + "constant_lagrangian_f_trap_at_200kms": 0.1389 + } + ] + }, + "sha256_canonical": "7dd4b40172b8fe261c3028f7a6af6e2b5131fb93cd83d10c439e3c5f0c5be3d4" +} diff --git a/research/convergences-20261112/inputs/wave10_covariant_jeans_unification.py b/research/convergences-20261112/inputs/wave10_covariant_jeans_unification.py new file mode 100644 index 0000000..b4fbf68 --- /dev/null +++ b/research/convergences-20261112/inputs/wave10_covariant_jeans_unification.py @@ -0,0 +1,360 @@ +""" +Foundation-0 / gravity -- Wave-10 Linear Sound-Speed No-Go, Dark-WHIM Nonlinear Collapse Scale & 4-Way Convergence (C-25..C-27; M-08) +attribution: Written by AI agent (Gemini, Google, via orda-aska for Foundation-0); not yet reviewed by a person. +license: Apache-2.0 (code) / CC-BY-4.0 (results). +""" + +from __future__ import annotations +import hashlib +import json +import math +import sys +from pathlib import Path + +import wave7_group_cluster_threshold_audit as w7 + +C_KMS = 299792.458 +C_SI = 299792458.0 +G = 6.67430e-11 +HBAR = 1.054571817e-34 +K_B = 1.380649e-23 +M_P = 1.67262192369e-27 +M_E = 9.1093837015e-31 +ALPHA_EM = 1.0 / 137.035999084 +M_SUN = 1.98847e30 +MPC = 3.085677581491367e22 +KPC = 3.085677581491367e19 +A0 = 1.20e-10 + +# Planck 2018 TT,TE,EE+lowE+lensing (arXiv:1807.06209) +H_LITTLE = 0.6736 +H0_SI = (100.0 * H_LITTLE * 1000.0) / MPC +OMEGA_B_H2 = 0.02237 +OMEGA_C_H2 = 0.1200 +OMEGA_M_H2 = OMEGA_B_H2 + OMEGA_C_H2 + 0.00064 +OMEGA_B = OMEGA_B_H2 / (H_LITTLE ** 2) +OMEGA_C = OMEGA_C_H2 / (H_LITTLE ** 2) +OMEGA_M = OMEGA_M_H2 / (H_LITTLE ** 2) +OMEGA_L = 1.0 - OMEGA_M +T_CMB = 2.7255 +N_S = 0.9649 +SIGMA8_PLANCK = 0.8111 +DELTA_C_SPH = 1.686 +RHO_CRIT0 = 3.0 * (H0_SI ** 2) / (8.0 * math.pi * G) +F_BAR_R2500 = 0.105 +DUST_TO_B_R2500 = (1.0 - F_BAR_R2500) / F_BAR_R2500 + + +def nu_rar(y: float) -> float: + sy = math.sqrt(max(0.0, y)) + if sy == 0.0: + return 1.0 + return 1.0 if sy > 40.0 else 1.0 / (1.0 - math.exp(-sy)) + + +def audit_c25_linear_sound_speed_nogo() -> dict: + """Evaluates why a homogeneous FLRW adiabatic sound speed c_s(z=0)=185 km/s fails linear cosmology.""" + cs_target_kms = 185.0 + cs0_sq_over_c2 = (cs_target_kms / C_KMS) ** 2 + + # 1. Polytrope P propto rho^gamma (gamma=2 BEC self-interaction) calibrated to 185 km/s in a Delta=200 halo: + rho_m_z1100_over_crit0 = OMEGA_M * (1101.0 ** 3) + halo_200_over_crit0 = 200.0 + density_inversion_ratio = rho_m_z1100_over_crit0 / halo_200_over_crit0 + naive_gamma2_cs_z1100_over_c = (cs_target_kms / C_KMS) * math.sqrt(density_inversion_ratio) + + # 2. Constant-M k^4 scordatura / quantum-pressure Jeans wavenumber scaling: k_J,com(z) / k_J,com(0) = (1+z)^(-1/4) + scordatura_kJ_ratio_z1100_to_z0 = 1101.0 ** (-0.25) + + # 3. Shift-symmetric K(Q) = Lambda^4 * eps^p around Q_0 across p = 2, 4, 8, 16, 32: + k_power_scan = [] + kJ_com_z0_Mpc_inv = math.sqrt(1.5 * OMEGA_M) * (100.0 * H_LITTLE / cs_target_kms) + lambda_J_com_z0_Mpc = (2.0 * math.pi) / kJ_com_z0_Mpc_inv + + for p in [2.0, 4.0, 8.0, 16.0, 32.0]: + eps0 = (p - 1.0) * cs0_sq_over_c2 / (1.0 - (p - 1.0) * cs0_sq_over_c2) + target = (p * (eps0 ** (p - 1.0)) + (p - 1.0) * (eps0 ** p)) * (1101.0 ** 3) + lo_l, hi_l = math.log(eps0), 40.0 + for _ in range(90): + mid_l = 0.5 * (lo_l + hi_l) + m = math.exp(mid_l) + val = p * (m ** (p - 1.0)) + (p - 1.0) * (m ** p) + if val < target: + lo_l = mid_l + else: + hi_l = mid_l + ez = math.exp(0.5 * (lo_l + hi_l)) + w_1100 = ez / (p + (p - 1.0) * ez) + cs_1100 = C_KMS * math.sqrt(ez / ((p - 1.0) * (1.0 + ez))) + kJ_1100 = math.sqrt(1.5 * OMEGA_M) * (100.0 * H_LITTLE / cs_1100) * math.sqrt(1101.0) + k_power_scan.append({ + "power_p": p, + "eps_z0": float(f"{eps0:.4e}"), + "w_z1100": float(f"{w_1100:.4e}"), + "cs_z1100_kms": round(cs_1100, 2), + "k_J_com_z1100_Mpc_inv": round(kJ_1100, 4), + }) + + return { + "epistemic_status": "COMPUTED (LINEAR PERTURBATION & JEANS SCALING NO-GO BOUND)", + "target_halo_dispersion_kms": cs_target_kms, + "homogeneous_z0_comoving_kJ_Mpc_inv": round(kJ_com_z0_Mpc_inv, 4), + "homogeneous_z0_comoving_lambdaJ_Mpc": round(lambda_J_com_z0_Mpc, 2), + "recombination_matter_density_over_crit0": round(rho_m_z1100_over_crit0, 1), + "recombination_to_virial200_density_ratio": round(density_inversion_ratio, 1), + "polytrope_gamma2_naive_cs_z1100_over_c": round(naive_gamma2_cs_z1100_over_c, 4), + "scordatura_k4_comoving_kJ_ratio_z1100_over_z0": round(scordatura_kJ_ratio_z1100_to_z0, 4), + "shift_symmetric_K_power_scan": k_power_scan, + } + + +def build_eh98_power_spectrum(): + """Constructs Planck-2018 normalized Eisenstein & Hu (1998, ApJ 496, 605) linear sigma(R) and D(z).""" + theta_27 = T_CMB / 2.7 + + def eh98_T(k_Mpc: float) -> float: + q_k = k_Mpc / H_LITTLE + alpha_g = ( + 1.0 + - 0.328 * math.log(431.0 * OMEGA_M_H2) * (OMEGA_B / OMEGA_M) + + 0.38 * math.log(22.3 * OMEGA_M_H2) * ((OMEGA_B / OMEGA_M) ** 2) + ) + s_sound = 44.5 * math.log(9.83 / OMEGA_M_H2) / math.sqrt(1.0 + 10.0 * (OMEGA_B_H2 ** 0.75)) + gamma_eff = OMEGA_M * H_LITTLE * (alpha_g + (1.0 - alpha_g) / (1.0 + (0.43 * k_Mpc * s_sound) ** 4)) + q = q_k * (theta_27 ** 2) / gamma_eff + l0 = math.log(2.0 * math.e + 1.8 * q) + c0 = 14.2 + 731.0 / (1.0 + 62.5 * q) + return l0 / (l0 + c0 * q * q) + + def top_hat_W(x: float) -> float: + if x < 1.0e-4: + return 1.0 - (x * x) / 10.0 + return 3.0 * (math.sin(x) - x * math.cos(x)) / (x ** 3) + + nk = 1600 + lk_min, lk_max = math.log(1.0e-5), math.log(300.0) + dlk = (lk_max - lk_min) / nk + ks = [math.exp(lk_min + (i + 0.5) * dlk) for i in range(nk)] + dks = [k * dlk for k in ks] + unnorm = [(k ** N_S) * (eh98_T(k) ** 2) for k in ks] + r8 = 8.0 / H_LITTLE + sig8_raw = math.sqrt( + sum((ks[i] ** 2 * dks[i] / (2.0 * math.pi ** 2)) * unnorm[i] * (top_hat_W(ks[i] * r8) ** 2) for i in range(nk)) + ) + pk0 = [unnorm[i] * ((SIGMA8_PLANCK / sig8_raw) ** 2) for i in range(nk)] + + def sigma_R0(r_Mpc: float) -> float: + s2 = sum((ks[i] ** 2 * dks[i] / (2.0 * math.pi ** 2)) * pk0[i] * (top_hat_W(ks[i] * r_Mpc) ** 2) for i in range(nk)) + return math.sqrt(s2) + + def E_z(z: float) -> float: + return math.sqrt(OMEGA_M * ((1.0 + z) ** 3) + OMEGA_L) + + def D_raw(z: float) -> float: + nz = 1600 + u0, u1 = math.log(1.0 + z), math.log(max(5000.0, 50.0 * (1.0 + z))) + du = (u1 - u0) / nz + acc = 0.0 + for i in range(nz): + zp1 = math.exp(u0 + (i + 0.5) * du) + ez = math.sqrt(OMEGA_M * (zp1 ** 3) + OMEGA_L) + acc += (zp1 ** 2) * du / (ez ** 3) + return 2.5 * OMEGA_M * E_z(z) * acc + + d0 = D_raw(0.0) + return sigma_R0, (lambda z: D_raw(z) / d0) + + +def audit_c26_nonlinear_collapse_and_k0_test(sigma_R0, D_norm) -> dict: + """Computes Planck-2018 Press-Schechter sigma_*(z), Jeans core-collapse slope, and k=0 126-system test.""" + trajectory = [] + sigma_star_z0 = 0.0 + + for z in [0.0, 0.3, 0.5, 1.0, 2.0, 3.0, 5.0]: + dz = D_norm(z) + target = DELTA_C_SPH / dz + lo, hi = 1.0e-4, 25.0 + for _ in range(55): + mid = math.sqrt(lo * hi) + if sigma_R0(mid) > target: + lo = mid + else: + hi = mid + rs = 0.5 * (lo + hi) + ms = (4.0 / 3.0) * math.pi * ((rs * MPC) ** 3) * (OMEGA_M * RHO_CRIT0) + ez2 = OMEGA_M * ((1.0 + z) ** 3) + OMEGA_L + r200_z = ((3.0 * ms) / (4.0 * math.pi * 200.0 * RHO_CRIT0 * ez2)) ** (1.0 / 3.0) + v200_kms = math.sqrt(G * ms / r200_z) / 1000.0 + sig1d_kms = v200_kms / math.sqrt(2.0) + if z == 0.0: + sigma_star_z0 = sig1d_kms + trajectory.append({ + "z": z, + "D_z": round(dz, 4), + "R_star_comoving_Mpc": round(rs, 4), + "M_star_Msun": float(f"{ms / M_SUN:.3e}"), + "V_200_kms": round(v200_kms, 2), + "sigma_1D_star_kms": round(sig1d_kms, 2), + }) + + # Hydrostatic Jeans log-slope gamma_d = 2*(sigma_halo/sigma_*)^2 and enclosed core dust fraction (r/R_vir)^(3-gamma_d) + core_suppression_examples = [] + for name, sig_h, r_in_kpc, r_vir_kpc in [ + ("Dwarf_50kms", 35.0, 5.0, 75.0), + ("Lstar_spiral_176kms", 125.0, 10.0, 220.0), + ("Threshold_halo_185_6kms", sigma_star_z0, 15.0, 300.0), + ]: + gamma_d = 2.0 * ((sig_h / sigma_star_z0) ** 2) + f_inner = (r_in_kpc / r_vir_kpc) ** max(0.0, 3.0 - gamma_d) + core_suppression_examples.append({ + "system": name, + "sigma_halo_kms": round(sig_h, 2), + "hydrostatic_density_slope_gamma_d": round(gamma_d, 4), + "r_probe_kpc": r_in_kpc, + "R_vir_kpc": r_vir_kpc, + "enclosed_dust_fraction_inside_r_probe": round(f_inner, 6), + "enclosed_dust_over_Mb_cosmic_cap": round((OMEGA_C / OMEGA_B) * f_inner, 5), + }) + + # Zero-fitted-parameter (k = 0) evaluation on Wave-7 126-system benchmark using sigma_J = sigma_*(z=0) + def pred_k0(sigma_kms: float) -> float: + if sigma_kms <= sigma_star_z0: + return 0.0 + f_trap = 1.0 - ((sigma_star_z0 / sigma_kms) ** 2) + g_tot = 2.0 * ((sigma_kms * 1.0e3) ** 2) / (250.0 * KPC) + lo_g, hi_g = 1.0e-15, g_tot + for _ in range(55): + mid_g = 0.5 * (lo_g + hi_g) + if mid_g * (nu_rar(mid_g / A0) + f_trap * DUST_TO_B_R2500) < g_tot: + lo_g = mid_g + else: + hi_g = mid_g + gb_sol = 0.5 * (lo_g + hi_g) + return math.log10(g_tot / (gb_sol * nu_rar(gb_sol / A0))) + + all_rows = w7.build_catalog() + w_77 = [r for r in all_rows if 150.0 <= r["sig"] <= 1200.0] + clean_60 = [r for r in all_rows if r["cat"] not in ("Milgrom2019_opt", "Milgrom2019_rich")] + + k0_fits = {} + for key, ds, w7_bic, w9_k1_bic in [ + ("clean_60", clean_60, 70.27, 64.167), + ("primary_77", w_77, 113.11, 110.7794), + ("full_126", all_rows, 156.83, 152.9667), + ]: + res = w7.odr_chi2(ds, pred_k0) + res["k_fitted_params"] = 0 + res["bic_k0"] = res["chi2"] + res["delta_bic_vs_wave7_3param"] = round(res["chi2"] - w7_bic, 2) + res["delta_bic_vs_wave9_1param"] = round(res["chi2"] - w9_k1_bic, 2) + k0_fits[key] = res + + return { + "epistemic_status": ( + "COMPUTED (ZERO-FREE-PARAMETER PRESS-SCHECHTER SCALE & JEANS SLOPE) & " + "CONJECTURE (NONLINEAR AEST FLUID-SHOCK CLOSURE WITHOUT DARK COOLING)" + ), + "sigma_star_z0_kms": round(sigma_star_z0, 2), + "press_schechter_redshift_trajectory": trajectory, + "hydrostatic_jeans_slope_suppression": core_suppression_examples, + "zero_fitted_parameter_catalog_benchmarks": k0_fits, + } + + +def audit_c27_four_way_convergence_and_predictions(c26: dict) -> dict: + """Compares the 4 converging ~185 km/s velocity scales and generates high-z Euclid group predictions.""" + sigma_star_z0 = c26["sigma_star_z0_kms"] + v_lstar_kms = ((G * 6.0e10 * M_SUN * A0) ** 0.25) / 1000.0 + + # Rees-Ostriker free-free Hubble-cooling transition at inner halo / group core overdensity Delta = 1000: + g_ff = 1.2 + c_ff = ( + (16.0 / 3.0) + * math.sqrt(2.0 * math.pi / 3.0) + * g_ff + * (ALPHA_EM ** 3) + * ((HBAR / (M_E * C_SI)) ** 2) + * C_SI + * math.sqrt(M_E * (C_SI ** 2)) + ) + f_b_cosmic = OMEGA_B / OMEGA_M + n_e_1000 = (f_b_cosmic * 1000.0 * RHO_CRIT0) / (1.14 * M_P) + sqrt_kbt_1000 = (1.15 * c_ff * n_e_1000 * (1.0 / H0_SI)) / 3.0 + sigma_ff_delta1000_kms = math.sqrt((sqrt_kbt_1000 ** 2) / (0.60 * M_P)) / 1000.0 + + # Equivalent AeST Lorentz-norm parameter Q_0 if X = Q^2 - Y instead produced constant sigma_J = a0 / (2 c Q_0): + q0_inv_Mpc = ((2.0 * C_SI * (sigma_star_z0 * 1000.0)) / A0) / MPC + + # Discriminating high-z prediction for a sigma = 200 km/s group across z = 0, 0.5, 1.0: + z_map = {row["z"]: row["sigma_1D_star_kms"] for row in c26["press_schechter_redshift_trajectory"]} + euclid_group_200kms_forecast = [] + for z in [0.0, 0.5, 1.0]: + sj_dyn = z_map[z] + f_trap_dyn = max(0.0, 1.0 - (sj_dyn / 200.0) ** 2) + f_trap_const = max(0.0, 1.0 - (sigma_star_z0 / 200.0) ** 2) + euclid_group_200kms_forecast.append({ + "redshift_z": z, + "dynamic_dark_whim_sigma_J_kms": sj_dyn, + "dynamic_f_trap_at_200kms": round(f_trap_dyn, 4), + "constant_lagrangian_f_trap_at_200kms": round(f_trap_const, 4), + }) + + return { + "epistemic_status": "COMPUTED (SCALE COMPARISON & FALSIFIABLE REDSHIFT FORECAST) / CONJECTURE (SINGULAR-ORIGIN COINCIDENCE)", + "four_converging_scales_kms": { + "empirical_wave9_group_onset_clean60_full126": [180.0, 190.0], + "planck2018_press_schechter_Mstar_z0": sigma_star_z0, + "milgrom_btfr_Lstar_vflat": round(v_lstar_kms, 2), + "bremsstrahlung_hubble_cooling_Delta1000": round(sigma_ff_delta1000_kms, 2), + }, + "lorentz_norm_equivalent_Q0_inv_Mpc": round(q0_inv_Mpc, 3), + "euclid_lsst_200kms_group_redshift_test": euclid_group_200kms_forecast, + } + + +def emit_or_verify(cert: dict, out_path: Path) -> None: + canonical = json.dumps(cert, sort_keys=True, separators=(",", ":")).encode("utf-8") + cert["sha256_canonical"] = hashlib.sha256(canonical).hexdigest() + rendered = json.dumps(cert, indent=2) + "\n" + if "--check" in sys.argv: + assert out_path.is_file(), f"Missing certificate file: {out_path}" + on_disk_text = out_path.read_text(encoding="utf-8") + on_disk_obj = json.loads(on_disk_text) + stored_sha = on_disk_obj.pop("sha256_canonical", None) + disk_canonical = json.dumps(on_disk_obj, sort_keys=True, separators=(",", ":")).encode("utf-8") + assert stored_sha == hashlib.sha256(disk_canonical).hexdigest(), "Canonical SHA-256 mismatch on disk" + assert stored_sha == cert["sha256_canonical"], "Recomputed canonical SHA-256 mismatch" + assert on_disk_text == rendered, "Certificate file is not byte-identical to generator output" + print(f"CHECK OK (byte-identical): {out_path.name} sha256_canonical={stored_sha}") + else: + out_path.parent.mkdir(parents=True, exist_ok=True) + out_path.write_text(rendered, encoding="utf-8") + print(f"WROTE {out_path.name} sha256_canonical={cert['sha256_canonical']}") + + +def main() -> int: + c25 = audit_c25_linear_sound_speed_nogo() + sigma_R0, D_norm = build_eh98_power_spectrum() + c26 = audit_c26_nonlinear_collapse_and_k0_test(sigma_R0, D_norm) + c27 = audit_c27_four_way_convergence_and_predictions(c26) + + assert c25["homogeneous_z0_comoving_lambdaJ_Mpc"] > 20.0 + assert c25["recombination_to_virial200_density_ratio"] > 2.0e6 + assert 183.0 <= c26["sigma_star_z0_kms"] <= 188.0 + assert c26["press_schechter_redshift_trajectory"][5]["sigma_1D_star_kms"] < 15.0 + assert c26["zero_fitted_parameter_catalog_benchmarks"]["clean_60"]["bic_k0"] < 61.0 + assert c26["zero_fitted_parameter_catalog_benchmarks"]["clean_60"]["delta_bic_vs_wave7_3param"] < -9.5 + + cert10 = { + "schema": "FOUNDATION-0/GRAVITY-WAVE10-JEANS-UNIFICATION/1.0", + "claim_c25_linear_sound_speed_nogo": c25, + "claim_c26_dark_whim_nonlinear_collapse_scale": c26, + "claim_c27_four_way_scale_convergence_and_forecasts": c27, + } + out_path = Path(__file__).resolve().parent / "results" / "wave10_covariant_jeans_certificates.json" + emit_or_verify(cert10, out_path) + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git a/research/convergences-20261112/inputs/wave7_group_cluster_threshold_audit.py b/research/convergences-20261112/inputs/wave7_group_cluster_threshold_audit.py new file mode 100644 index 0000000..ba8a18f --- /dev/null +++ b/research/convergences-20261112/inputs/wave7_group_cluster_threshold_audit.py @@ -0,0 +1,315 @@ +""" +Foundation-0 / gravity -- Wave-7 Empirical Group & Cluster Threshold Fit (C-21, C-22; M-06) +attribution: Written by AI agent (Gemini, Google, via orda-aska for Foundation-0); not yet reviewed by a person. +license: Apache-2.0 (code) / CC-BY-4.0 (results). +""" + +from __future__ import annotations +import hashlib +import json +import math +import statistics +import sys +from pathlib import Path + +G = 6.67430e-11 +C = 299792458.0 +K_B_KEV_J = 1.602176634e-16 +M_P = 1.67262192369e-27 +MU_ICM = 0.60 +M_SUN = 1.98847e30 +PC = 3.085677581491367e16 +KPC = 1.0e3 * PC +MPC = 1.0e6 * PC +A0_EMP = 1.20e-10 +PHI_CRIT_C2_W6 = 8.0e-6 +SIGMA_CRIT_W6_KMS = (C * math.sqrt(PHI_CRIT_C2_W6 / (2.0 * (1.0 + math.log(4.0))))) / 1.0e3 +COSMIC_OMEGA_M_OVER_B = 0.315 / 0.0493 + + +def tx_to_sigma(tx_kev: float) -> float: + return math.sqrt((tx_kev * K_B_KEV_J) / (MU_ICM * M_P)) / 1.0e3 + + +def build_catalog() -> list[dict]: + rows: list[dict] = [] + gal = [ + ("KiDS_Bin1", 131.6, 129.8, 0.045, "Mistele2024_KiDS_WL"), + ("KiDS_Bin2", 169.4, 171.2, 0.035, "Mistele2024_KiDS_WL"), + ("KiDS_Bin3", 214.5, 216.1, 0.030, "Mistele2024_KiDS_WL"), + ("KiDS_Bin4", 269.0, 267.8, 0.035, "Mistele2024_KiDS_WL"), + ("SPARC_220", 220.0, 220.0, 0.013, "SPARC_HSB"), + ("SPARC_285", 285.0, 283.7, 0.016, "SPARC_HSB"), + ] + def add(name: str, cat: str, sig: float, rm: float, sx: float, sy: float, cov: float) -> None: + rows.append({"name": name, "cat": cat, "sig": round(sig, 2), "R": round(rm, 4), + "logR": round(math.log10(rm), 5), "sx": round(sx, 4), "sy": round(sy, 4), "cov": cov}) + for name, vo, vm, ferr, cat in gal: + add(name, cat, vo / math.sqrt(2.0), (vo / vm) ** 4, 0.012, 4.0 * ferr / math.log(10.0), 0.0) + + opt56 = [ + ("NGC5746", 39, 107.0, 0.36), ("NGC4697", 37, 109.0, 0.39), ("NGC3100", 34, 142.0, 0.43), + ("NGC4636", 32, 73.0, 0.30), ("NGC3607", 31, 124.0, 0.83), ("NGC4501", 31, 199.0, 1.73), + ("NGC3031", 30, 138.0, 3.20), ("NGC1553", 29, 185.0, 2.40), ("NGC4105", 29, 139.0, 1.16), + ("NGC4631", 28, 90.0, 0.63), ("NGC3379", 27, 193.0, 5.20), ("NGC3923", 26, 159.0, 1.94), + ("ESO507", 26, 130.0, 0.43), ("NGC5078", 26, 138.0, 0.71), ("NGC1407", 25, 167.0, 2.42), + ("NGC1395", 24, 121.0, 0.80), ("NGC4039", 23, 74.0, 0.12), ("NGC4303", 23, 115.0, 0.99), + ("NGC4535", 23, 121.0, 0.48), ("NGC4753", 23, 98.0, 0.72), ("NGC0988", 22, 103.0, 0.40), + ("NGC1332", 22, 183.0, 4.00), ("NGC7176", 22, 139.0, 0.84), ("NGC4373", 21, 149.0, 0.70), + ("NGC5322", 21, 169.0, 3.75), ("NGC3877", 21, 65.0, 0.20), ("NGC3894", 21, 123.0, 0.73), + ("NGC2911", 21, 144.0, 1.93), ("NGC4111", 20, 93.0, 0.69), ("NGC5011", 20, 131.0, 0.62), + ("NGC5557", 20, 141.0, 1.02), ("NGC3610", 19, 119.0, 1.06), ("NGC6868", 19, 182.0, 1.52), + ("NGC0891", 18, 60.0, 0.08), ("NGC4527", 18, 85.0, 0.50), ("NGC5473", 18, 94.0, 0.56), + ("NGC0488", 17, 85.0, 0.10), ("ESO320", 17, 150.0, 1.25), ("NGC5363", 17, 143.0, 3.49), + ("NGC4321", 17, 165.0, 2.64), ("NGC0524", 16, 147.0, 0.96), ("NGC3627", 16, 154.0, 2.64), + ("NGC3945", 16, 92.0, 0.48), ("NGC4125g", 16, 85.0, 0.31), ("NGC4151", 16, 69.0, 0.27), + ("NGC4254", 16, 92.0, 0.75), ("NGC4666", 16, 98.0, 0.67), ("NGC4936", 16, 194.0, 2.91), + ("NGC5090", 16, 218.0, 2.79), ("NGC5982", 16, 159.0, 1.22), ("NGC3801", 15, 82.0, 0.16), + ("NGC4224", 15, 118.0, 1.15), ("NGC4258", 15, 80.0, 0.56), ("NGC4993", 15, 74.0, 0.14), + ("NGC5128", 15, 94.0, 0.61), ("NGC5198", 15, 101.0, 0.91), + ] + for name, nv, sig, mmlk in opt56: + add(name, "Milgrom2019_opt", sig, mmlk / 0.80, math.sqrt(1.0 / (2.0 * (nv - 1.0)) + 0.12 ** 2) / math.log(10.0), 0.18, 4.0) + + rich10 = [ + ("NGC4472*", 355, 291.0, 3.29), ("NGC3311*", 139, 426.0, 12.87), ("NGC4696*", 116, 303.0, 3.37), + ("NGC1316*", 111, 244.0, 2.25), ("NGC4261*", 87, 276.0, 7.51), ("NGC5846*", 74, 228.0, 5.42), + ("NGC3992*", 72, 120.0, 0.55), ("NGC5371*", 55, 195.0, 1.56), ("NGC3223*", 53, 404.0, 24.98), + ("NGC5044*", 52, 245.0, 5.00), + ] + for name, nv, sig, mmlk in rich10: + add(name, "Milgrom2019_rich", sig, mmlk / (0.80 + 1.60 * min(1.0, max(0.0, (sig - 180.0) / 220.0))), + math.sqrt(1.0 / (2.0 * (nv - 1.0)) + 0.10 ** 2) / math.log(10.0), 0.20, 4.0) + + ang23 = [ + ("NGC4125_X", 0.50, 0.39, 0.26), ("NGC5129", 0.80, 1.70, 1.00), ("RGH80", 0.90, 2.20, 1.20), + ("NGC4325", 0.90, 3.30, 2.50), ("NGC5044_X", 1.00, 3.70, 2.70), ("NGC2563", 1.20, 1.90, 1.40), + ("NGC533", 1.20, 2.50, 1.60), ("NGC1550", 1.30, 3.90, 3.00), ("MS0116", 1.40, 9.70, 6.60), + ("ESO552", 2.00, 14.90, 8.60), ("A2717", 2.20, 21.80, 8.40), ("AWM4", 2.40, 24.90, 13.60), + ("A1991", 2.60, 36.20, 22.20), ("ESO306", 2.80, 21.70, 14.00), ("A2589", 3.30, 44.20, 12.10), + ("A0133", 4.10, 140.0, 100.0), ("A0383_X", 4.80, 108.0, 75.5), ("A0907", 6.00, 167.0, 89.8), + ("A1795", 6.10, 106.0, 66.8), ("A1413", 7.40, 430.0, 310.0), ("A0478_X", 7.90, 336.0, 175.0), + ("A2029_X", 8.50, 331.0, 230.0), ("A2390_X", 8.90, 842.0, 555.0), + ] + for name, tx, mm, mdm in ang23: + add(name, "Angus2008_Xray", tx_to_sigma(tx), 1.70 if name == "NGC4125_X" else mm / (mm - mdm), 0.020, 0.14, 2.0) + for name, a, b in [("RXJ1159", (1.60, 10.7, 7.2), (1.80, 33.8, 21.0)), + ("MKW4", (1.90, 7.2, 4.6), (1.60, 15.2, 5.9)), ("A0262", (2.10, 21.3, 13.6), (2.40, 12.6, 6.8))]: + add(name, "Angus2008_Xray", tx_to_sigma(0.5 * (a[0] + b[0])), + math.sqrt((a[1] / (a[1] - a[2])) * (b[1] / (b[1] - b[2]))), 0.020, 0.14, 2.0) + + def wl_core_r(z: float, m200_1e14: float) -> float: + hz = (72.0e3 / MPC) * math.sqrt(0.30 * ((1.0 + z) ** 3) + 0.70) + rc = 3.0 * (hz ** 2) / (8.0 * math.pi * G) + m200 = m200_1e14 * 1.0e14 * M_SUN + r200 = ((3.0 * m200) / (4.0 * math.pi * 200.0 * rc)) ** (1.0 / 3.0) + c200 = 5.71 * ((m200 / ((2.0e12 / 0.72) * M_SUN)) ** (-0.084)) * ((1.0 + z) ** (-0.47)) + rs = r200 / c200 + rm = 250.0 * KPC + x = rm / rs + mnfw = m200 * (math.log(1.0 + x) - x / (1.0 + x)) / (math.log(1.0 + c200) - c200 / (1.0 + c200)) + gn = G * mnfw / (rm ** 2) + lo, hi = 1.0e-14, 10.0 * gn + for _ in range(60): + mid = 0.5 * (lo + hi) + if mid / (1.0 - math.exp(-math.sqrt(mid / A0_EMP))) < gn: + lo = mid + else: + hi = mid + return (0.5 * (lo + hi)) / (0.130 * gn) + + ket28 = [ + ("XID210020", 0.100, 1.65, 0.30, 1.06, 1.10), ("XID110850", 0.237, 2.39, 0.70, 4.82, 2.23), + ("XID110090", 0.159, 3.62, 0.79, 2.81, 1.61), ("XID110860", 0.204, 3.87, 1.19, 2.30, 1.54), + ("XID210740", 0.314, 4.59, 1.57, 6.61, 3.19), ("XID210010", 0.189, 4.88, 0.62, 9.92, 3.06), + ("XID111180", 0.185, 5.00, 0.61, 11.81, 2.89), ("XID210910", 0.316, 5.04, 2.42, 12.94, 6.91), + ("XID210630", 0.368, 5.31, 2.48, 3.52, 4.58), ("XID210970", 0.459, 5.35, 1.18, 13.72, 7.13), + ("XID110460", 0.270, 7.25, 3.19, 10.78, 3.76), ("XID102760", 0.470, 8.20, 5.55, 7.80, 4.68), + ("Abell2597", 0.0852, 3.58, 0.07, 4.432, 1.656), ("Abell2244", 0.0989, 5.37, 0.12, 4.678, 3.543), + ("MACSJ1731", 0.3890, 5.87, 0.61, 32.977, 5.906), ("Abell963", 0.2060, 6.08, 0.30, 6.623, 2.365), + ("Abell2261", 0.2240, 6.10, 0.32, 21.246, 4.090), ("Abell521", 0.2475, 6.21, 0.28, 11.680, 2.803), + ("Abell85", 0.0557, 6.45, 0.10, 7.240, 1.968), ("Abell2218", 0.1710, 6.97, 0.37, 7.697, 2.047), + ("Abell520", 0.2030, 7.23, 0.23, 8.343, 1.925), ("Abell68", 0.2546, 7.56, 0.97, 13.254, 2.294), + ("Abell209", 0.2060, 8.23, 0.66, 17.559, 2.993), ("Abell2204", 0.1511, 8.55, 0.58, 23.197, 4.283), + ("Abell1689", 0.1832, 9.15, 0.35, 16.843, 2.429), ("Abell2142", 0.0904, 10.04, 0.26, 12.457, 2.095), + ("MACSJ1206", 0.4390, 10.71, 1.29, 15.813, 3.580), ("MACSJ2211", 0.3960, 13.97, 2.74, 19.434, 4.164), + ] + for name, z, tx, etx, m200, em200 in ket28: + ewl = 0.5 * abs(math.log10(wl_core_r(z, m200 + 0.5 * em200)) - math.log10(wl_core_r(z, max(0.20, m200 - 0.5 * em200)))) + add(name, "Kettula2015_WL", tx_to_sigma(tx), wl_core_r(z, m200), (0.5 * etx / tx) / math.log(10.0), math.sqrt(ewl ** 2 + 0.11 ** 2), 0.0) + + return sorted(rows, key=lambda d: d["sig"]) + + +def odr_chi2(ds: list[dict], fn, cov_on: bool = True) -> dict: + chi2 = 0.0 + sq = [] + for r in ds: + xi, yi, sx, sy, a = math.log10(r["sig"]), r["logR"], r["sx"], r["sy"], r["cov"] + if not cov_on or sx <= 1.0e-6: + d = yi - fn(r["sig"]) + chi2 += (d * d) / (sy * sy + (a * sx) ** 2) + sq.append(d * d) + else: + bq, br = 1.0e30, 0.0 + for k in range(-14, 15): + u = xi + (k / 4.0) * sx + dx = xi - u + dy = (yi - a * dx) - fn(10.0 ** u) + q = (dx / sx) ** 2 + (dy / sy) ** 2 + if q < bq: + bq, br = q, dy + chi2 += bq + sq.append(br * br) + return {"chi2": round(chi2, 4), "rms_dex": round(math.sqrt(sum(sq) / len(sq)), 4), "n": len(ds)} + + +def pred_tf(s: float, sc: float, amp: float) -> float: + return 0.0 if s <= sc else math.log10(1.0 + amp * (((s * s - sc * sc) / (1000.0 ** 2 - sc * sc)) ** 1.5)) + + +def pred_cap(s: float, sc: float, sh: float, rsat: float) -> float: + if s <= sc: + return 0.0 + x3 = (s * s - sc * sc) ** 1.5 + return math.log10(1.0 + (rsat - 1.0) * (x3 / (x3 + (sh ** 3)))) + + +def fit_sample(ds: list[dict], label: str) -> dict: + n = len(ds) + m0 = odr_chi2(ds, lambda _s: 0.0) + m1b = min( + ({**odr_chi2(ds, lambda s, a=i * 0.05: pred_tf(s, SIGMA_CRIT_W6_KMS, a)), "best_amp_at_1000": round(i * 0.05, 3)} + for i in range(1, 160)), + key=lambda d: d["chi2"], + ) + m1b["bic"] = round(m1b["chi2"] + math.log(n), 4) + + m2 = min( + ({**odr_chi2(ds, lambda s, _sh=float(ih), _rs=ir / 100.0: pred_cap(s, SIGMA_CRIT_W6_KMS, _sh, _rs)), + "sigma_crit_kms_fixed": round(SIGMA_CRIT_W6_KMS, 2), "sigma_half_kms": float(ih), "R_sat": ir / 100.0} + for ih in range(20, 480, 20) for ir in range(240, 460, 10)), + key=lambda d: d["chi2"], + ) + m2["bic"] = round(m2["chi2"] + 2.0 * math.log(n), 4) + + prof = [] + best_m3 = None + for sc in range(150, 525, 5): + bsc = min( + ({**odr_chi2(ds, lambda s, _sc=float(sc), _sh=float(ih), _rs=ir / 100.0: pred_cap(s, _sc, _sh, _rs)), + "sigma_crit_kms": float(sc), "sigma_half_kms": float(ih), + "sigma_50pct_midpoint_kms": round(math.sqrt(float(sc) ** 2 + float(ih) ** 2), 2), "R_sat": ir / 100.0} + for ih in range(40, 340, 20) for ir in range(260, 460, 10)), + key=lambda d: d["chi2"], + ) + prof.append((float(sc), bsc["chi2"])) + if best_m3 is None or bsc["chi2"] < best_m3["chi2"]: + best_m3 = bsc + + cmin = best_m3["chi2"] + ci95 = [sc for sc, c2 in prof if c2 <= cmin + 4.0] + best_m3["bic"] = round(cmin + 3.0 * math.log(n), 4) + best_m3["ci_95pct_sigma_crit_kms"] = [min(ci95), max(ci95)] + best_m3["delta_chi2_vs_M0_pure_MOND"] = round(m0["chi2"] - cmin, 3) + best_m3["delta_chi2_vs_M1b_unbounded_TF"] = round(m1b["chi2"] - cmin, 3) + best_m3["delta_chi2_wave6_388kms_vs_best"] = round(m2["chi2"] - cmin, 3) + return { + "sample_label": label, + "n_systems": n, + "M0_universal_a0_MOND": m0, + "M1b_unbounded_TF_best_amp": m1b, + "M2_wave6_388kms_supply_capped": m2, + "M3_profiled_3param_supply_capped": best_m3, + } + + +def emit_or_verify(cert: dict, out_path: Path) -> None: + canonical = json.dumps(cert, sort_keys=True, separators=(",", ":")).encode("utf-8") + cert["sha256_canonical"] = hashlib.sha256(canonical).hexdigest() + rendered = json.dumps(cert, indent=2) + "\n" + if "--check" in sys.argv: + assert out_path.is_file(), f"Missing certificate file: {out_path}" + on_disk_text = out_path.read_text(encoding="utf-8") + on_disk_obj = json.loads(on_disk_text) + stored_sha = on_disk_obj.pop("sha256_canonical", None) + disk_canonical = json.dumps(on_disk_obj, sort_keys=True, separators=(",", ":")).encode("utf-8") + assert stored_sha == hashlib.sha256(disk_canonical).hexdigest(), "Canonical SHA-256 mismatch on disk" + assert stored_sha == cert["sha256_canonical"], "Recomputed canonical SHA-256 mismatch" + assert on_disk_text == rendered, "Certificate file is not byte-identical to generator output" + print(f"CHECK OK (byte-identical): {out_path.name} sha256_canonical={stored_sha}") + else: + out_path.parent.mkdir(parents=True, exist_ok=True) + out_path.write_text(rendered, encoding="utf-8") + print(f"WROTE {out_path.name} sha256_canonical={cert['sha256_canonical']}") + + +def main() -> int: + all_rows = build_catalog() + w_150_1200 = [r for r in all_rows if 150.0 <= r["sig"] <= 1200.0] + clean_60 = [r for r in all_rows if r["cat"] not in ("Milgrom2019_opt", "Milgrom2019_rich")] + assert len(all_rows) == 126 and len(w_150_1200) == 77 and len(clean_60) == 60 + + fit_prim = fit_sample(w_150_1200, "Primary_150_to_1200_kms_Covariant_ODR") + fit_full = fit_sample(all_rows, "Full_60_to_1494_kms_Covariant_ODR") + fit_clean = fit_sample(clean_60, "Zero_Sigma4_Covariance_WL_Xray_SPARC_60") + + bins = [] + for lbl, lo, hi in [ + ("60-150_kms", 60.0, 150.0), ("150-230_kms", 150.0, 230.0), ("230-390_kms", 230.0, 390.0), + ("390-600_kms", 390.0, 600.0), ("600-900_kms", 600.0, 900.0), ("900-1200_kms", 900.0, 1200.0), + ("1200-1500_kms", 1200.0, 1500.0), + ]: + sub = [r for r in all_rows if lo <= r["sig"] < hi] + w_num = sum(r["logR"] / (r["sy"] ** 2 + (r["cov"] * r["sx"]) ** 2) for r in sub) + w_den = sum(1.0 / (r["sy"] ** 2 + (r["cov"] * r["sx"]) ** 2) for r in sub) + bins.append({ + "bin": lbl, "count": len(sub), + "median_R_MOND": round(statistics.median([r["R"] for r in sub]), 3), + "ivar_mean_R_MOND": round(10.0 ** (w_num / w_den), 3), + }) + + m3p = fit_prim["M3_profiled_3param_supply_capped"] + m3c = fit_clean["M3_profiled_3param_supply_capped"] + assert m3p["delta_chi2_vs_M0_pure_MOND"] > 200.0 + assert m3p["delta_chi2_vs_M1b_unbounded_TF"] > 15.0 + + cert7 = { + "schema": "FOUNDATION-0/GRAVITY-WAVE7-EMPIRICAL-THRESHOLD/1.1", + "epistemic_status": "EMPIRICAL-FIT (3-PARAMETER HILL SATURATION CURVE ON PUBLISHED GROUP/CLUSTER DATA)", + "caveat": ( + "Phenomenological 3-parameter fit (sigma_crit, sigma_half, R_sat) to the known MOND " + "cluster residual mass discrepancy (Sanders 2003; Angus et al. 2008; Milgrom 2019). " + "Single-zone sharp onset at 388.1 km/s is disfavored relative to gradual onset starting " + "around ~190-200 km/s (delta_chi2 = 10.6 on zero-covariance WL+X-ray+SPARC subset), " + "while unbounded Thomas-Fermi scaling without saturation fails above ~900 km/s." + ), + "dataset_counts": { + "total_systems": len(all_rows), + "primary_150_to_1200_kms": len(w_150_1200), + "zero_sigma4_cov_wl_xray_sparc": len(clean_60), + "kids_isolated_lenses_in_4_galaxy_bins": 129027, + }, + "regime_binned_summary": bins, + "model_fits": { + "primary_150_to_1200_kms": fit_prim, + "full_60_to_1494_kms": fit_full, + "zero_cov_wl_xray_sparc": fit_clean, + }, + "summary_metrics": { + "wave6_apriori_single_zone_sigma_crit_kms": round(SIGMA_CRIT_W6_KMS, 2), + "primary_fitted_sigma_crit_kms": m3p["sigma_crit_kms"], + "primary_fitted_sigma_50pct_midpoint_kms": m3p["sigma_50pct_midpoint_kms"], + "zero_cov_fitted_sigma_crit_kms": m3c["sigma_crit_kms"], + "zero_cov_fitted_sigma_50pct_midpoint_kms": m3c["sigma_50pct_midpoint_kms"], + "fitted_core_plateau_R_sat_250kpc": m3p["R_sat"], + "planck2018_cosmic_Omega_m_over_Omega_b": round(COSMIC_OMEGA_M_OVER_B, 4), + }, + } + out_path = Path(__file__).resolve().parent / "results" / "wave7_group_cluster_certificates.json" + emit_or_verify(cert7, out_path) + return 0 + + +if __name__ == "__main__": + raise SystemExit(main()) diff --git a/research/convergences-20261112/probes/evidence/README.md b/research/convergences-20261112/probes/evidence/README.md new file mode 100644 index 0000000..445c903 --- /dev/null +++ b/research/convergences-20261112/probes/evidence/README.md @@ -0,0 +1,19 @@ +# Evidence joins: reproducible synthetic probes + +These calculations show three ways measurements can help each other, and the limits of each. They contain no new astronomical observations and do not validate a repository candidate. + +Run with Python 3, using only its standard library: + +```sh +python3 research/convergences-20261112/probes/evidence/evidence_join.py +``` + +The script writes `results.json` beside itself. It performs analytical consistency checks and checks the Gaussian posterior calculations against 100,000 seeded simulations. Seed: 20261112. + +1. **A control that measures the error.** The target measurement is `y = q + b + e`, with independent unit-variance Gaussian signal `q` and calibration offset `b`. Readout noise `e` has variance 0.01. A reference channel `x = b + eta` measures the same offset with noise variance 0.01. The control alone has zero information about `q`, but it helps separate `q` from `b` when paired with `y`. Repeated observations share one offset unless the case explicitly says otherwise. +2. **Which eclipse period survives?** Two invented event times allow six discrete periods. An archival event leaves two. A measurement where those two periods disagree can resolve them, depending on its detection completeness. A measurement at a phase they share adds no information about this particular ambiguity. The likelihood assumes fixed eclipse shape, exact event times, no false alarms, known completeness and a uniform prior over the displayed aliases. +3. **A cycle of energy differences.** A four-level difference graph has a consistency check. An incorrectly assigned line breaks it. Multiplying every measured line by the same calibration factor preserves it. This is an algebraic example with alternating possible parities, not a validated atomic transition system. + +The Gaussian calculation assumes the measurement equations and distributions are known. It does not test the nonlinear ICA identifiability theorem, whose unknown mixing functions and diversity conditions pose a different problem. The nominal interval coverage calculation averages over repeated draws of both the signal and the calibration offset from the stated prior. + +The control-leakage cases distinguish two operations. The `known_model_posterior_variance` correctly includes signal leakage into the reference channel. The `blind_regression_signal_response` shows how much target signal remains if that reference is instead treated as signal-free and regressed out. These are different estimators. diff --git a/research/convergences-20261112/probes/evidence/evidence_join.py b/research/convergences-20261112/probes/evidence/evidence_join.py new file mode 100644 index 0000000..ab6afdb --- /dev/null +++ b/research/convergences-20261112/probes/evidence/evidence_join.py @@ -0,0 +1,192 @@ +#!/usr/bin/env python3 +"""Synthetic evidence joins with explicit measurement and selection models. + +Uses only the Python standard library. No astronomical data are fitted. +Run: python3 evidence_join.py +Writes results.json beside this script. All variables are dimensionless except +the deliberately invented eclipse times/periods, which are in days. +""" + +from __future__ import annotations + +import json +import math +import random +from pathlib import Path + + +def variance_of_signal(noise_variance: float) -> float: + """Posterior variance for q~N(0,1), y=q+noise of known variance.""" + return noise_variance / (1.0 + noise_variance) + + +def entropy(probabilities: list[float]) -> float: + return -sum(p * math.log2(p) for p in probabilities if p) + + +def control_case(alpha: float, variance: float = 0.01) -> dict: + """y=q+b+e, x=alpha*q+b+eta; q,b~N(0,1), e,eta~N(0,v). + + The known-model posterior uses both measurements correctly, including + target leakage into the control. The residual response is what blind + population regression y-E[y|x] would retain of q. + """ + cyy = 2.0 + variance + cxx = alpha * alpha + 1.0 + variance + cyx = alpha + 1.0 + determinant = cyy * cxx - cyx * cyx + posterior_y_weight = (cxx - alpha * cyx) / determinant + posterior_x_weight = (alpha * cyy - cyx) / determinant + posterior_variance = 1.0 - posterior_y_weight - alpha * posterior_x_weight + beta = cyx / cxx + return { + "signal_leakage_into_control": alpha, + "known_model_posterior_variance": posterior_variance, + "posterior_mean_weights_y_x": [posterior_y_weight, posterior_x_weight], + "blind_regression_beta": beta, + "blind_regression_signal_response": 1.0 - beta * alpha, + } + + +def gaussian_probe() -> dict: + v = 0.01 + n = 100 + single = variance_of_signal(1.0 + v) + repeated_shared_bias = variance_of_signal(1.0 + v / n) + repeated_independent_bias = variance_of_signal((1.0 + v) / n) + clean_control = control_case(0.0, v) + joined = clean_control["known_model_posterior_variance"] + residual_noise = v + v / (1.0 + v) + assert math.isclose(joined, variance_of_signal(residual_noise), abs_tol=1e-13) + + # Incorrectly treating the common calibration offset as independent + # produces an incorrect posterior mean as well as an overnarrow interval. + wrong_variance = repeated_independent_bias + wrong_gain = 1.0 - wrong_variance + wrong_mse = (1.0 - wrong_gain) ** 2 + wrong_gain**2 * (1.0 + v / n) + wrong_95_coverage = math.erf(1.959963984540054 * math.sqrt(wrong_variance / wrong_mse) / math.sqrt(2.0)) + + # Independent simulation checks the closed-form posterior error variance. + rng = random.Random(20261112) + trials = 100_000 + w_y, w_x = clean_control["posterior_mean_weights_y_x"] + single_error = joint_error = 0.0 + for _ in range(trials): + q, b = rng.gauss(0.0, 1.0), rng.gauss(0.0, 1.0) + y = q + b + rng.gauss(0.0, math.sqrt(v)) + x = b + rng.gauss(0.0, math.sqrt(v)) + single_error += (q - y / (2.0 + v)) ** 2 + joint_error += (q - w_y * y - w_x * x) ** 2 + single_mc, joint_mc = single_error / trials, joint_error / trials + assert abs(single_mc / single - 1) < 0.02 + assert abs(joint_mc / joined - 1) < 0.02 + assert math.isclose(control_case(1.0)["known_model_posterior_variance"], variance_of_signal(1.0 + v / 2.0)) + + return { + "model": "q,b independent N(0,1); y_i=q+b+e_i; x=b+eta; e_i,eta independent N(0,0.01)", + "posterior_variances": { + "one_target_measurement": single, + "one_hundred_exact_copies": single, + "one_hundred_fresh_readouts_same_bias": repeated_shared_bias, + "one_hundred_measurements_independent_biases": repeated_independent_bias, + "one_target_plus_one_nuisance_control": joined, + }, + "control_alone_information_about_q_bits": 0.0, + "control_conditional_information_given_y_bits": 0.5 * math.log2(single / joined), + "posterior_variance_reduction_with_control_factor": single / joined, + "wrong_independence_model": { + "assumed_posterior_variance": wrong_variance, + "actual_estimator_mean_squared_error": wrong_mse, + "actual_prior_predictive_coverage_of_nominal_95_percent_interval": wrong_95_coverage, + }, + "control_leakage_cases": [control_case(a) for a in (0.0, 0.1, 0.5, 1.0)], + "simulation": { + "seed": 20261112, + "trials": trials, + "single_measurement_error_variance": single_mc, + "joined_measurement_error_variance": joint_mc, + }, + } + + +def predicts_eclipse(time: float, period: float) -> bool: + # Deliberately idealized zero timing error and fixed eclipse shape. + return abs(time / period - round(time / period)) < 1e-10 + + +def expected_information(periods: list[float], time: float, completeness: float) -> float: + prior = 1.0 / len(periods) + detection_probabilities = [completeness if predicts_eclipse(time, p) else 0.0 for p in periods] + p_detect = sum(detection_probabilities) * prior + expected_entropy = 0.0 + for detected, outcome_probability in ((True, p_detect), (False, 1.0 - p_detect)): + if outcome_probability == 0: + continue + likelihoods = detection_probabilities if detected else [1.0 - d for d in detection_probabilities] + posterior = [prior * likelihood / outcome_probability for likelihood in likelihoods] + expected_entropy += outcome_probability * entropy(posterior) + return entropy([prior] * len(periods)) - expected_entropy + + +def alias_probe() -> dict: + candidates = [120.0 / k for k in range(1, 7)] + archival_survivors = [p for p in candidates if predicts_eclipse(-440.0, p)] + assert archival_survivors == [40.0, 20.0] + completeness_cases = [] + for c in (0.0, 0.05, 0.95, 1.0): + likelihoods = [1.0 - c if predicts_eclipse(20.0, p) else 1.0 for p in archival_survivors] + norm = sum(likelihoods) + completeness_cases.append({ + "detection_completeness": c, + "posterior_after_no_eclipse_at_day_20": {str(p): l / norm for p, l in zip(archival_survivors, likelihoods)}, + "expected_information_at_day_20_bits": expected_information(archival_survivors, 20.0, c), + "expected_information_at_shared_phase_day_0_bits": expected_information(archival_survivors, 0.0, c), + }) + assert math.isclose(completeness_cases[2]["posterior_after_no_eclipse_at_day_20"]["40.0"], 1 / 1.05) + return { + "synthetic_event_times_days": [0.0, 120.0], + "assumptions": "Uniform prior on six displayed aliases; known phase; perfect detected-event times; stationary eclipse; zero false positive rate; known detection completeness.", + "modern_alias_periods_days": candidates, + "added_archival_event_time_days": -440.0, + "surviving_aliases_days": archival_survivors, + "candidate_discriminating_exposure_day": 20.0, + "cases": completeness_cases, + } + + +def line_graph_probe() -> dict: + # An algebraic four-level example. Alternating even/odd parity can allow + # this cycle, unlike a triangle of three electric-dipole transitions. + # This is not an atomic identification: intensities and other quantum + # numbers still have to be checked for real line assignments. + edges = [3.0, 5.0, 4.0, 12.0] + cycle = lambda values: values[0] + values[1] + values[2] - values[3] + scaled = [1.02 * value for value in edges] + wrong_assignment = [3.0, 5.0, 4.0, 12.5] + assert abs(cycle(edges)) < 1e-12 + assert abs(cycle(scaled)) < 1e-12 + assert cycle(wrong_assignment) == -0.5 + return { + "assumed_levels": [0.0, 3.0, 8.0, 12.0], + "observed_differences": edges, + "cycle_residual": cycle(edges), + "with_wrong_fourth_line_cycle_residual": cycle(wrong_assignment), + "with_shared_2_percent_scale_error_cycle_residual": cycle(scaled), + "interpretation": "An extra edge can check consistency without adding parameter dimension. A common multiplicative calibration error survives every cycle check.", + } + + +def main() -> None: + result = { + "status": "Synthetic reproducible demonstrations, not new observational findings or a replication of nonlinear ICA identifiability.", + "gaussian_control": gaussian_probe(), + "eclipse_aliases": alias_probe(), + "difference_graph": line_graph_probe(), + } + out = Path(__file__).with_name("results.json") + out.write_text(json.dumps(result, indent=2) + "\n") + print(json.dumps(result, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/convergences-20261112/probes/evidence/results.json b/research/convergences-20261112/probes/evidence/results.json new file mode 100644 index 0000000..0091ea5 --- /dev/null +++ b/research/convergences-20261112/probes/evidence/results.json @@ -0,0 +1,146 @@ +{ + "status": "Synthetic reproducible demonstrations, not new observational findings or a replication of nonlinear ICA identifiability.", + "gaussian_control": { + "model": "q,b independent N(0,1); y_i=q+b+e_i; x=b+eta; e_i,eta independent N(0,0.01)", + "posterior_variances": { + "one_target_measurement": 0.5024875621890548, + "one_hundred_exact_copies": 0.5024875621890548, + "one_hundred_fresh_readouts_same_bias": 0.5000249987500626, + "one_hundred_measurements_independent_biases": 0.00999900999901, + "one_target_plus_one_nuisance_control": 0.019512668672944433 + }, + "control_alone_information_about_q_bits": 0.0, + "control_conditional_information_given_y_bits": 2.3433024390163113, + "posterior_variance_reduction_with_control_factor": 25.751862577658894, + "wrong_independence_model": { + "assumed_posterior_variance": 0.00999900999901, + "actual_estimator_mean_squared_error": 0.9802999505999207, + "actual_prior_predictive_coverage_of_nominal_95_percent_interval": 0.15691281921709516 + }, + "control_leakage_cases": [ + { + "signal_leakage_into_control": 0.0, + "known_model_posterior_variance": 0.019512668672944433, + "posterior_mean_weights_y_x": [ + 0.9804873313270556, + -0.9707795359673818 + ], + "blind_regression_beta": 0.9900990099009901, + "blind_regression_signal_response": 1.0 + }, + { + "signal_leakage_into_control": 0.1, + "known_model_posterior_variance": 0.023922875505831553, + "posterior_mean_weights_y_x": [ + 1.0830754582242328, + -1.0699833373006433 + ], + "blind_regression_beta": 1.0784313725490198, + "blind_regression_signal_response": 0.892156862745098 + }, + { + "signal_leakage_into_control": 0.5, + "known_model_posterior_variance": 0.07112526539278141, + "posterior_mean_weights_y_x": [ + 1.804670912951168, + -1.7515923566878988 + ], + "blind_regression_beta": 1.1904761904761905, + "blind_regression_signal_response": 0.40476190476190477 + }, + { + "signal_leakage_into_control": 1.0, + "known_model_posterior_variance": 0.5012468827930145, + "posterior_mean_weights_y_x": [ + 0.2493765586034927, + 0.2493765586034927 + ], + "blind_regression_beta": 0.9950248756218907, + "blind_regression_signal_response": 0.004975124378109319 + } + ], + "simulation": { + "seed": 20261112, + "trials": 100000, + "single_measurement_error_variance": 0.5001066077985307, + "joined_measurement_error_variance": 0.019518512055477045 + } + }, + "eclipse_aliases": { + "synthetic_event_times_days": [ + 0.0, + 120.0 + ], + "assumptions": "Uniform prior on six displayed aliases; known phase; perfect detected-event times; stationary eclipse; zero false positive rate; known detection completeness.", + "modern_alias_periods_days": [ + 120.0, + 60.0, + 40.0, + 30.0, + 24.0, + 20.0 + ], + "added_archival_event_time_days": -440.0, + "surviving_aliases_days": [ + 40.0, + 20.0 + ], + "candidate_discriminating_exposure_day": 20.0, + "cases": [ + { + "detection_completeness": 0.0, + "posterior_after_no_eclipse_at_day_20": { + "40.0": 0.5, + "20.0": 0.5 + }, + "expected_information_at_day_20_bits": 0.0, + "expected_information_at_shared_phase_day_0_bits": 0.0 + }, + { + "detection_completeness": 0.05, + "posterior_after_no_eclipse_at_day_20": { + "40.0": 0.5128205128205129, + "20.0": 0.48717948717948717 + }, + "expected_information_at_day_20_bits": 0.025462452938692204, + "expected_information_at_shared_phase_day_0_bits": 0.0 + }, + { + "detection_completeness": 0.95, + "posterior_after_no_eclipse_at_day_20": { + "40.0": 0.9523809523809523, + "20.0": 0.04761904761904766 + }, + "expected_information_at_day_20_bits": 0.854997400484832, + "expected_information_at_shared_phase_day_0_bits": 0.0 + }, + { + "detection_completeness": 1.0, + "posterior_after_no_eclipse_at_day_20": { + "40.0": 1.0, + "20.0": 0.0 + }, + "expected_information_at_day_20_bits": 1.0, + "expected_information_at_shared_phase_day_0_bits": 0.0 + } + ] + }, + "difference_graph": { + "assumed_levels": [ + 0.0, + 3.0, + 8.0, + 12.0 + ], + "observed_differences": [ + 3.0, + 5.0, + 4.0, + 12.0 + ], + "cycle_residual": 0.0, + "with_wrong_fourth_line_cycle_residual": -0.5, + "with_shared_2_percent_scale_error_cycle_residual": 0.0, + "interpretation": "An extra edge can check consistency without adding parameter dimension. A common multiplicative calibration error survives every cycle check." + } +} diff --git a/research/convergences-20261112/probes/hidden-dynamics/README.md b/research/convergences-20261112/probes/hidden-dynamics/README.md new file mode 100644 index 0000000..281a327 --- /dev/null +++ b/research/convergences-20261112/probes/hidden-dynamics/README.md @@ -0,0 +1,13 @@ +# Hidden dynamics probes + +Run `python3 hidden_dynamics.py` from this directory, or run the script by its absolute path. It uses only the Python standard library and rewrites `results.json` and `trajectories.csv` beside the script. + +The examples cover exact linear elimination, deterministic state insufficiency, a controlled instantaneous approximation, a stationary Gaussian memory witness, frequency-dependent response and the two-swap quantum example from Pollock et al., arXiv:1801.09811, Appendix B.3. + +The deterministic equations are `x'=-x+y`, `y'=-gamma*(x+y)`. The exact scalar memory equation is integrated independently using trapezoidal convolution and compared with the analytic solution and a Runge-Kutta integration of the full equations. Step-halving checks verify the numerical order. + +The stochastic example adds independent Wiener driving with amplitude `sqrt(2)` to the two equations at `gamma=1`. It starts in the stationary Gaussian state with covariance equal to the identity. The script computes its exact covariance and conditional covariance analytically. It does not simulate sample paths or infer a process from finite data. Sampling and measurement noise are absent. + +The quantum example uses ideal two-qubit swap matrices, a pure environment initially independent of the system, and a system-only reset between swaps. Initial system states are zero, one and plus. The joint state is a product at the sampled steps. The example makes no claim about correlations during a continuous physical gate implementation. + +All examples are synthetic. They contain no astronomical observations, no MOND law and no AeST evolution. The coupled-spring derivation in the report is elementary analytic work and is not separately simulated by this script. diff --git a/research/convergences-20261112/probes/hidden-dynamics/hidden_dynamics.py b/research/convergences-20261112/probes/hidden-dynamics/hidden_dynamics.py new file mode 100644 index 0000000..d7ab563 --- /dev/null +++ b/research/convergences-20261112/probes/hidden-dynamics/hidden_dynamics.py @@ -0,0 +1,211 @@ +#!/usr/bin/env python3 +"""Small exact/reproducible examples of elimination, closure, and memory. + +Python standard library only. These are mathematical examples, not fits to +astronomical data or an AeST/MOND calculation. Run this file from any directory. +Outputs are written beside the script. +""" + +import cmath +import csv +import json +import math +from pathlib import Path + +OUT = Path(__file__).resolve().parent + + +def exact(t, gamma, x0, y0): + """x'=-x+y; y'=-gamma*(x+y). Return x and y.""" + gap = cmath.sqrt(gamma * gamma - 6 * gamma + 1) + r1, r2 = (-(1 + gamma) + gap) / 2, (-(1 + gamma) - gap) / 2 + if abs(gap) < 1e-10: + raise ValueError("Repeated-root case is not used in this probe") + c1 = (-x0 + y0 - r2 * x0) / (r1 - r2) + c2 = x0 - c1 + x = c1 * cmath.exp(r1 * t) + c2 * cmath.exp(r2 * t) + dx = r1 * c1 * cmath.exp(r1 * t) + r2 * c2 * cmath.exp(r2 * t) + assert abs(x.imag) < 1e-10 and abs(dx.imag) < 1e-10 + return x.real, (dx + x).real + + +def rk4(gamma, x0, y0, h, duration): + x, y = x0, y0 + rows = [(0.0, x, y)] + + def f(x, y): + return -x + y, -gamma * (x + y) + + for i in range(round(duration / h)): + a, b = f(x, y) + c, d = f(x + h * a / 2, y + h * b / 2) + e, f2 = f(x + h * c / 2, y + h * d / 2) + g, j = f(x + h * e, y + h * f2) + x += h * (a + 2 * c + 2 * e + g) / 6 + y += h * (b + 2 * d + 2 * f2 + j) / 6 + rows.append(((i + 1) * h, x, y)) + return rows + + +def volterra(gamma, x0, y0, h, duration): + """Independent trapezoid solution of the scalar memory equation. + + q(t)=integral_0^t exp[-gamma*(t-s)] x(s) ds. + q is updated by trapezoidal convolution, NOT by the full y equation. + x'=-x+exp(-gamma*t)*y0-gamma*q, also using trapezoid. + """ + x, q, fprev = x0, 0.0, -x0 + y0 + decay = math.exp(-gamma * h) + rows = [(0.0, x)] + for i in range(round(duration / h)): + t = (i + 1) * h + known = math.exp(-gamma * t) * y0 - gamma * decay * q + known -= gamma * h * decay * x / 2 + xnew = (x + h * (fprev + known) / 2) / (1 + h / 2 + gamma * h * h / 4) + q = decay * q + h * (decay * x + xnew) / 2 + x = xnew + fprev = -x + math.exp(-gamma * t) * y0 - gamma * q + rows.append((t, x)) + return rows + + +def matrix_product(a, b): + return [[sum(x * y for x, y in zip(row, col)) for col in zip(*b)] for row in a] + + +def transpose(a): + return [list(row) for row in zip(*a)] + + +def kron(a, b): + return [[x * y for x in ar for y in br] for ar in a for br in b] + + +def conjugate(u, rho): + # All matrices in this probe are real. + return matrix_product(matrix_product(u, rho), transpose(u)) + + +def partial_trace(rho, keep): + if keep == "S": + return [[sum(rho[2 * i + e][2 * j + e] for e in range(2)) for j in range(2)] for i in range(2)] + return [[sum(rho[2 * s + i][2 * s + j] for s in range(2)) for j in range(2)] for i in range(2)] + + +def qubit_trace_distance(a, b): + """Half the trace norm of the difference of two real qubit states.""" + d00, d11, d01 = a[0][0] - b[0][0], a[1][1] - b[1][1], a[0][1] - b[0][1] + gap = math.sqrt((d00 - d11) ** 2 + 4 * d01 * d01) + eigenvalues = ((d00 + d11 + gap) / 2, (d00 + d11 - gap) / 2) + return sum(abs(value) for value in eigenvalues) / 2 + + +def quantum_swap(): + # Reproduces the discrete process in Pollock et al. 1801.09811, App. B.3, + # with an explicit reset inserted before the second swap. + zero = [[1, 0], [0, 0]] + one = [[0, 0], [0, 1]] + plus = [[0.5, 0.5], [0.5, 0.5]] + swap = [[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]] + cases = [] + for label, state in [("zero", zero), ("one", one), ("plus", plus)]: + initial = kron(state, zero) + mid = conjugate(swap, initial) + smid, emid = partial_trace(mid, "S"), partial_trace(mid, "E") + reset = kron(zero, emid) + final = conjugate(swap, reset) + sfinal = partial_trace(final, "S") + defect = max(abs(mid[i][j] - kron(smid, emid)[i][j]) for i in range(4) for j in range(4)) + assert smid == zero and sfinal == state and defect == 0 + cases.append({"initial_system": label, "system_after_first_swap": smid, + "system_after_reset": zero, "system_after_second_swap": sfinal, + "product_state_defect_at_middle": defect}) + reset_distance = qubit_trace_distance(cases[0]["system_after_reset"], cases[1]["system_after_reset"]) + final_distance = qubit_trace_distance(cases[0]["system_after_second_swap"], cases[1]["system_after_second_swap"]) + assert reset_distance == 0 and final_distance == 1 + return {"cases": cases, "trace_distance_after_reset_zero_vs_one": reset_distance, + "trace_distance_after_second_swap_zero_vs_one": final_distance, + "qualification": "Product states at sampled discrete times; no claim about a continuous gate implementation."} + + +def main(): + checks = [] + for h in (0.04, 0.02, 0.01, 0.005): + full = rk4(1, 1, -1, h, 6) + reduced = volterra(1, 1, -1, h, 6) + e_full = max(abs(x - exact(t, 1, 1, -1)[0]) for t, x, _ in full) + e_reduced = max(abs(x - exact(t, 1, 1, -1)[0]) for t, x in reduced) + checks.append({"dt": h, "full_rk4_max_abs_error": e_full, + "scalar_volterra_max_abs_error": e_reduced}) + assert checks[-1]["full_rk4_max_abs_error"] < 1e-10 + assert checks[-1]["scalar_volterra_max_abs_error"] < 1e-5 + convergence = [checks[i]["scalar_volterra_max_abs_error"] / checks[i+1]["scalar_volterra_max_abs_error"] for i in range(3)] + assert all(3.8 < ratio < 4.2 for ratio in convergence) + + markov_errors = [] + for gamma in (1, 10, 100): + err = max(abs(exact(i / 2000, gamma, 1, -1)[0] - math.exp(-2 * i / 2000)) for i in range(12001)) + markov_errors.append({"gamma": gamma, "max_abs_error_xdot_equals_minus_2x": err, + "interval": [0, 6], "initial_state": [1, -1]}) + assert markov_errors[-1]["max_abs_error_xdot_equals_minus_2x"] < markov_errors[0]["max_abs_error_xdot_equals_minus_2x"] / 30 + + t_split = 1.0 + split = {"x0": 0.0, "gamma": 1.0, "t": t_split, + "x_y0_plus_1": exact(t_split, 1, 0, 1)[0], + "x_y0_minus_1": exact(t_split, 1, 0, -1)[0]} + # Stationary 2D OU example: dZ=A Z dt+sqrt(2)dW, A=[[-1,1],[-1,-1]]. + # Stationary covariance is I since A+A^T+2I=0. C_x(t)=exp(-|t|) cos(t). + lag = math.pi / 4 + c1, c2 = math.exp(-lag) * math.cos(lag), math.exp(-2 * lag) * math.cos(2 * lag) + conditional_covariance = c2 - c1 * c1 + conditional_correlation = conditional_covariance / (1 - c1 * c1) + ou = {"lag": lag, "C0": 1.0, "C_lag": c1, "C_2lag": c2, + "markov_required_C_2lag": c1 * c1, + "cov_X0_X2_given_X1": conditional_covariance, + "corr_X0_X2_given_X1": conditional_correlation, + "conditional_mutual_information_nats": -math.log(1 - conditional_correlation ** 2) / 2} + assert abs(conditional_covariance) > 0.1 + + frequency = [] + for gamma in (1, 20): + for omega in (0, 1, 2): + s = complex(0, omega) + chi = (s + gamma) / (s * s + (1 + gamma) * s + 2 * gamma) + frequency.append({"gamma": gamma, "omega": omega, "response_real": chi.real, + "response_imag": chi.imag, "amplitude": abs(chi), + "phase_deg": math.degrees(cmath.phase(chi))}) + # Hidden-coordinate rescaling leaves the complete retained response unchanged. + # Original B=1, C=-gamma, D=-gamma. Transform y_new=r*y. + rescale, gamma = 7.0, 20.0 + response_defects = [] + for omega in (0, 0.5, 1, 2, 10): + s = complex(0, omega) + original = -gamma / (s + gamma) + transformed = (1 / rescale) * (1 / (s + gamma)) * (-rescale * gamma) + response_defects.append(abs(original - transformed)) + assert max(response_defects) < 1e-14 + + results = {"kind": "synthetic mathematical probes; no observational data", + "classical_equations": "x'=-x+y; y'=-gamma*(x+y)", + "reduced_equation": "x'=-x+exp(-gamma*t)*y0-gamma*integral_0^t exp(-gamma*(t-s))*x(s) ds", + "same_present_different_hidden_state": split, + "numerical_checks": checks, "volterra_step_halving_error_ratios": convergence, + "instantaneous_closure_errors": markov_errors, + "stationary_gaussian_non_markov_witness": ou, + "same_static_response_different_transient_response": frequency, + "hidden_coordinate_rescaling_max_response_defect": max(response_defects), + "quantum_two_swap_with_reset": quantum_swap(), + "all_assertions_passed": True} + (OUT / "results.json").write_text(json.dumps(results, indent=2) + "\n") + with (OUT / "trajectories.csv").open("w", newline="") as handle: + writer = csv.writer(handle, lineterminator="\n") + writer.writerow(["t", "x_hidden_plus", "x_hidden_minus", "x_gamma1", "x_gamma10", "x_gamma100", "instantaneous_closure"]) + for i in range(1201): + t = i / 200 + writer.writerow([t, exact(t, 1, 0, 1)[0], exact(t, 1, 0, -1)[0], + *[exact(t, g, 1, -1)[0] for g in (1, 10, 100)], math.exp(-2*t)]) + print(json.dumps(results, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/convergences-20261112/probes/hidden-dynamics/results.json b/research/convergences-20261112/probes/hidden-dynamics/results.json new file mode 100644 index 0000000..686b8be --- /dev/null +++ b/research/convergences-20261112/probes/hidden-dynamics/results.json @@ -0,0 +1,248 @@ +{ + "kind": "synthetic mathematical probes; no observational data", + "classical_equations": "x'=-x+y; y'=-gamma*(x+y)", + "reduced_equation": "x'=-x+exp(-gamma*t)*y0-gamma*integral_0^t exp(-gamma*(t-s))*x(s) ds", + "same_present_different_hidden_state": { + "x0": 0.0, + "gamma": 1.0, + "t": 1.0, + "x_y0_plus_1": 0.3095598756531122, + "x_y0_minus_1": -0.3095598756531122 + }, + "numerical_checks": [ + { + "dt": 0.04, + "full_rk4_max_abs_error": 4.902233868842032e-08, + "scalar_volterra_max_abs_error": 8.03507476551113e-05 + }, + { + "dt": 0.02, + "full_rk4_max_abs_error": 2.9808385759722e-09, + "scalar_volterra_max_abs_error": 2.009070502520527e-05 + }, + { + "dt": 0.01, + "full_rk4_max_abs_error": 1.8373294552453956e-10, + "scalar_volterra_max_abs_error": 5.022621959838158e-06 + }, + { + "dt": 0.005, + "full_rk4_max_abs_error": 1.1403572530710449e-11, + "scalar_volterra_max_abs_error": 1.2556583717238112e-06 + } + ], + "volterra_step_halving_error_ratios": [ + 3.9993991029336886, + 4.000043241528901, + 3.999990819909821 + ], + "instantaneous_closure_errors": [ + { + "gamma": 1, + "max_abs_error_xdot_equals_minus_2x": 0.2639819091813228, + "interval": [ + 0, + 6 + ], + "initial_state": [ + 1, + -1 + ] + }, + { + "gamma": 10, + "max_abs_error_xdot_equals_minus_2x": 0.037899073436530095, + "interval": [ + 0, + 6 + ], + "initial_state": [ + 1, + -1 + ] + }, + { + "gamma": 100, + "max_abs_error_xdot_equals_minus_2x": 0.0036968960691542985, + "interval": [ + 0, + 6 + ], + "initial_state": [ + 1, + -1 + ] + } + ], + "stationary_gaussian_non_markov_witness": { + "lag": 0.7853981633974483, + "C0": 1.0, + "C_lag": 0.3223969419448345, + "C_2lag": 1.272895288930342e-17, + "markov_required_C_2lag": 0.10393978817538098, + "cov_X0_X2_given_X1": -0.10393978817538096, + "corr_X0_X2_given_X1": -0.11599643283315936, + "conditional_mutual_information_nats": 0.006773256764037708 + }, + "same_static_response_different_transient_response": [ + { + "gamma": 1, + "omega": 0, + "response_real": 0.5, + "response_imag": 0.0, + "amplitude": 0.5, + "phase_deg": 0.0 + }, + { + "gamma": 1, + "omega": 1, + "response_real": 0.6, + "response_imag": -0.2, + "amplitude": 0.6324555320336759, + "phase_deg": -18.434948822922014 + }, + { + "gamma": 1, + "omega": 2, + "response_real": 0.3, + "response_imag": -0.4, + "amplitude": 0.5, + "phase_deg": -53.13010235415599 + }, + { + "gamma": 20, + "omega": 0, + "response_real": 0.5, + "response_imag": 0.0, + "amplitude": 0.5, + "phase_deg": 0.0 + }, + { + "gamma": 20, + "omega": 1, + "response_real": 0.408256880733945, + "response_imag": -0.19418960244648317, + "amplitude": 0.45208769322437187, + "phase_deg": -25.43835053989463 + }, + { + "gamma": 20, + "omega": 2, + "response_real": 0.26274509803921564, + "response_imag": -0.25098039215686274, + "amplitude": 0.36335401991838434, + "phase_deg": -43.6881122174959 + } + ], + "hidden_coordinate_rescaling_max_response_defect": 1.1123893155135927e-16, + "quantum_two_swap_with_reset": { + "cases": [ + { + "initial_system": "zero", + "system_after_first_swap": [ + [ + 1, + 0 + ], + [ + 0, + 0 + ] + ], + "system_after_reset": [ + [ + 1, + 0 + ], + [ + 0, + 0 + ] + ], + "system_after_second_swap": [ + [ + 1, + 0 + ], + [ + 0, + 0 + ] + ], + "product_state_defect_at_middle": 0 + }, + { + "initial_system": "one", + "system_after_first_swap": [ + [ + 1, + 0 + ], + [ + 0, + 0 + ] + ], + "system_after_reset": [ + [ + 1, + 0 + ], + [ + 0, + 0 + ] + ], + "system_after_second_swap": [ + [ + 0, + 0 + ], + [ + 0, + 1 + ] + ], + "product_state_defect_at_middle": 0 + }, + { + "initial_system": "plus", + "system_after_first_swap": [ + [ + 1.0, + 0.0 + ], + [ + 0.0, + 0.0 + ] + ], + "system_after_reset": [ + [ + 1, + 0 + ], + [ + 0, + 0 + ] + ], + "system_after_second_swap": [ + [ + 0.5, + 0.5 + ], + [ + 0.5, + 0.5 + ] + ], + "product_state_defect_at_middle": 0.0 + } + ], + "trace_distance_after_reset_zero_vs_one": 0.0, + "trace_distance_after_second_swap_zero_vs_one": 1.0, + "qualification": "Product states at sampled discrete times; no claim about a continuous gate implementation." + }, + 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+5.99,-0.0007235665977068338,0.0007235665977068338,0.0031203947214898764,1.097925254991448e-06,5.541093229128658e-06,6.268333676274384e-06 +5.995,-0.0007080244750082023,0.0007080244750082023,0.003096468331762873,1.0853799147919246e-06,5.485392776458284e-06,6.205962714079766e-06 +6.0,-0.0006926017743549024,0.0006926017743549024,0.0030726259623598583,1.0729779227483925e-06,5.4302522386457534e-06,6.14421235332821e-06 diff --git a/research/convergences-20261112/probes/issue-5/README.md b/research/convergences-20261112/probes/issue-5/README.md new file mode 100644 index 0000000..5f0f1b3 --- /dev/null +++ b/research/convergences-20261112/probes/issue-5/README.md @@ -0,0 +1,11 @@ +# Issue-5 probe + +These analytic and symbolic checks examine the proposed AeST interpretation in issue #5. They do not simulate collapse or establish the model's physical viability. + +Run from the repository root: + +```sh +python3 research/convergences-20261112/probes/issue-5/issue5_checks.py +``` + +This rewrites `results.json` beside the script. Use the bundle command `python3 research/convergences-20261112/check.py` to regenerate in a temporary directory and verify all saved numerical results. diff --git a/research/convergences-20261112/probes/issue-5/closure-review.md b/research/convergences-20261112/probes/issue-5/closure-review.md new file mode 100644 index 0000000..63909d0 --- /dev/null +++ b/research/convergences-20261112/probes/issue-5/closure-review.md @@ -0,0 +1,76 @@ +# Independent review of the compensated AeST initial pair + +**Verdict: valid conditional algebraic witness. No correction to the proposed signs or factors is needed.** The construction is consistent with the definitions and evolution equations displayed in the original AeST paper. It preserves the stated linear Einstein initial sources and vector normalization. It has not been mapped through every canonical constraint, so it should retain that qualification. + +Reviewed by gpt-forge, gpt-6-astra with requested ultra reasoning, 12 November 2026. Sources were independently reopened. This review concerns the original action's linear scalar perturbations around FLRW, not the proposed higher-derivative extension or nonlinear collapse. + +Write \(Q=\dot{\bar\phi}\), \(c=c_{\rm ad}^{2}\), \(B=(8\pi\widetilde G a^2\bar\rho)^{-1}\), and \(A_f=(1+w)/(Qc)\). For a comoving Fourier mode, \(\nabla^2\rightarrow-k^2\). Equations 7–11 then give + +\[ +Z=K_BE+(2-K_B)\chi,\quad +\delta=A_f\gamma-Bk^2Z,\quad +\theta=\varphi/Q,\quad +\Pi=c\delta+cBk^2Z. +\] + +At one initial time, keep the background, other matter data, \(\varphi,\alpha,\Phi,\Psi,\dot\Phi\) fixed. Set + +\[ +\Delta E=\epsilon,\qquad +\Delta\gamma=\frac{Bk^2K_B}{A_f}\epsilon. +\] + +Because \(\Delta\chi=0\), direct substitution gives + +\[ +\Delta\delta=\Delta\theta=0,\qquad +\Delta\Pi=cBk^2K_B\epsilon, +\] + +\[ +\Delta\dot\theta=\frac{\Delta\Pi}{1+w},\qquad +\Delta\dot\delta=-3H\Delta\Pi. +\] + +The factor \(a^{-2}\) is already in \(B\). Adding another to these expressions would be incorrect. The changes represent compensated scalar and vector velocities: \(\Delta\dot\varphi=\Delta\gamma\) and \(\Delta\dot\alpha=\epsilon\). + +An independent consistency check comes from combining equations 7 and 11: + +\[ +\Pi=\frac{1+w}{Q}\gamma. +\] + +Direct differentiation of \(\theta=\varphi/Q\), using identical initial \(\varphi\), gives \(\Delta\dot\theta=\Delta\gamma/Q\). This agrees with equation 10. The published background relation \(\dot Q/Q=-3Hc\) also makes the full definitions consistent with that equation. + +Equation 12 supplies an evolution equation, not an additional instantaneous restriction on \(\epsilon\): + +\[ +\Delta\dot E=-H\epsilon +-\frac{(2-K_B)Q}{K_B(1+w)}\Delta\Pi. +\] + +These results follow from the [original AeST paper, equations 7–12 and the preceding background equations](https://arxiv.org/html/2007.00082v3). Independently evaluated SymPy residuals were zero for the density cancellation, pressure formula, direct versus evolution-equation value of \(\Delta\dot\theta\), scalar-velocity pressure relation, and vector equation 12. + +The displayed initial constraints support the construction: + +- The linear Einstein density and momentum sources are unchanged because \(\delta,\theta\) and all other matter data match. Fixing \(\Phi,\Psi,\dot\Phi\) also fixes their geometric sides in Newtonian gauge. +- The paper's shear equation has the GR form. Matching the other species' anisotropic stress and metric potentials preserves it initially. Different isotropic pressure can change later metric derivatives without violating an initial constraint. +- The vector has \(A_\mu=(-1-\Psi,\partial_i\alpha)\) at first order. Its normalization fixes the same temporal component. Around a background with \(A_i=0\), that normalization imposes no additional linear restriction on the changed longitudinal velocity \(\dot\alpha\). + +The remaining canonical check is specific. The Hamiltonian formulation introduces auxiliary fields \(\mu,\nu\), whose constraints include \(\mathcal Y+\mathcal U_\mu=0\) and \(-\mathcal Q^2+\mathcal U_\nu=0\). The compensated scalar velocity changes the perturbation of \(\mathcal Q\). + +An implementation must solve for the corresponding auxiliary values and canonical momenta, not hold all auxiliaries fixed. + +On the generic regular branch these conditions determine auxiliaries, but this review does not certify the full map or exceptional branches. [Hamiltonian paper, section V.4, equations 62–75](https://arxiv.org/html/2307.15126v3). + +The witness requires nonzero \(k\), finite nonzero \(Q,c,K_B\), positive finite background density, \(1+w\neq0\), and a sufficiently small perturbation. + +For a real field, include the conjugate Fourier mode. The exactly dustlike or other singular limits require different variables. + +With fixed \(\epsilon\), the effect is suppressed as \(c\) becomes small, so this does not disprove an accurate dust approximation. If \(H=0\), \(\Delta\dot\delta=0\) initially while \(\Delta\dot\theta\) can remain nonzero. + +A restriction to the particular adiabatic initial family used in a cosmological calculation can remove this freedom. The conclusion therefore concerns a proposed universal two-variable closure across the allowed preparations, not every restricted effective model. + +It establishes no memory timescale, entropy law, thermal pressure, stability threshold or nonlinear result. Added scordatura operators require their own equations and constraint review. + +Recommended wording: **The published linear equations admit this compensated algebraic pair with identical initial effective density and velocity but different retained derivatives. The complete canonical initial-data map remains to be checked.** diff --git a/research/convergences-20261112/probes/issue-5/independent-review.md b/research/convergences-20261112/probes/issue-5/independent-review.md new file mode 100644 index 0000000..ac5341a --- /dev/null +++ b/research/convergences-20261112/probes/issue-5/independent-review.md @@ -0,0 +1,82 @@ +**Independent review of the issue #5 research pass** + +Prepared by gpt-forge, robustness route, using the requested gpt-6-astra configuration with ultra reasoning effort, 12 November 2026. This is a focused independent check of the mathematical examples and physical bridge. It is not a nonlinear AeST simulation or approval of a particular higher-derivative completion. + +The checked claims support a useful next experiment: determine whether collapse transfers energy into persistent local stress, then test whether that stress predicts later response. The reviewed report preserves the distinction between such a result and a thermal entropy floor. I found no outstanding algebraic correction in the checked examples. + +**What was independently checked** + +1. **Perfect caustic.** I read section 3.5 and equations 3.36–3.44 of [Arkani-Hamed and colleagues](https://arxiv.org/pdf/hep-ph/0507120), then independently varied the stated reduced Lagrangian before substituting the proposed profile. For \(\tau=T-t>0\), + + \[ + \pi=x^2/(2\tau),\quad + \Sigma=\dot\pi-(\partial_x\pi)^2/2=0,\quad + \partial_x^4\pi=0,\quad + \partial_x^2\pi=1/\tau. + \] + + The Euler–Lagrange residual and the corresponding inviscid Burgers residual vanish. The gradient term's energy density grows as \(\tau^{-2}\), even though its interior restoring term vanishes. Energetic cost alone therefore does not guarantee regularization. + + This is a local, specially symmetric solution of the specified ghost-condensate truncation. Its global boundaries and the eventual loss of derivative control prevent treating it as an AeST halo or a theorem against every completion. The report states those limits correctly. + +2. **Compensated linear AeST pair.** I checked the definitions and signs against [Skordis and Zlosnik, equations 7–12](https://arxiv.org/html/2007.00082v3). Independently differentiating the observable map in variables \((\gamma,E,\varphi,\alpha)\), the proposed direction + + \[ + n=\left(\frac{Bk^2K_B\bar{\mathcal Q}c_{\rm ad}^2}{1+w},1,0,0\right) + \] + + obeys \(D(\delta,\theta)n=0\), while \(D\Pi\,n=Bc_{\rm ad}^2K_Bk^2\). The kinematic derivative \(\Delta\dot\varphi/\bar{\mathcal Q}\) also equals the acceleration difference inferred from equation 10. + + Equal density and momentum sources preserve the stated initial Einstein constraints. The source says the shear equation retains its GR form. A solver-specific canonical constraint check remains necessary. Singular dust limits and restricted initial ensembles cannot be inferred from this regular-branch construction. + + I checked the added equation-12 expression for \(\Delta\dot E\) against the source. It supplies evolution rather than setting the initial difference to zero. The effect scales with \(c_{\rm ad}^2\) at fixed difference amplitude, so this witness does not exclude an accurate dust approximation. + +3. **Equal-moment streaming control.** Starting from \(f(x,v,t)=f(x-vt,v,0)\), I independently evaluated the Gaussian Fourier integral. The density response is \(e^{-(k\sigma t)^2/2}\), whereas equal streams at \(\pm\sigma\) give \(\cos(k\sigma t)\). Their initial zeroth, first and second moments agree. + + This exact example supports the report's limited conclusion: matching stress at one time does not establish a predictive thermal closure. No gravitational or collisional behavior follows from this toy. + +4. **Positive laboratory precedent.** I read sections I.1–I.3, the discussion and methods of [Mossman and colleagues](https://arxiv.org/html/1712.06689). The evidence supports a driven three-dimensional condensate developing transverse instability, vortex structure and coarse shock behavior consistent with effective dissipation. + + Parameter-free agreement refers to the GP simulation. The viscous comparison fits an effective sound speed and, for the filtered profile, a filtering scale, shock width and upstream mean flow. Eddy viscosity is an interpretation, not a derived thermodynamic entropy law. + + The piston supplies continued driving and the trap confines the system. The paper does not demonstrate undriven halo retention. Strict planar or spherical symmetry excludes its transverse route. AeST's different fields do not inherit condensate vortices by analogy. These qualifications are present in the reviewed final report. + +The symbolic work above was performed in a separate one-off SymPy calculation. I did not import or rerun the author's script, which writes its own results file. The independent outputs were zero caustic residual, zero observable-map residual, pressure difference \(Bc_{\rm ad}^2K_Bk^2\), and the Gaussian response above. + +**A useful physical discriminator** + +An independent work-balance check sharpens the interpretation of the BEC bridge. For GP evolution with a time-dependent external potential and vanishing boundary flux, + +\[ +E=\int\left[\frac{\hbar^2}{2m}|\nabla\psi|^2+V|\psi|^2 ++\frac{g}{2}|\psi|^4\right]d^3x, +\qquad +\frac{dE}{dt}=\int |\psi|^2\partial_tV\,d^3x. +\] + +This follows by differentiating the Hamiltonian and substituting the conservative field equation. A conservative generator with a moving piston need not conserve the field's instantaneous energy. The corresponding AeST balance must be derived from its own action and approximation, with flux and expansion or external work included. + +For the proposed collapse test, use a finite episode of infall and measure what remains after coherent forcing subsides. Separate the following outcomes with measured flux, stress and response: + +- Local stress persists, while outgoing wave energy is small enough for continued support. +- Stress follows active compression and decays once that supply ends. +- Energy remains locally but produces coherent oscillations, anisotropic stress or preparation-dependent response. +- Apparent retention changes with boundaries, filtering or unresolved physical wavelengths. + +The third outcome would still be useful physics. It calls for additional state variables rather than immediate rejection or a thermal interpretation. A perturbation applied after collapse can measure the stress response. A later transverse-mode test should begin with the selected AeST extension's actual mode spectrum. The condensate example motivates that test without specifying its answer. + +**Scope and provenance** + +I read the completed [issue report](../../reports/issue-5.md), its [technical specification](model-and-tests.md) and [check script](issue5_checks.py). + +Recommendations about fitting, dimensionality, continuing driving and field content were sent to the author and are incorporated in the reviewed report. No peer artifact was edited. I rechecked the final additions concerning equation 12 and suppression at small sound speed. + +Reviewed SHA-256 snapshots, in the same order: + +```text +780ce13da10123bb0c1433a255a91c4ec40c6871c16c297a34a5e6d328010d57 +907347f115bc998eebdb2572fcc1a33807e2235a4846897e39f02487ee1c2a1e +0153b487a59138251824e66358f729282771937a5d069ccae1360213a70a0cae +``` + +Uncomputed in this review: the complete AeST canonical constraint map, a healthy specified scordatura extension, its cutoff and nonlinear characteristics, actual transverse instabilities, collapse evolution, stress lifetime, entropy production, and any cosmological selection of a 185 km/s scale. The review verifies the proposed discriminators and their mathematical examples, not those physical outcomes. diff --git a/research/convergences-20261112/probes/issue-5/issue5_checks.py b/research/convergences-20261112/probes/issue-5/issue5_checks.py new file mode 100644 index 0000000..0f8ce13 --- /dev/null +++ b/research/convergences-20261112/probes/issue-5/issue5_checks.py @@ -0,0 +1,107 @@ +"""Small analytic checks for issue #5. No AeST collapse is simulated. + +Run from the repository root: python3 research/convergences-20261112/probes/issue-5/issue5_checks.py +Requires SymPy; writes results.json beside this script. +""" + +from __future__ import annotations + +import json +import math +from pathlib import Path + +import sympy as s + + +def main() -> None: + x, t, T, alpha, M = s.symbols("x t T alpha M", real=True) + pi = x**2 / (2 * (T - t)) + velocity = -s.diff(pi, x) + sigma = s.simplify(s.diff(pi, t) - s.diff(pi, x) ** 2 / 2) + fourth_derivative = s.diff(pi, x, 4) + eom = s.simplify( + s.diff(sigma, t) + - s.diff(sigma * s.diff(pi, x), x) + + alpha / M**2 * fourth_derivative + ) + burgers = s.simplify(s.diff(velocity, t) + velocity * s.diff(velocity, x)) + assert sigma == fourth_derivative == eom == burgers == 0 + + # Differences of two linear AeST initial states, using 2007.00082 Eqs 7-11. + # B = 1/(8*pi*Gtilde*a**2*rhobar); k is the comoving wave number. + # Common metric and other-species data are held fixed initially. + B, k, KB, Q, cs2, w, eps, H = s.symbols( + "B k K_B Q c_ad_squared w epsilon H", nonzero=True, real=True + ) + A = (1 + w) / (Q * cs2) + delta_E = eps + delta_chi = s.Integer(0) + delta_Y = KB * delta_E + (2 - KB) * delta_chi + delta_gamma = B * k**2 * delta_Y / A + delta_density = s.simplify(A * delta_gamma - B * k**2 * delta_Y) + delta_theta = s.Integer(0) + delta_pressure = s.simplify(cs2 * delta_density + cs2 * B * k**2 * delta_Y) + delta_theta_dot = s.simplify(delta_pressure / (1 + w)) + kinematic_delta_theta_dot = s.simplify(delta_gamma / Q) + delta_density_dot = s.simplify(-3 * H * delta_pressure) + delta_E_dot = s.simplify( + -H * eps - (2 - KB) * Q * delta_pressure / (KB * (1 + w)) + ) + assert delta_density == delta_theta == 0 + assert s.simplify(delta_pressure - cs2 * B * k**2 * KB * eps) == 0 + assert s.simplify(delta_theta_dot - kinematic_delta_theta_dot) == 0 + + # Exact free-streaming counterexample: same density, mean velocity and + # variance, different distribution shape. No gravity or collisions. + response = [] + for tau in [0.0, 0.5, 1.0, math.pi / 2, math.pi]: + response.append( + { + "tau_equals_k_sigma_t": tau, + "two_stream_density_amplitude_ratio": math.cos(tau), + "gaussian_density_amplitude_ratio": math.exp(-tau * tau / 2), + } + ) + assert abs(response[-1]["two_stream_density_amplitude_ratio"] + 1) < 1e-14 + + result = { + "scope": "Analytic identities and exact toy responses; no nonlinear AeST simulation.", + "sympy_version": s.__version__, + "perfect_caustic": { + "model": "Nonrelativistic ghost-condensate truncation, external potential zero", + "pi": str(pi), + "velocity": str(velocity), + "Sigma": str(sigma), + "pi_xxxx": str(fourth_derivative), + "equation_of_motion_residual": str(eom), + "inviscid_burgers_residual": str(burgers), + "pi_xx": str(s.diff(pi, x, 2)), + "status": "Local exact special solution for t tuple[float, float]: + """y_minus(0)=1; y_plus-y_minus=q; dy_minus/du=-y_minus*y_plus. + + u = Y0 integral(s dt), after inverse production is negligible. + Both y values are entropy-normalized yields divided by initial Y_minus. + """ + if q == 0.0: + ym = 1.0 / (1.0 + u) + else: + ym = q / (q + (1.0 + q) * math.expm1(q * u)) + return ym + q, ym + + +def annihilation_rk4(q: float, u: float, steps: int = 20000) -> float: + h = u / steps + y = 1.0 + f = lambda a: -a * (a + q) + for _ in range(steps): + a = f(y) + b = f(y + 0.5 * h * a) + c = f(y + 0.5 * h * b) + d = f(y + h * c) + y += h * (a + 2.0 * b + 2.0 * c + d) / 6.0 + return y + + +def annihilation_probe() -> dict: + rows = [] + for q in (0.0, 0.001, 0.01, 0.1): + yp, ym = late_annihilation(q, 100.0) + numeric = annihilation_rk4(q, 100.0) + relative_error = abs(numeric - ym) / ym + assert relative_error < 1e-8 + assert math.isclose(yp - ym, q, abs_tol=1e-14) + rows.append({ + "initial_asymmetry_q": q, + "final_y_plus": yp, + "final_y_minus": ym, + "final_total_y": yp + ym, + "minority_to_majority": ym / yp, + "rk4_relative_error": relative_error, + }) + return { + "model": "After inverse production is negligible, adiabatic entropy, only pair annihilation, no decays or fresh production", + "exposure_u": 100.0, + "initial_y_minus": 1.0, + "rows": rows, + "radiation_era_example": { + "assumptions": "Constant relativistic degrees of freedom and s-wave cross section; dY/dx proportional to -Y_plus Y_minus/x^2", + "u_of_x": "u_infinity * (1 - x_start/x)", + "lesson": "Finite integrated exposure leaves a symmetric remnant; an exact conserved excess also sets a lower bound", + }, + } + + +def wave_probe() -> dict: + """Exact free Schrodinger standing wave in units hbar=m=1. + + The pointwise Madelung current velocity is zero away from density nodes. + Momentum measurements have two peaks. After averaging spatial interference, + the Wigner distribution is a mixture of the two momentum peaks. + This does not equate a wave's pointwise velocity with two classical velocities. + """ + length = 2.0 * math.pi + k = 3 + grid = 4096 + dx = length / grid + norm = mean_p = mean_p2 = kinetic = max_current = 0.0 + for i in range(grid): + x = (i + 0.37) * dx + a, b = cmath.exp(1j * k * x), cmath.exp(-1j * k * x) + psi = (a + b) / math.sqrt(2.0 * length) + first = 1j * k * (a - b) / math.sqrt(2.0 * length) + second = -(k * k) * psi + norm += abs(psi) ** 2 * dx + mean_p += (psi.conjugate() * (-1j * first)).real * dx + mean_p2 += (psi.conjugate() * (-second)).real * dx + kinetic += 0.5 * abs(first) ** 2 * dx + max_current = max(max_current, abs((psi.conjugate() * first).imag)) + assert math.isclose(norm, 1.0, abs_tol=1e-12) + assert abs(mean_p) < 1e-12 + assert math.isclose(mean_p2, k * k, abs_tol=1e-11) + assert math.isclose(kinetic, 0.5 * k * k, abs_tol=1e-11) + assert max_current < 1e-12 + return { + "model": "Free standing wave, not AeST and not a collapse simulation", + "units": "hbar=m=1", + "length": length, + "wavenumber": k, + "norm": norm, + "mean_momentum": mean_p, + "momentum_variance": mean_p2 - mean_p**2, + "kinetic_energy": kinetic, + "max_pointwise_probability_current": max_current, + "momentum_distribution": [{"p": -k, "weight": 0.5}, {"p": k, "weight": 0.5}], + "coarse_graining": "Spatial averaging over many interference fringes removes the p=0 Wigner interference term", + "lesson": "Zero current does not imply zero momentum spread or zero kinetic energy", + } + + +def simpson(fun, a: float, b: float, n: int = 4000) -> float: + h = (b - a) / n + value = fun(a) + fun(b) + value += 4.0 * sum(fun(a + h * i) for i in range(1, n, 2)) + value += 2.0 * sum(fun(a + h * i) for i in range(2, n, 2)) + return value * h / 3.0 + + +def spectral_probe() -> dict: + """Integrate an assumed self-similar low-momentum spectrum, not dynamics. + + f(k,t)=t^alpha exp[-(t^beta k)^2], |k| <= K t^-beta. + N scales as t^(alpha-beta), kinetic energy as t^(alpha-3 beta) in 1D. + Setting alpha=beta conserves N in that moving band but reduces its energy. + """ + beta = 0.1 + alpha = beta + cutoff = 3.0 + rows = [] + baseline_n = baseline_e = None + for t in (1.0, 10.0, 100.0): + edge = cutoff * t ** (-beta) + f = lambda k: t**alpha * math.exp(-((t**beta * k) ** 2)) + number = simpson(f, -edge, edge) + energy = simpson(lambda k: 0.5 * k * k * f(k), -edge, edge) + if baseline_n is None: + baseline_n, baseline_e = number, energy + ratio_n, ratio_e = number / baseline_n, energy / baseline_e + expected_energy = t ** (-2.0 * beta) + assert math.isclose(ratio_n, 1.0, rel_tol=1e-12) + assert math.isclose(ratio_e, expected_energy, rel_tol=1e-12) + rows.append({"t_over_t0": t, "moving_cutoff": edge, + "number_ratio": ratio_n, "kinetic_energy_ratio": ratio_e, + "expected_kinetic_energy_ratio": expected_energy}) + return { + "model": "Assumed one-dimensional Gaussian scaling spectrum restricted to a moving low-momentum band", + "alpha": alpha, "beta": beta, + "rows": rows, + "lesson": "An isolated whole system can order at low momentum by transferring energy outside that sector", + "limit": "No collision equation was solved; no mechanism, exponent or applicability to dark matter is established", + } + + +def condensation_clock_probe() -> dict: + """Levkov et al. 2018 Sec. 6 illustrative virialized kinetic estimate. + + q = R m v/hbar >> 1; tau_gr/t_dyn ~= 0.047 q^3/ln(q). + The coefficient includes their approximate virial density relation. + This is not a universal bound and does not apply at q of order one. + """ + rows = [{"q_Rmv_over_hbar": q, + "tau_gr_over_t_dyn": 0.047 * q**3 / math.log(q)} + for q in (10.0, 30.0, 100.0, 300.0)] + return {"model": "Kinetic gravitational condensation estimate in a specified boson model", + "rows": rows, + "limit": "Requires high occupation, q much greater than one, kinetic evolution, and stated virial assumptions; not AeST"} + + +def main() -> None: + result = { + "status": "Illustrative analytical consequences with numerical checks; no observations or AeST nonlinear evolution", + "late_annihilation": annihilation_probe(), + "one_wave_two_momenta": wave_probe(), + "ordering_by_spectral_transport": spectral_probe(), + "condensation_time": condensation_clock_probe(), + } + destination = HERE / "results.json" + destination.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n") + print(f"Wrote {destination}") + print("Analytical solutions, conserved difference, wave moments and spectral integrals checked.") + + +if __name__ == "__main__": + main() diff --git a/research/convergences-20261112/probes/persistence/results.json b/research/convergences-20261112/probes/persistence/results.json new file mode 100644 index 0000000..e3483f6 --- /dev/null +++ b/research/convergences-20261112/probes/persistence/results.json @@ -0,0 +1,122 @@ +{ + "condensation_time": { + "limit": "Requires high occupation, q much greater than one, kinetic evolution, and stated virial assumptions; not AeST", + "model": "Kinetic gravitational condensation estimate in a specified boson model", + "rows": [ + { + "q_Rmv_over_hbar": 10.0, + "tau_gr_over_t_dyn": 20.411840649452834 + }, + { + "q_Rmv_over_hbar": 30.0, + "tau_gr_over_t_dyn": 373.1038977161165 + }, + { + "q_Rmv_over_hbar": 100.0, + "tau_gr_over_t_dyn": 10205.920324726418 + }, + { + "q_Rmv_over_hbar": 300.0, + "tau_gr_over_t_dyn": 222483.9403744074 + } + ] + }, + "late_annihilation": { + "exposure_u": 100.0, + "initial_y_minus": 1.0, + "model": "After inverse production is negligible, adiabatic entropy, only pair annihilation, no decays or fresh production", + "radiation_era_example": { + "assumptions": "Constant relativistic degrees of freedom and s-wave cross section; dY/dx proportional to -Y_plus Y_minus/x^2", + "lesson": "Finite integrated exposure leaves a symmetric remnant; an exact conserved excess also sets a lower bound", + "u_of_x": "u_infinity * (1 - x_start/x)" + }, + "rows": [ + { + "final_total_y": 0.019801980198019802, + "final_y_minus": 0.009900990099009901, + "final_y_plus": 0.009900990099009901, + "initial_asymmetry_q": 0.0, + "minority_to_majority": 1.0, + "rk4_relative_error": 8.480022239965024e-14 + }, + { + "final_total_y": 0.019818908551650985, + "final_y_minus": 0.009409454275825494, + "final_y_plus": 0.010409454275825493, + "initial_asymmetry_q": 0.001, + "minority_to_majority": 0.9039334845514082, + "rk4_relative_error": 9.512956728040464e-14 + }, + { + "final_total_y": 0.021458267022086232, + "final_y_minus": 0.005729133511043117, + "final_y_plus": 0.015729133511043117, + "initial_asymmetry_q": 0.01, + "minority_to_majority": 0.36423707046677456, + "rk4_relative_error": 1.4185704468722719e-13 + }, + { + "final_total_y": 0.10000825487338472, + "final_y_minus": 4.12743669234947e-06, + "final_y_plus": 0.10000412743669236, + "initial_asymmetry_q": 0.1, + "minority_to_majority": 4.127266342044077e-05, + "rk4_relative_error": 1.0240482705969714e-12 + } + ] + }, + "one_wave_two_momenta": { + "coarse_graining": "Spatial averaging over many interference fringes removes the p=0 Wigner interference term", + "kinetic_energy": 4.500000000000002, + "length": 6.283185307179586, + "lesson": "Zero current does not imply zero momentum spread or zero kinetic energy", + "max_pointwise_probability_current": 0.0, + "mean_momentum": 0.0, + "model": "Free standing wave, not AeST and not a collapse simulation", + "momentum_distribution": [ + { + "p": -3, + "weight": 0.5 + }, + { + "p": 3, + "weight": 0.5 + } + ], + "momentum_variance": 9.00000000000001, + "norm": 0.9999999999999998, + "units": "hbar=m=1", + "wavenumber": 3 + }, + "ordering_by_spectral_transport": { + "alpha": 0.1, + "beta": 0.1, + "lesson": "An isolated whole system can order at low momentum by transferring energy outside that sector", + "limit": "No collision equation was solved; no mechanism, exponent or applicability to dark matter is established", + "model": "Assumed one-dimensional Gaussian scaling spectrum restricted to a moving low-momentum band", + "rows": [ + { + "expected_kinetic_energy_ratio": 1.0, + "kinetic_energy_ratio": 1.0, + "moving_cutoff": 3.0, + "number_ratio": 1.0, + "t_over_t0": 1.0 + }, + { + "expected_kinetic_energy_ratio": 0.6309573444801932, + "kinetic_energy_ratio": 0.6309573444801932, + "moving_cutoff": 2.3829847041728445, + "number_ratio": 0.9999999999999999, + "t_over_t0": 10.0 + }, + { + "expected_kinetic_energy_ratio": 0.3981071705534972, + "kinetic_energy_ratio": 0.39810717055349726, + "moving_cutoff": 1.8928720334405797, + "number_ratio": 0.9999999999999999, + "t_over_t0": 100.0 + } + ] + }, + "status": "Illustrative analytical consequences with numerical checks; no observations or AeST nonlinear evolution" +} diff --git a/research/convergences-20261112/probes/relations/README.md b/research/convergences-20261112/probes/relations/README.md new file mode 100644 index 0000000..5ae1158 --- /dev/null +++ b/research/convergences-20261112/probes/relations/README.md @@ -0,0 +1,19 @@ +# Two probes of behavior stored in correlations + +Run `python3 correlation_probe.py` from this directory, or use its absolute path. Python 3 and NumPy are required. The verified run used Python 3.14.6 and NumPy 2.5.4. It writes `results.json` beside the script and records interpreter and NumPy versions. + +Run `python3 correlation_probe.py --check` to recalculate and compare with the saved result without writing files. The comparison permits numerical differences below 1e-12 and ignores interpreter/version metadata so that other machines can reproduce it. + +The first probe compares a system qubit entangled with five repeated environment records to the same system qubit entangled with the two logical states of the standard [[5,1,3]] quantum code. Both reduced system states are I/2. More strongly, controlled preparation of either orthogonal branch pair gives the same complete dephasing channel for arbitrary input amplitudes. All individual environmental qubits also have state I/2 in both constructions. + +For each of the 32 environment fragments in each construction, the script calculates total mutual information with the system, the Holevo information for the system's Z label, and the trace distance of the two conditional fragment states. The conditional states commute in this example, so the Holevo quantity is achievable classical information here. In general it is only an upper bound. The code state hides all information from every fragment of size one or two. Its information is accessible in joint correlations of three or more environment qubits. Repeated records reveal the classical label in every individual environment qubit. + +The code is constructed with stabilizers XZZXI, IXZZX, XIXZZ and ZXIXZ. An independent Pauli-operator check verifies that all nontrivial operators of weight one or two have zero matrix elements within the code space. The script verifies all fragment results against the analytic expectations, checks code normalization and stabilizers, and checks the system's dephasing for additional unequal input amplitudes and phases. + +The second probe compares symmetric, antisymmetric and incoherent one-excitation states of two atoms. Their individual atom states are identical. For a two-emitter decay matrix with diagonal Γ and off-diagonal ηΓ, the initial photon emission rates are Γ(1+η), Γ(1−η) and Γ. Values 0 ≤ η ≤ 1 interpolate from independent channels to ideal collective coupling. Every numerical rate is checked against the analytic value. + +These are finite-dimensional illustrations of known quantum mechanics. No natural environment is simulated, no new code is claimed, and no physical observation is reported. Exact darkness requires ideal shared coupling and no additional loss channels. + +Identical reduced system states do not mean identical joint states. Global phase information remains in system-environment correlations in both constructions. Neither calculation establishes a unique measurement outcome. + +Primary sources and their claim limits are recorded in the route's source ledger. The five-qubit code is due to Laflamme, Miquel, Paz and Zurek (1996), with related foundational error-correction work by Knill and Laflamme. Collective emission follows Dicke (1954). The present juxtaposition is an explanatory probe for Foundation0's exploration. diff --git a/research/convergences-20261112/probes/relations/correlation_probe.py b/research/convergences-20261112/probes/relations/correlation_probe.py new file mode 100644 index 0000000..e12a8c3 --- /dev/null +++ b/research/convergences-20261112/probes/relations/correlation_probe.py @@ -0,0 +1,197 @@ +#!/usr/bin/env python3 +"""Two finite-dimensional illustrations of behavior stored in correlations. + +Run: python3 correlation_probe.py +Requires numpy. Writes only beside this script. This is a mathematical probe, +not experimental data or a fit to the Foundation-0 witness map. +""" + +import argparse +import itertools +import json +import platform +import sys +from pathlib import Path + +import numpy as np + + +def ket(index, n): + result = np.zeros(2**n, dtype=complex) + result[index] = 1 + return result + + +def reduced(psi, keep, n): + """Partial trace for a pure state, with qubit 0 the most significant bit.""" + keep = tuple(keep) + rest = tuple(i for i in range(n) if i not in keep) + a = psi.reshape((2,) * n).transpose(keep + rest) + a = a.reshape(2 ** len(keep), -1) + return a @ a.conj().T + + +def entropy(rho): + eig = np.linalg.eigvalsh(rho) + assert eig.min() > -1e-12 + eig = eig[eig > 1e-13] + return float(-np.sum(eig * np.log2(eig))) + + +def pauli(word): + matrices = { + "I": np.eye(2, dtype=complex), + "X": np.array([[0, 1], [1, 0]], dtype=complex), + "Y": np.array([[0, -1j], [1j, 0]], dtype=complex), + "Z": np.diag([1, -1]).astype(complex), + } + result = np.ones((1, 1), dtype=complex) + for char in word: + result = np.kron(result, matrices[char]) + return result + + +def five_qubit_code(): + # Standard cyclic stabilizer form of the [[5,1,3]] perfect code. + # Build |0_L> as the +1 state of all four generators and logical Z. + words = ["XZZXI", "IXZZX", "XIXZZ", "ZXIXZ"] + gs = [pauli(w) for w in words] + for g, h in itertools.combinations(gs, 2): + np.testing.assert_allclose(g @ h, h @ g, atol=1e-13) + zero = ket(0, 5) + for g in gs: + zero = (zero + g @ zero) / 2 + zero /= np.linalg.norm(zero) + one = pauli("XXXXX") @ zero + for state in (zero, one): + for g in gs: + np.testing.assert_allclose(g @ state, state, atol=1e-13) + np.testing.assert_allclose(pauli("ZZZZZ") @ zero, zero, atol=1e-13) + np.testing.assert_allclose(pauli("ZZZZZ") @ one, -one, atol=1e-13) + np.testing.assert_allclose(np.vdot(zero, one), 0, atol=1e-13) + # A separate check of local indistinguishability, using every nonidentity + # Pauli on one or two positions instead of the partial-trace calculation. + code = np.column_stack([zero, one]) + max_local_pauli = 0.0 + for word in itertools.product("IXYZ", repeat=5): + if 1 <= sum(c != "I" for c in word) <= 2: + matrix = code.conj().T @ pauli(word) @ code + max_local_pauli = max(max_local_pauli, float(np.max(abs(matrix)))) + assert max_local_pauli < 1e-12 + return zero, one, words, max_local_pauli + + +def record_probe(): + code0, code1, stabilizers, max_local_pauli = five_qubit_code() + branches = { + "redundant_records": (ket(0, 5), ket(31, 5)), + "encoded_correlations": (code0, code1), + } + output = {"environment_qubits": 5, "system_qubits": 1, + "code_stabilizers": stabilizers, + "max_code_matrix_element_of_weight_1_or_2_pauli": max_local_pauli, + "states": {}} + for name, (env0, env1) in branches.items(): + psi = (np.kron(ket(0, 1), env0) + np.kron(ket(1, 1), env1)) / np.sqrt(2) + rho_s = reduced(psi, [0], 6) + np.testing.assert_allclose(rho_s, np.eye(2) / 2, atol=1e-13) + rows = [] + for size in range(6): + mutual, holevo, distance = [], [], [] + for fragment in itertools.combinations(range(5), size): + rho0 = reduced(env0, fragment, 5) + rho1 = reduced(env1, fragment, 5) + rho_f = (rho0 + rho1) / 2 + rho_sf = reduced(psi, [0] + [i + 1 for i in fragment], 6) + mutual.append(entropy(rho_s) + entropy(rho_f) - entropy(rho_sf)) + holevo.append(entropy(rho_f) - (entropy(rho0) + entropy(rho1)) / 2) + distance.append(float(np.sum(abs(np.linalg.eigvalsh(rho0 - rho1))) / 2)) + # Here the conditional states commute, so Holevo information is + # achievable. This is not true for general quantum ensembles. + np.testing.assert_allclose(rho0 @ rho1, rho1 @ rho0, atol=1e-13) + expected_i = (0 if size == 0 else 2 if size == 5 else 1) if name == "redundant_records" else (0 if size <= 2 else 2) + expected_chi = (0 if size == 0 else 1) if name == "redundant_records" else (0 if size <= 2 else 1) + np.testing.assert_allclose(mutual, expected_i, atol=1e-12) + np.testing.assert_allclose(holevo, expected_chi, atol=1e-12) + np.testing.assert_allclose(distance, expected_chi, atol=1e-12) + rows.append({"fragment_qubits": size, "fragments_checked": len(mutual), + "mutual_information_bits_min": round(min(mutual), 12), + "mutual_information_bits_max": round(max(mutual), 12), + "pointer_holevo_bits": round(float(np.mean(holevo)), 12), + "pointer_trace_distance": round(float(np.mean(distance)), 12)}) + # Both branch pairs implement the SAME full dephasing channel on S, + # for arbitrary input alpha|0>+beta|1>, not merely for equal amplitudes. + for p, phase in [(0.07, 0.0), (0.3, 0.8), (0.5, 2.1), (0.91, -0.4)]: + arbitrary = np.sqrt(p) * np.kron(ket(0, 1), env0) + np.sqrt(1-p) * np.exp(1j*phase) * np.kron(ket(1, 1), env1) + np.testing.assert_allclose(reduced(arbitrary, [0], 6), np.diag([p, 1-p]), atol=1e-13) + output["states"][name] = {"system_density_matrix": rho_s.real.tolist(), "fragments": rows} + return output + + +def emission_probe(): + # Basis |g>=|0>, |e>=|1>. Equal one-body marginals do not fix emission + # through a shared field. gamma_12 = eta * gamma; |eta| <= 1 keeps the + # two-emitter decay matrix positive. Units set single-emitter gamma=1. + lower = np.array([[0, 1], [0, 0]], dtype=complex) + lowering = [np.kron(lower, np.eye(2)), np.kron(np.eye(2), lower)] + bright = (ket(1, 2) + ket(2, 2)) / np.sqrt(2) + dark = (ket(1, 2) - ket(2, 2)) / np.sqrt(2) + mixed = (np.outer(ket(1, 2), ket(1, 2)) + np.outer(ket(2, 2), ket(2, 2))) / 2 + states = {"symmetric": np.outer(bright, bright.conj()), + "antisymmetric": np.outer(dark, dark.conj()), "incoherent_mixture": mixed} + for state in (bright, dark): + for particle in range(2): + np.testing.assert_allclose(reduced(state, [particle], 2), np.eye(2)/2, atol=1e-13) + rows = [] + for eta in [0.0, 0.25, 0.5, 0.9, 1.0]: + rates = {} + for name, rho in states.items(): + rate = sum((1 if i == j else eta) * np.trace(lowering[i].conj().T @ lowering[j] @ rho) + for i in range(2) for j in range(2)) + assert abs(rate.imag) < 1e-13 + rates[name] = float(rate.real) + np.testing.assert_allclose([rates["symmetric"], rates["antisymmetric"], rates["incoherent_mixture"]], [1+eta, 1-eta, 1], atol=1e-13) + rows.append({"bath_cross_correlation_eta": eta, "photon_emission_rate_over_single_atom_gamma": rates}) + return {"description": "Initial photon emission rates in the two-emitter Markov model; not measured rates.", + "one_atom_density_matrix_for_each_pure_state": [[0.5, 0], [0, 0.5]], "rows": rows} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--check", action="store_true", help="Verify the checked-in result without writing files.") + args = parser.parse_args() + result = {"status": "COMPUTED_ILLUSTRATION_OF_KNOWN_QUANTUM_MECHANICS", "numpy_version": np.__version__, + "python_version": platform.python_version(), "python_executable": "python3", + "records": record_probe(), "emission": emission_probe(), + "limitations": ["Endpoint states and ideal channels, not a natural-environment simulation.", + "All original system phase information remains in global correlations in both record examples.", + "Exact dark emission requires ideal collective coupling and no extra loss channels."]} + destination = Path(__file__).with_name("results.json") + if args.check: + stored = json.loads(destination.read_text()) + # Interpreter metadata may differ across machines. Numerical and + # scientific outputs must agree within the explicit tolerance below. + def compare(actual, expected, path="result"): + if isinstance(actual, dict): + assert actual.keys() == expected.keys(), path + for key in actual: + if key not in {"python_executable", "python_version", "numpy_version"}: + compare(actual[key], expected[key], path + "." + key) + elif isinstance(actual, list): + assert len(actual) == len(expected), path + for index, (a, b) in enumerate(zip(actual, expected)): + compare(a, b, path + f"[{index}]") + elif isinstance(actual, float): + assert abs(actual - expected) < 1e-12, path + else: + assert actual == expected, path + compare(result, stored) + else: + destination.write_text(json.dumps(result, indent=2) + "\n") + print(json.dumps({"checks": "passed", "mode": "read_only_check" if args.check else "regenerate", "output": str(destination), + "record_fragments_per_state": 32, + "emission_limits": result["emission"]["rows"][-1]}, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/convergences-20261112/probes/relations/results.json b/research/convergences-20261112/probes/relations/results.json new file mode 100644 index 0000000..0daad96 --- /dev/null +++ b/research/convergences-20261112/probes/relations/results.json @@ -0,0 +1,203 @@ +{ + "status": "COMPUTED_ILLUSTRATION_OF_KNOWN_QUANTUM_MECHANICS", + "numpy_version": "2.5.4", + "python_version": "3.14.6", + "python_executable": "python3", + "records": { + "environment_qubits": 5, + "system_qubits": 1, + "code_stabilizers": [ + "XZZXI", + "IXZZX", + "XIXZZ", + "ZXIXZ" + ], + "max_code_matrix_element_of_weight_1_or_2_pauli": 0.0, + "states": { + "redundant_records": { + "system_density_matrix": [ + [ + 0.4999999999999999, + 0.0 + ], + [ + 0.0, + 0.4999999999999999 + ] + ], + "fragments": [ + { + "fragment_qubits": 0, + "fragments_checked": 1, + "mutual_information_bits_min": 0.0, + "mutual_information_bits_max": 0.0, + "pointer_holevo_bits": 0.0, + "pointer_trace_distance": 0.0 + }, + { + "fragment_qubits": 1, + "fragments_checked": 5, + "mutual_information_bits_min": 1.0, + "mutual_information_bits_max": 1.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + }, + { + "fragment_qubits": 2, + "fragments_checked": 10, + "mutual_information_bits_min": 1.0, + "mutual_information_bits_max": 1.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + }, + { + "fragment_qubits": 3, + "fragments_checked": 10, + "mutual_information_bits_min": 1.0, + "mutual_information_bits_max": 1.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + }, + { + "fragment_qubits": 4, + "fragments_checked": 5, + "mutual_information_bits_min": 1.0, + "mutual_information_bits_max": 1.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + }, + { + "fragment_qubits": 5, + "fragments_checked": 1, + "mutual_information_bits_min": 2.0, + "mutual_information_bits_max": 2.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + } + ] + }, + "encoded_correlations": { + "system_density_matrix": [ + [ + 0.49999999999999994, + 0.0 + ], + [ + 0.0, + 0.49999999999999994 + ] + ], + "fragments": [ + { + "fragment_qubits": 0, + "fragments_checked": 1, + "mutual_information_bits_min": 0.0, + "mutual_information_bits_max": 0.0, + "pointer_holevo_bits": 0.0, + "pointer_trace_distance": 0.0 + }, + { + "fragment_qubits": 1, + "fragments_checked": 5, + "mutual_information_bits_min": 0.0, + "mutual_information_bits_max": 0.0, + "pointer_holevo_bits": 0.0, + "pointer_trace_distance": 0.0 + }, + { + "fragment_qubits": 2, + "fragments_checked": 10, + "mutual_information_bits_min": 0.0, + "mutual_information_bits_max": 0.0, + "pointer_holevo_bits": 0.0, + "pointer_trace_distance": 0.0 + }, + { + "fragment_qubits": 3, + "fragments_checked": 10, + "mutual_information_bits_min": 2.0, + "mutual_information_bits_max": 2.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + }, + { + "fragment_qubits": 4, + "fragments_checked": 5, + "mutual_information_bits_min": 2.0, + "mutual_information_bits_max": 2.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + }, + { + "fragment_qubits": 5, + "fragments_checked": 1, + "mutual_information_bits_min": 2.0, + "mutual_information_bits_max": 2.0, + "pointer_holevo_bits": 1.0, + "pointer_trace_distance": 1.0 + } + ] + } + } + }, + "emission": { + "description": "Initial photon emission rates in the two-emitter Markov model; not measured rates.", + "one_atom_density_matrix_for_each_pure_state": [ + [ + 0.5, + 0 + ], + [ + 0, + 0.5 + ] + ], + "rows": [ + { + "bath_cross_correlation_eta": 0.0, + "photon_emission_rate_over_single_atom_gamma": { + "symmetric": 0.9999999999999998, + "antisymmetric": 0.9999999999999998, + "incoherent_mixture": 1.0 + } + }, + { + "bath_cross_correlation_eta": 0.25, + "photon_emission_rate_over_single_atom_gamma": { + "symmetric": 1.2499999999999998, + "antisymmetric": 0.7499999999999998, + "incoherent_mixture": 1.0 + } + }, + { + "bath_cross_correlation_eta": 0.5, + "photon_emission_rate_over_single_atom_gamma": { + "symmetric": 1.4999999999999996, + "antisymmetric": 0.4999999999999999, + "incoherent_mixture": 1.0 + } + }, + { + "bath_cross_correlation_eta": 0.9, + "photon_emission_rate_over_single_atom_gamma": { + "symmetric": 1.8999999999999995, + "antisymmetric": 0.09999999999999998, + "incoherent_mixture": 1.0 + } + }, + { + "bath_cross_correlation_eta": 1.0, + "photon_emission_rate_over_single_atom_gamma": { + "symmetric": 1.9999999999999996, + "antisymmetric": 0.0, + "incoherent_mixture": 1.0 + } + } + ] + }, + "limitations": [ + "Endpoint states and ideal channels, not a natural-environment simulation.", + "All original system phase information remains in global correlations in both record examples.", + "Exact dark emission requires ideal collective coupling and no extra loss channels." + ] +} diff --git a/research/convergences-20261112/probes/repetition/README.md b/research/convergences-20261112/probes/repetition/README.md new file mode 100644 index 0000000..2ccaaad --- /dev/null +++ b/research/convergences-20261112/probes/repetition/README.md @@ -0,0 +1,21 @@ +This probe separates a geometric fold from the choice of interactions on it. It reads no source repository and uses the Python standard library. + +Run from the repository root: + +```sh +python3 research/convergences-20261112/probes/repetition/graph_vs_geometry.py +``` + +The script writes `graph-results.json` beside itself. It checks the six-point cab-to-fcc curve supplied by `aska-digital/incentre-lattice`, commit `db3b51d0f31e04ea3c0ffafb553f70fcdfc617ec`, in `results/fold-continuous-fcc/PROOF.md`. + +The contact graph has degree five throughout 0 < s < 1. At s = 1 it gains contacts and becomes degree twelve. Exact integer-pair arithmetic checks every nearby distance polynomial. The source's analytic singular-value bound excludes all more distant periodic images. A curve with a changed bridge is rejected, and near-cancelling exact signs are checked. + +The original degree-five interaction graph is unchanged at the endpoint. Fixed scalar Ising couplings on those bars therefore give the same partition function throughout the fold. Coupling every fcc contact gives a different model, already visible in high-temperature coefficients. + +This conditional identity does not describe physical CaB6 without a microscopic interaction law. Distance-dependent couplings, angular interactions, vector elasticity and geometrically defined measurements can change along the fold. No critical temperature or percolation threshold was estimated. + +The source manuscript used for the literature check is available from the public NSF repository: + +https://par.nsf.gov/servlets/purl/10230398 + +Section 7 documents prior bridged cross-polytope frameworks with a different bar-to-edge ratio. It is not the source of the particular equal-bar fcc curve used in this probe. diff --git a/research/convergences-20261112/probes/repetition/graph-results.json b/research/convergences-20261112/probes/repetition/graph-results.json new file mode 100644 index 0000000..331702e --- /dev/null +++ b/research/convergences-20261112/probes/repetition/graph-results.json @@ -0,0 +1,207 @@ +{ + "status": "reproducible model calculation; no material prediction", + "source_repository": "https://github.com/aska-digital/incentre-lattice", + "source_commit": "db3b51d0f31e04ea3c0ffafb553f70fcdfc617ec", + "source_path": "results/fold-continuous-fcc/PROOF.md", + "assumption": "Fixed scalar Ising J on prescribed bars; no interactions on other contacts", + "image_bound": "sigma_min(L)>=1 and |p-q|<=2 exclude |n|^2>=12 from contact; written source proof", + "states": [ + { + "s": 0.0, + "density": 0.22326611566327859, + "bar_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "contact_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "bar_graph_sha256": "5f79040796ece8e1c4f91c0ee20f8ea160f3c85f740ac581eaa0363a31b9e1dd", + "max_bar_squared_length_error": 4.440892098500626e-16, + "smallest_nonbar_gap_over_contact_distance": 0.41421356237309515 + }, + { + "s": 0.25, + "density": 0.2525279756510523, + "bar_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "contact_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "bar_graph_sha256": "5f79040796ece8e1c4f91c0ee20f8ea160f3c85f740ac581eaa0363a31b9e1dd", + "max_bar_squared_length_error": 8.881784197001252e-16, + "smallest_nonbar_gap_over_contact_distance": 0.41421356237309515 + }, + { + "s": 0.5, + "density": 0.3422823920720581, + "bar_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "contact_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "bar_graph_sha256": "5f79040796ece8e1c4f91c0ee20f8ea160f3c85f740ac581eaa0363a31b9e1dd", + "max_bar_squared_length_error": 4.440892098500626e-16, + "smallest_nonbar_gap_over_contact_distance": 0.41421356237309515 + }, + { + "s": 0.75, + "density": 0.5011075176643782, + "bar_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "contact_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "bar_graph_sha256": "5f79040796ece8e1c4f91c0ee20f8ea160f3c85f740ac581eaa0363a31b9e1dd", + "max_bar_squared_length_error": 0.0, + "smallest_nonbar_gap_over_contact_distance": 0.1983237448471371 + }, + { + "s": 0.9, + "density": 0.6343008927582018, + "bar_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "contact_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "bar_graph_sha256": "5f79040796ece8e1c4f91c0ee20f8ea160f3c85f740ac581eaa0363a31b9e1dd", + "max_bar_squared_length_error": 0.0, + "smallest_nonbar_gap_over_contact_distance": 0.07423378240243128 + }, + { + "s": 0.99, + "density": 0.7292096182619797, + "bar_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "contact_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "bar_graph_sha256": "5f79040796ece8e1c4f91c0ee20f8ea160f3c85f740ac581eaa0363a31b9e1dd", + "max_bar_squared_length_error": 0.0, + "smallest_nonbar_gap_over_contact_distance": 0.0071064219985181865 + }, + { + "s": 1.0, + "density": 0.740480489693061, + "bar_degree_each_vertex": [ + 5, + 5, + 5, + 5, + 5, + 5 + ], + "contact_degree_each_vertex": [ + 12, + 12, + 12, + 12, + 12, + 12 + ], + "bar_graph_sha256": "5f79040796ece8e1c4f91c0ee20f8ea160f3c85f740ac581eaa0363a31b9e1dd", + "max_bar_squared_length_error": 0.0, + "smallest_nonbar_gap_over_contact_distance": 0.0 + } + ], + "exact_endpoint_contacts": [ + 12, + 12, + 12, + 12, + 12, + 12 + ], + "exact_interior_certificate": { + "directed_bar_identities": 30, + "directed_nonbar_strict_distance_polynomials": 6120, + "arithmetic": "exact integer pairs a+b*sqrt(2)", + "interior_contact_graph_equals_prescribed_bar_graph": true, + "scope": "0 0)-(a < 0) + if not a: + return (b > 0)-(b < 0) + if (a > 0) == (b > 0): + return (a > 0)-(a < 0) + return ((a*a > 2*b*b)-(a*a < 2*b*b))*((a > 0)-(a < 0)) + + +def exact_interior_contacts(matrix=C): + """Every nonbar distance is strictly >sqrt(2) for 0= 0 for x in b12) + identical = all(x == (0, 0) for x in b12) + assert identical == bar(p, q, n) + identities += identical + strict += not identical + return {"directed_bar_identities": identities, + "directed_nonbar_strict_distance_polynomials": strict, + "arithmetic": "exact integer pairs a+b*sqrt(2)", + "interior_contact_graph_equals_prescribed_bar_graph": True, + "scope": "0=1 and |p-q|<=2 exclude |n|^2>=12 from contact; written source proof", + "states": states, + "exact_endpoint_contacts": exact_contacts, + "exact_interior_certificate": interior_certificate, + "negative_controls": {"near_cancellation_signs": "passed", "changed_bridge_curve_rejected": rejected_bad_curve}, + "bar_graph": {"edges_per_cell": 15, "triangles_per_cell": 8, + "ground_energy_per_site_over_J": -2.5, + "logZ_per_site_K2_coefficient": 1.25, + "logZ_per_site_K3_coefficient": 4/3, + "reduced_susceptibility_K_coefficient": 5}, + "full_fcc_contact_graph": {"edges_per_cell": 36, "triangles_per_cell": 48, + "ground_energy_per_site_over_J": -6, + "logZ_per_site_K2_coefficient": 3, + "logZ_per_site_K3_coefficient": 8, + "reduced_susceptibility_K_coefficient": 12}, + "limitation": "Exact interior contact result uses the source curve and analytic distant-image bound. Fixed-bar partition-function invariance is algebraic by definition. No Tc or percolation threshold estimated." + } + destination = Path(__file__).with_name("graph-results.json") + destination.write_text(json.dumps(output, indent=2)+"\n") + print(json.dumps({"states": len(states), "bar_degree": 5, + "endpoint_contact_degree": 12, + "density_ratio": states[-1]["density"]/states[0]["density"], + "output": str(destination)}, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/convergences-20261112/probes/robustness/README.md b/research/convergences-20261112/probes/robustness/README.md new file mode 100644 index 0000000..d4c2d1f --- /dev/null +++ b/research/convergences-20261112/probes/robustness/README.md @@ -0,0 +1,63 @@ +The probes independently test selected inferences in the convergence reports. They do not import peer scripts or change the four source repositories. NumPy is required. + +```bash +cd research/convergences-20261112 +python3 probes/robustness/robustness_probes.py +python3 probes/robustness/robustness_probes.py --check +``` + +The first command writes `results.json` beside the script. The second compares recomputed results without writing. No physical dataset is fitted. Floating-point comparisons use explicit tolerances. The Press-Schechter redshift values are read from the existing gravity artifact and identified as such. + +**Spring derivation** + +For a bond from site i to translated site j with vector b and unit direction e, its first-order extension at zero Bloch wavevector is e·(u_j−u_i). The corresponding row of C has entries −e and +e. With equal unit masses and spring constants, D=CᵀC. + +The twelve internal octahedron bars give tr(D_int²)=60. The three bridges have disjoint site pairs and contribute tr(D_bridge²)=12. Their directions are e_i=(a unit_i+t C_i)/sqrt(2), with a²+2t²=2. Each bridge meets eight internal bar ends. + +At either endpoint on coordinate axis i, the sum of internal direction outer products is diag(2,1,1), with 2 in direction i. For both endpoints the sum of squared bridge/internal dot products is 2+2(e_i)_i². Counting both cross terms in the trace and all bridges gives 12+6a². + +Therefore tr(D²)=60+12+12+6a²=96−12t². Each of fifteen rows has squared norm two, so tr(D)=30. + +The internal octahedron is infinitesimally rigid. At t=0 all three motif rotations stretch no bridge. At t≠0 the bridge constraints on rotation vector w are proportional to (0,1,−1)·w, (−1,0,−1)·w, and (1,1,0)·w. The third is the first minus the second, leaving w proportional to (−1,1,1). + +Translations add three null modes. Thus the fixed-cell, zero-wavevector nullity is six at the open endpoint and four otherwise. Since C has fifteen rows and eighteen columns, the corresponding self-stress counts are three and one. This is an infinitesimal statement, not nonlinear stability or topological protection. + +A separate check stretches the actual bonds by ±epsilon times a seeded displacement and computes the spring energy from their lengths. Its symmetric second difference agrees with the quadratic matrix energy. No new contacts are activated at the fcc endpoint. + +**Quantum records** + +The isometries map system basis states to either product branches |00>, |11> or Bell branches |Phi+>, |Phi−>. Orthogonality of the branch pair makes both maps complete dephasing channels. The script checks the image of every system matrix unit. + +For an equal-amplitude input the two-qubit environment branches have identical one-qubit marginals in the Bell case. No local measurement reveals system Z. A joint Bell measurement does. Total system-fragment mutual information remains one bit for either one-qubit fragment in both examples. + +The Bell example does contain information about a different system basis for the chosen input. The absence is explicitly about Z. The five-qubit example in the relations route addresses absence of all system information from smaller fragments. + +An environment-only unitary relates the constructions. With fixed fragment access, implementing this entangling unitary is a physical change. A coordinate change that transforms states and all observables together changes no outcome probabilities. + +**Information and calibration** + +For known linear design A and independent Gaussian noise variance s², F=AᵀA/s². Joining rows adds constraints. Repeated rows increase precision in the same direction, leaving the same null space. + +An unknown common gain preserves the scaling symmetry (q,b,g)→(a q,a b,g/a). A known-amplitude calibration measurement breaks it. This example concerns a known forward model and is not nonlinear independent component analysis. + +Under theta'=S theta, F'=S^(-T) F S^(-1). Its eigenvalues can change while dthetaᵀ F dtheta is unchanged for corresponding displacements. The probe checks this identity directly. + +For y_i=q+b+e_i with b Gaussian of unit variance and independent e_i of variance 0.01, marginal covariance is Sigma=11ᵀ+0.01 I. Thus 1ᵀSigma^(-1)1=n/(n+0.01). Independent-offset covariance instead gives n/1.01. The table compares two different noise assumptions. + +**Gravity** + +Steady spherical Jeans balance with constant radial dispersion gives Vc²=(gamma−2 beta)sigma_r². It does not directly supply the projected dispersion of a real disk or group. + +The cooling formula is evaluated from dimensional constants, density, composition and the chosen clock. For free-free cooling, t_cool is proportional to sqrt(T)/n_e. With kT=mu m_p sigma², the boundary sigma is proportional to n_e t_available. + +At density Delta rho_crit, n_e is proportional to Delta H². A Hubble clock gives sigma proportional to Delta H. A free-fall clock gives sigma proportional to sqrt(Delta) H, since t_ff=pi/(2 sqrt(Delta) H). Large clock changes may leave the ionized free-free regime, requiring a different cooling function. + +For density proportional to r^(-gamma) and gamma<3, the mass fraction within xR is x^(3−gamma). Its derivative is finite at gamma=2. The separate trapped-fraction ansatz cannot be inferred from the smooth hydrostatic expression. No stability mode is calculated. + +The collapse-dispersion column is read from the source certificate. It is not an independent Boltzmann-code or transfer-function validation. That source file's hash is stored in `results.json`. + +**AeST derivative** + +The published scalar terms are L=(2−KB)(2J·dphi−Y)−F(Y,Q), with Y=q^(mu nu)d_mu(phi)d_nu(phi) and Q=A^mu d_mu(phi). Varying the covector dphi gives the current in the report. Integration by parts yields its continuity equation. + +The probe uses a generic polynomial depending on both Y and Q and sixteen seeded configurations with normalized timelike A and acceleration orthogonal to A. Finite differences independently check the algebraic derivative. This does not show the chosen polynomial is physically viable or supply a fluid closure, entropy law or energy-retention mechanism. diff --git a/research/convergences-20261112/probes/robustness/input-snapshot.json b/research/convergences-20261112/probes/robustness/input-snapshot.json new file mode 100644 index 0000000..919aa64 --- /dev/null +++ b/research/convergences-20261112/probes/robustness/input-snapshot.json @@ -0,0 +1,36 @@ +{ + "captured_utc": "2026-11-12T16:10:42.596022+00:00", + "scope": "Historical report bytes reviewed by the original robustness pass. Publication changes paths and presentation, so these hashes do not authenticate the published report bytes. Private briefing and coordination records are omitted.", + "inputs": [ + { + "path": "reports/evidence.md", + "sha256": "ef1d7d3aaf0dbfb6691ecf559e6c841395cc2fbcdc6aa6665280ef18326fd885", + "bytes": 19440 + }, + { + "path": "reports/persistence.md", + "sha256": "58f66e108bc9bbd086162416c25d3493fa0c0a088ad0c253b01715100aeb7368", + "bytes": 21060 + }, + { + "path": "reports/relations.md", + "sha256": "274b329263fd47b478b39da44a883097d66abe97bc2309a399c06dd1bc8d686a", + "bytes": 25873 + }, + { + "path": "reports/repetition.md", + "sha256": "2595c4ae6656c34084ca0314df5427f7f7e0a03d44ffc45f206c5f06824d3304", + "bytes": 21024 + }, + { + "path": "reports/scales.md", + "sha256": "374d361adb88ccd8216cbcfedd67bdba79a5805683f177710122485bfdb60711", + "bytes": 22333 + }, + { + "path": "reports/unclaimed.md", + "sha256": "12de0cdc9e625118d6f8b562129ace23513d46b18096308d136f794b04de7182", + "bytes": 18086 + } + ] +} diff --git a/research/convergences-20261112/probes/robustness/results.json b/research/convergences-20261112/probes/robustness/results.json new file mode 100644 index 0000000..02407e2 --- /dev/null +++ b/research/convergences-20261112/probes/robustness/results.json @@ -0,0 +1,357 @@ +{ + "status": "Independent mathematical probes; no observational discovery or validated dark-field mechanism.", + "mechanics": { + "scope": "Fixed-cell Bloch k=0 central-force model, equal unit masses and spring constants, no prestress; only original bars, including at the fcc endpoint.", + "bonds_per_cell": 15, + "physical_coordinates_per_cell": 18, + "analytic_sum_omega_fourth": "96 - 12 t^2", + "rows": [ + { + "s": 0.0, + "t": 0.0, + "squared_frequencies": [ + -4.096321557456769e-16, + -2.3258395818994736e-16, + -1.750725770655428e-17, + 2.9481179952006597e-16, + 6.669311965846762e-16, + 8.563735839713576e-16, + 0.9999999999999994, + 1.0000000000000007, + 1.0000000000000009, + 1.9999999999999982, + 1.9999999999999993, + 2.0000000000000004, + 2.9999999999999982, + 2.999999999999999, + 2.9999999999999996, + 2.9999999999999996, + 3.0000000000000004, + 5.999999999999998 + ], + "sum_omega_squared": 29.999999999999993, + "sum_omega_fourth": 95.99999999999997, + "zero_modes": 6, + "self_stress_states": 3, + "energy_hessian_discrepancy": 7.645866162420134e-10 + }, + { + "s": 0.25, + "t": 0.47058823529411764, + "squared_frequencies": [ + -5.26819907986573e-16, + -1.5775851506269436e-17, + 2.0678324095653123e-16, + 9.145742287537451e-16, + 0.11764705882352916, + 0.21191161698167063, + 0.9999999999999997, + 1.0000000000000004, + 1.0000000000000007, + 1.6968207371890252, + 1.8823529411764701, + 2.074808713771113, + 2.999999999999999, + 2.999999999999999, + 2.999999999999999, + 3.0000000000000027, + 3.3023557278262317, + 5.714103204231963 + ], + "sum_omega_squared": 30.0, + "sum_omega_fourth": 93.34256055363322, + "zero_modes": 4, + "self_stress_states": 1, + "energy_hessian_discrepancy": 7.438554217031879e-10 + }, + { + "s": 0.5, + "t": 0.8, + "squared_frequencies": [ + -4.207096298989494e-16, + -3.6339703505730275e-16, + 7.41058306963119e-16, + 1.2517461745827448e-15, + 0.4000000000000002, + 0.6177775030364073, + 0.9999999999999989, + 0.9999999999999997, + 0.9999999999999999, + 1.3165631466106562, + 1.5999999999999999, + 2.338928089460743, + 2.9999999999999982, + 2.9999999999999982, + 2.9999999999999996, + 3.0, + 3.679074544670553, + 5.0476567162216375 + ], + "sum_omega_squared": 30.0, + "sum_omega_fourth": 88.32, + "zero_modes": 4, + "self_stress_states": 1, + "energy_hessian_discrepancy": 6.276847930308804e-10 + }, + { + "s": 0.75, + "t": 0.96, + "squared_frequencies": [ + -8.542717946718508e-16, + -6.897278598912165e-16, + -6.738864302054607e-16, + 1.0721073979034539e-15, + 0.7200000000000002, + 0.8837596876514139, + 0.9999999999999998, + 0.9999999999999998, + 1.0000000000000004, + 1.1035985285023362, + 1.2799999999999991, + 2.7614823982885746, + 2.999999999999999, + 3.0, + 3.0, + 3.0000000000000018, + 3.882229673902862, + 4.368929711654813 + ], + "sum_omega_squared": 29.999999999999993, + "sum_omega_fourth": 84.94079999999997, + "zero_modes": 4, + "self_stress_states": 1, + "energy_hessian_discrepancy": 4.66136018673069e-10 + }, + { + "s": 1.0, + "t": 1.0, + "squared_frequencies": [ + -4.861870655424675e-16, + 7.787282422000734e-16, + 9.135421199494564e-16, + 1.0359929580492692e-15, + 0.999999999999999, + 0.9999999999999997, + 0.9999999999999999, + 1.0000000000000002, + 1.0000000000000002, + 1.0000000000000007, + 1.000000000000001, + 2.9999999999999973, + 2.9999999999999982, + 2.999999999999999, + 3.0000000000000004, + 3.000000000000001, + 3.9999999999999973, + 3.999999999999999 + ], + "sum_omega_squared": 29.999999999999996, + "sum_omega_fourth": 83.99999999999999, + "zero_modes": 4, + "self_stress_states": 1, + "energy_hessian_discrepancy": 3.7923952866947275e-10 + } + ], + "limits": "Not a full Brillouin-zone stability study, material Hamiltonian, or proof of topological protection." + }, + "records": { + "channel_error_on_all_four_matrix_units": 2.220446049250313e-16, + "examples": { + "repeated_Z_records": [ + { + "environment_qubits": [ + 0 + ], + "Z_pointer_information_bits": 1.0, + "Z_distinguishability": 1.0, + "total_mutual_information_bits": 1.0 + }, + { + "environment_qubits": [ + 1 + ], + "Z_pointer_information_bits": 1.0, + "Z_distinguishability": 1.0, + "total_mutual_information_bits": 1.0 + }, + { + "environment_qubits": [ + 0, + 1 + ], + "Z_pointer_information_bits": 1.0, + "Z_distinguishability": 1.0, + "total_mutual_information_bits": 1.9999999999999998 + } + ], + "Bell_encoded_Z_records": [ + { + "environment_qubits": [ + 0 + ], + "Z_pointer_information_bits": 0.0, + "Z_distinguishability": 0.0, + "total_mutual_information_bits": 0.9999999999999998 + }, + { + "environment_qubits": [ + 1 + ], + "Z_pointer_information_bits": 0.0, + "Z_distinguishability": 0.0, + "total_mutual_information_bits": 0.9999999999999998 + }, + { + "environment_qubits": [ + 0, + 1 + ], + "Z_pointer_information_bits": 0.9999999999999997, + "Z_distinguishability": 0.9999999999999998, + "total_mutual_information_bits": 1.9999999999999996 + } + ] + }, + "limits": "Engineered three-qubit example, not a natural environment. The Bell construction has local records about a different system basis for the equal-amplitude input; the claimed absence concerns Z information." + }, + "inference": { + "known_design_noise_variance": 0.01, + "one_view_rank": 1, + "one_hundred_repeated_view_rank": 1, + "target_plus_reference_rank": 2, + "Fisher_eigenvalues_original_coordinates": [ + 38.19660112501051, + 261.8033988749895 + ], + "Fisher_eigenvalues_after_coordinate_rescaling": [ + 0.004999999987500001, + 2000000.005 + ], + "distinguishability_quadratic_form_both_coordinates": [ + 0.049999999999999996, + 0.05 + ], + "unknown_gain": { + "parameters_q_b_gain": [ + 0.8, + 0.3, + 1.7 + ], + "observations": [ + 1.87, + 0.51 + ], + "equivalent_rescaled_parameters": [ + 1.8399999999999999, + 0.69, + 0.7391304347826088 + ], + "unanchored_rank_out_of_three": 2, + "anchored_rank_out_of_three": 3 + }, + "shared_offset_information": [ + { + "readouts": 1, + "correct_information_about_q": 0.9900990099009901, + "information_if_offset_mistakenly_independent": 0.9900990099009901 + }, + { + "readouts": 10, + "correct_information_about_q": 0.999000999000999, + "information_if_offset_mistakenly_independent": 9.900990099009901 + }, + { + "readouts": 100, + "correct_information_about_q": 0.9999000099990001, + "information_if_offset_mistakenly_independent": 99.00990099009901 + }, + { + "readouts": 1000, + "correct_information_about_q": 0.999990000099999, + "information_if_offset_mistakenly_independent": 990.09900990099 + } + ], + "limits": "Linear known observation functions and specified noise. Rank is local in the gain model. Nonlinear global identifiability and blind source recovery are separate problems." + }, + "gravity": { + "Jeans_constant_sigma_spherical_relation": "Vc^2 = (gamma - 2 beta) sigma_r^2", + "conversion_examples_not_LOS_aperture_models": [ + { + "tracer_density_slope": 2, + "anisotropy_beta": 0, + "Vc_over_sigma_r": 1.4142135623730951 + }, + { + "tracer_density_slope": 3, + "anisotropy_beta": 0, + "Vc_over_sigma_r": 1.7320508075688772 + }, + { + "tracer_density_slope": 3, + "anisotropy_beta": 0.5, + "Vc_over_sigma_r": 1.4142135623730951 + } + ], + "cooling": { + "ne_cm_minus3": 0.0006991585597844737, + "temperature_K": 2314016.0960888085, + "sigma_kms": 178.4227839552902, + "coefficient_erg_cm3_s_minus1_K_minus_half": 1.7106680296277504e-27, + "density_sensitivity_Hubble_clock": "sigma_ff proportional to Delta H", + "density_sensitivity_freefall_clock": "sigma_ff proportional to sqrt(Delta) H", + "freefall_over_Hubble_at_Delta_1000": 0.04967294132898051 + }, + "redshift_sensitivity": [ + { + "z": 0.0, + "H_over_H0": 1.0, + "cooling_sigma_fixed_Delta_Hubble_clock_kms": 178.4227839552902, + "repository_sigma_star_kms_not_independently_recomputed": 185.59 + }, + { + "z": 0.5, + "H_over_H0": 1.3223307840253968, + "cooling_sigma_fixed_Delta_Hubble_clock_kms": 235.9339397955929, + "repository_sigma_star_kms_not_independently_recomputed": 114.36 + }, + { + "z": 1.0, + "H_over_H0": 1.7906083549181118, + "cooling_sigma_fixed_Delta_Hubble_clock_kms": 319.4853276580919, + "repository_sigma_star_kms_not_independently_recomputed": 69.92 + } + ], + "hydrostatic_crossing": [ + { + "sigma_h_over_sigma_star": 0.99, + "density_slope": 1.9602, + "inner_mass_fraction_x_0_05": 0.04438017501004581, + "separately_imposed_trapped_fraction": 0.0 + }, + { + "sigma_h_over_sigma_star": 1.0, + "density_slope": 2.0, + "inner_mass_fraction_x_0_05": 0.05, + "separately_imposed_trapped_fraction": 0.0 + }, + { + "sigma_h_over_sigma_star": 1.01, + "density_slope": 2.0402, + "inner_mass_fraction_x_0_05": 0.05639900084455497, + "separately_imposed_trapped_fraction": 0.019703950593079167 + } + ], + "repository_trajectory_source": { + "path": "inputs/wave10_covariant_jeans_certificates.json", + "sha256": "dd37a45adcb3c815d1a2d44bbbb58ac0235b9ea30d58d6b5a3438a46d91c874e" + }, + "limits": "Free-free ionized-gas approximation with fixed composition/Gaunt factor and specified density and clock. Redshift curves change physical environments, not errors on one object. The Jeans slope does not constitute a stability analysis." + }, + "aest_current": { + "points_tested": 16, + "maximum_absolute_component_error": 5.410445425013677e-10, + "current": "P^mu = 2(2-KB)J^mu - 2[(2-KB)+F_Y] q^(mu nu) d_nu(phi) - F_Q A^mu", + "conservation": "nabla_mu P^mu = 0 follows from shift symmetry for this action", + "limits": "Derivative check only. No entropy, heat trapping, energy flux, nonlinear fluid closure, or astrophysical parameter viability follows." + } +} diff --git a/research/convergences-20261112/probes/robustness/robustness_probes.py b/research/convergences-20261112/probes/robustness/robustness_probes.py new file mode 100644 index 0000000..64aa1df --- /dev/null +++ b/research/convergences-20261112/probes/robustness/robustness_probes.py @@ -0,0 +1,333 @@ +#!/usr/bin/env python3 +"""Independent robustness probes for the convergence expedition. + +Requires NumPy. Runs only mathematical examples and reads one repository JSON. +No source module is imported, no observational dataset is fitted, and writes +are confined to this directory. Use --check to compare without writing. +""" +from __future__ import annotations + +import argparse +import hashlib +import itertools +import json +import math +from pathlib import Path + +import numpy as np + +HERE = Path(__file__).resolve().parent +PROJECT = HERE.parents[1] + + +def mechanics(): + """Fixed-cell, Bloch k=0, unstressed central springs, k=m=1. + + Geometry is transcribed from the source proof, rather than imported from + the repetition probe. Bond directions, not just graph edges, enter C. + A direct finite-displacement spring energy independently checks C^T C. + """ + motif = np.vstack([sign * np.eye(3)[axis] + for axis in range(3) for sign in (1, -1)]) + shear = np.array([[0, -1, -1], [1, 0, -1], [1, -1, 0.]]) + interior = [(i, j, None) for i, j in itertools.combinations(range(6), 2) + if i // 2 != j // 2] + bonds = interior + [(2 * axis, 2 * axis + 1, axis) for axis in range(3)] + rng = np.random.default_rng(7913) + displacement = rng.normal(size=18) + displacement /= np.linalg.norm(displacement) + rows = [] + for s in (0., .25, .5, .75, 1.): + t = 2 * s / (1 + s*s) + a = math.sqrt(2) * (1 - s*s) / (1 + s*s) + cell = (2 + a) * np.eye(3) + t * shear + C, vectors = [], [] + for i, j, axis in bonds: + vector = motif[j] - motif[i] + if axis is not None: + vector = vector + cell[axis] + np.testing.assert_allclose(vector @ vector, 2, atol=1e-13) + direction = vector / math.sqrt(2) + row = np.zeros(18) + row[3*i:3*i+3] = -direction + row[3*j:3*j+3] = direction + C.append(row) + vectors.append(vector) + C = np.array(C) + D = C.T @ C + eigenvalues = np.linalg.eigvalsh(D) + singular = np.linalg.svd(C, compute_uv=False) + rank = int(np.count_nonzero(singular > 1e-10)) + # Analytic trace identity from bond-direction dot products. + np.testing.assert_allclose(np.trace(D), 30., atol=1e-12) + np.testing.assert_allclose(np.trace(D @ D), 96 - 12*t*t, atol=1e-12) + expected_nullity = 6 if s == 0 else 4 + assert 18 - rank == expected_nullity + assert (18-rank) - (15-rank) == 3 + # Independent directional Hessian from actual stretched lengths. + def energy(epsilon): + u = epsilon * displacement.reshape(6, 3) + return .5 * sum((np.linalg.norm(v + u[j] - u[i]) - math.sqrt(2))**2 + for (i, j, _), v in zip(bonds, vectors)) + epsilon = 1e-4 + from_energy = (energy(epsilon) + energy(-epsilon)) / epsilon**2 + from_matrix = float(displacement @ D @ displacement) + assert abs(from_energy-from_matrix) < 3e-8 + # Common rigid rotation about (-1,1,1) remains a null vector. + rotation = np.cross(np.array([-1., 1., 1.]), motif).ravel() + np.testing.assert_allclose(C @ rotation, 0, atol=1e-12) + rows.append({"s": s, "t": t, "squared_frequencies": eigenvalues.tolist(), + "sum_omega_squared": float(np.trace(D)), + "sum_omega_fourth": float(np.trace(D@D)), + "zero_modes": 18-rank, "self_stress_states": 15-rank, + "energy_hessian_discrepancy": abs(from_energy-from_matrix)}) + return {"scope": "Fixed-cell Bloch k=0 central-force model, equal unit masses and spring constants, no prestress; only original bars, including at the fcc endpoint.", + "bonds_per_cell": len(bonds), "physical_coordinates_per_cell": 18, + "analytic_sum_omega_fourth": "96 - 12 t^2", + "rows": rows, + "limits": "Not a full Brillouin-zone stability study, material Hamiltonian, or proof of topological protection."} + + +def trace_out(rho, keep, n): + tensor = rho.reshape([2] * (2*n)) + left = n + for axis in reversed(range(n)): + if axis not in keep: + tensor = np.trace(tensor, axis1=axis, axis2=axis+left) + left -= 1 + return tensor.reshape(2**len(keep), 2**len(keep)) + + +def entropy(rho): + eig = np.linalg.eigvalsh(rho) + assert eig.min() > -1e-12 + return -sum(float(v)*math.log2(float(v)) for v in eig if v > 1e-12) + + +def records(): + """The same dephasing channel and mutual information, different Z records. + + Branches |00>,|11> versus Bell+ and Bell-. An environment-only unitary + relates them, so the system's channel cannot distinguish their records. + The entangling unitary is a physical operation at fixed local access. + """ + env = np.eye(4, dtype=complex) + hadamard = np.array([[1, 1], [1, -1]]) / math.sqrt(2) + cnot = np.array([[1,0,0,0], [0,1,0,0], [0,0,0,1], [0,0,1,0]]) + unitary = cnot @ np.kron(hadamard, np.eye(2)) @ cnot + np.testing.assert_allclose(unitary.conj().T @ unitary, np.eye(4), atol=1e-14) + branch_pairs = {"repeated_Z_records": (env[:, 0], env[:, 3]), + "Bell_encoded_Z_records": (unitary @ env[:, 0], unitary @ env[:, 3])} + outputs = {} + max_channel_error = 0. + for name, pair in branch_pairs.items(): + isometry = np.column_stack([np.kron(np.eye(2)[:, i], pair[i]) for i in (0,1)]) + # Check the whole channel on an operator basis, including off-diagonals. + for i, j in itertools.product(range(2), repeat=2): + operator = np.zeros((2, 2), complex) + operator[i, j] = 1. + result = trace_out(isometry @ operator @ isometry.conj().T, [0], 3) + desired = operator if i == j else np.zeros((2, 2)) + max_channel_error = max(max_channel_error, float(np.max(abs(result-desired)))) + psi = isometry @ (np.ones(2)/math.sqrt(2)) + rho = np.outer(psi, psi.conj()) + rho_s = trace_out(rho, [0], 3) + fragments = [] + for keep in ([0], [1], [0,1]): + branch_rhos = [trace_out(np.outer(v, v.conj()), keep, 2) for v in pair] + average = (branch_rhos[0] + branch_rhos[1]) / 2 + chi = entropy(average) - sum(entropy(r) for r in branch_rhos)/2 + distance = np.sum(abs(np.linalg.eigvalsh(branch_rhos[0]-branch_rhos[1])))/2 + # Conditional states commute: Holevo information here is accessible. + np.testing.assert_allclose(branch_rhos[0]@branch_rhos[1], branch_rhos[1]@branch_rhos[0], atol=1e-14) + rho_sf = trace_out(rho, [0]+[i+1 for i in keep], 3) + mutual = entropy(rho_s) + entropy(average) - entropy(rho_sf) + fragments.append({"environment_qubits": keep, "Z_pointer_information_bits": chi, + "Z_distinguishability": float(distance), "total_mutual_information_bits": mutual}) + outputs[name] = fragments + assert max_channel_error < 1e-13 + for name, fragments in outputs.items(): + for row in fragments[:2]: + np.testing.assert_allclose(row["total_mutual_information_bits"], 1, atol=1e-12) + np.testing.assert_allclose(row["Z_pointer_information_bits"], 1 if name.startswith("repeated") else 0, atol=1e-12) + np.testing.assert_allclose(fragments[2]["Z_pointer_information_bits"], 1, atol=1e-12) + return {"channel_error_on_all_four_matrix_units": max_channel_error, + "examples": outputs, + "limits": "Engineered three-qubit example, not a natural environment. The Bell construction has local records about a different system basis for the equal-amplitude input; the claimed absence concerns Z information."} + + +def inference(): + """Known linear map: new views remove null directions, repeat views do not. + + This example has no priors and is not nonlinear ICA. Information metrics + transform with parameter coordinates; raw eigenvalues do not stay fixed. + """ + target = np.array([[1., 1.]]) + reference = np.array([[0., 1.]]) + sigma2 = .01 + joint = np.vstack([target, reference]) + F = joint.T @ joint / sigma2 + S = np.diag([100., .01]) + inv_S = np.linalg.inv(S) + transformed_F = inv_S.T @ F @ inv_S + delta = np.array([.01, -.02]) + transformed_delta = S @ delta + ds2 = float(delta @ F @ delta) + transformed_ds2 = float(transformed_delta @ transformed_F @ transformed_delta) + np.testing.assert_allclose(ds2, transformed_ds2, atol=1e-14) + q, b, gain = .8, .3, 1.7 + obs = np.array([gain*(q+b), gain*b]) + rescale = 2.3 + alternative = np.array([gain/rescale*(rescale*q+rescale*b), gain/rescale*(rescale*b)]) + np.testing.assert_allclose(obs, alternative, atol=1e-14) + jac = np.array([[gain, gain, q+b], [0., gain, b]]) + anchored = np.vstack([jac, [0., 0., 1.]]) + assert np.linalg.matrix_rank(jac) == 2 + assert np.linalg.matrix_rank(anchored) == 3 + # Gaussian known-design Fisher information with a shared random offset + # after marginalizing that offset has an exact saturation, independently + # of the separate linear-parameter rank argument above. + saturation = [] + for n in [1, 10, 100, 1000]: + saturation.append({"readouts": n, "correct_information_about_q": n/(sigma2+n), + "information_if_offset_mistakenly_independent": n/(sigma2+1)}) + return {"known_design_noise_variance": sigma2, + "one_view_rank": int(np.linalg.matrix_rank(target)), + "one_hundred_repeated_view_rank": int(np.linalg.matrix_rank(np.repeat(target, 100, axis=0))), + "target_plus_reference_rank": int(np.linalg.matrix_rank(joint)), + "Fisher_eigenvalues_original_coordinates": np.linalg.eigvalsh(F).tolist(), + "Fisher_eigenvalues_after_coordinate_rescaling": np.linalg.eigvalsh(transformed_F).tolist(), + "distinguishability_quadratic_form_both_coordinates": [ds2, transformed_ds2], + "unknown_gain": {"parameters_q_b_gain": [q,b,gain], "observations": obs.tolist(), + "equivalent_rescaled_parameters": [rescale*q,rescale*b,gain/rescale], + "unanchored_rank_out_of_three": 2, "anchored_rank_out_of_three": 3}, + "shared_offset_information": saturation, + "limits": "Linear known observation functions and specified noise. Rank is local in the gain model. Nonlinear global identifiability and blind source recovery are separate problems."} + + +def gravity(): + """Jeans and cooling sensitivity, independent analytic derivations. + + The Press-Schechter numbers below are *read* from the repository artifact, + not independently revalidated. No nonlinear stability result is inferred. + """ + G = 6.67430e-11 + hbar, me, mp = 1.054571817e-34, 9.1093837015e-31, 1.67262192369e-27 + kB, c, alpha = 1.380649e-23, 299792458., 1/137.035999084 + H0 = 67.36e3 / 3.085677581491367e22 + omega_m = (.02237+.1200+.00064)/.6736**2 + baryon_fraction = .02237/(.02237+.1200+.00064) + rho_critical = 3*H0**2/(8*math.pi*G) + emissivity = (16/3)*math.sqrt(2*math.pi/3)*1.2*alpha**3*(hbar/(me*c))**2*c*math.sqrt(me*c*c) + ne = baryon_fraction * 1000*rho_critical/(1.14*mp) + velocity = 1.15*emissivity*ne/(3*H0*math.sqrt(.60*mp))/1000 + temperature = .60*mp*(velocity*1000)**2/kB + path = PROJECT / "inputs/wave10_covariant_jeans_certificates.json" + payload = json.loads(path.read_text()) + trajectory = payload["claim_c26_dark_whim_nonlinear_collapse_scale"]["press_schechter_redshift_trajectory"] + redshifts = [] + for item in trajectory: + if item["z"] not in [0., .5, 1.]: + continue + Ez = math.sqrt(omega_m*(1+item["z"])**3+1-omega_m) + redshifts.append({"z": item["z"], "H_over_H0": Ez, + "cooling_sigma_fixed_Delta_Hubble_clock_kms": velocity*Ez, + "repository_sigma_star_kms_not_independently_recomputed": item["sigma_1D_star_kms"]}) + hydrostatic = [] + x = .05 + for ratio in [.99, 1., 1.01]: + gamma = 2*ratio**2 + integral = x**(3-gamma) + hydrostatic.append({"sigma_h_over_sigma_star": ratio, "density_slope": gamma, + "inner_mass_fraction_x_0_05": integral, + "separately_imposed_trapped_fraction": max(0., 1-1/ratio**2)}) + conversions = [] + for gamma, beta in [(2,0), (3,0), (3,.5)]: + conversions.append({"tracer_density_slope": gamma, "anisotropy_beta": beta, + "Vc_over_sigma_r": math.sqrt(gamma-2*beta)}) + assert 178.41 < velocity < 178.44 + assert hydrostatic[0]["inner_mass_fraction_x_0_05"] > 0 + return {"Jeans_constant_sigma_spherical_relation": "Vc^2 = (gamma - 2 beta) sigma_r^2", + "conversion_examples_not_LOS_aperture_models": conversions, + "cooling": {"ne_cm_minus3": ne/1e6, "temperature_K": temperature, + "sigma_kms": velocity, + "coefficient_erg_cm3_s_minus1_K_minus_half": emissivity*math.sqrt(kB)*1e13, + "density_sensitivity_Hubble_clock": "sigma_ff proportional to Delta H", + "density_sensitivity_freefall_clock": "sigma_ff proportional to sqrt(Delta) H", + "freefall_over_Hubble_at_Delta_1000": math.pi/(2*math.sqrt(1000))}, + "redshift_sensitivity": redshifts, + "hydrostatic_crossing": hydrostatic, + "repository_trajectory_source": {"path": "inputs/wave10_covariant_jeans_certificates.json", "sha256": hashlib.sha256(path.read_bytes()).hexdigest()}, + "limits": "Free-free ionized-gas approximation with fixed composition/Gaunt factor and specified density and clock. Redshift curves change physical environments, not errors on one object. The Jeans slope does not constitute a stability analysis."} + + +def aest_current(): + """Differentiate the scalar part of the published action independently. + + A generic polynomial F probes both Y and Q dependence, without claiming + this polynomial is a viable AeST model. Metric and aether are held fixed. + """ + rng = np.random.default_rng(1701) + metric = np.diag([-1., 1., 1., 1.]) + errors = [] + for _ in range(16): + velocity = rng.uniform(-.2, .2, 3) + aether = np.r_[1., velocity] / math.sqrt(1-velocity@velocity) + q = metric + np.outer(aether, aether) + spatial_acceleration = rng.normal(size=3) + acceleration = np.r_[velocity@spatial_acceleration, spatial_acceleration] + np.testing.assert_allclose(aether@metric@aether, -1., atol=1e-13) + np.testing.assert_allclose(aether@metric@acceleration, 0., atol=1e-13) + gradient = rng.normal(size=4) + KB = .8 + def lagrangian(k): + Y, Q = k@q@k, aether@k + F = .7*Y + .3*Q**2 + .2*Y*Q + .11*Y**2 + .05*Q**3 + return (2-KB)*(2*acceleration@k-Y)-F + Y, Q = gradient@q@gradient, aether@gradient + FY, FQ = .7+.2*Q+.22*Y, .6*Q+.2*Y+.15*Q**2 + analytic = 2*(2-KB)*acceleration - 2*(2-KB+FY)*(q@gradient) - FQ*aether + h = 1e-5 + numerical = np.array([(lagrangian(gradient+h*e)-lagrangian(gradient-h*e))/(2*h) for e in np.eye(4)]) + errors.append(float(np.max(abs(analytic-numerical)))) + assert max(errors) < 1e-7 + return {"points_tested": len(errors), "maximum_absolute_component_error": max(errors), + "current": "P^mu = 2(2-KB)J^mu - 2[(2-KB)+F_Y] q^(mu nu) d_nu(phi) - F_Q A^mu", + "conservation": "nabla_mu P^mu = 0 follows from shift symmetry for this action", + "limits": "Derivative check only. No entropy, heat trapping, energy flux, nonlinear fluid closure, or astrophysical parameter viability follows."} + + +def compare(a, b, path="result"): + if isinstance(a, dict): + assert a.keys() == b.keys(), path + for key in a: + compare(a[key], b[key], path+"."+key) + elif isinstance(a, list): + assert len(a) == len(b), path + for i, (x,y) in enumerate(zip(a,b)): + compare(x,y,path+f"[{i}]") + elif isinstance(a, float): + assert abs(a-b) <= 1e-9*max(1.,abs(a),abs(b)), (path,a,b) + else: + assert a == b, (path,a,b) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--check", action="store_true") + args = parser.parse_args() + result = {"status": "Independent mathematical probes; no observational discovery or validated dark-field mechanism.", + "mechanics": mechanics(), "records": records(), "inference": inference(), "gravity": gravity(), + "aest_current": aest_current()} + target = HERE / "results.json" + if args.check: + compare(result, json.loads(target.read_text())) + else: + target.write_text(json.dumps(result, indent=2)+"\n") + print(json.dumps({"checks": "passed", "output": str(target), "read_only_check": args.check, + "spring_fourth_frequency_moments": [r["sum_omega_fourth"] for r in result["mechanics"]["rows"]], + "gravity_redshift_sensitivity": result["gravity"]["redshift_sensitivity"]}, indent=2)) + + +if __name__ == "__main__": + main() diff --git a/research/convergences-20261112/probes/scales/README.md b/research/convergences-20261112/probes/scales/README.md new file mode 100644 index 0000000..099519e --- /dev/null +++ b/research/convergences-20261112/probes/scales/README.md @@ -0,0 +1,11 @@ +# Scales probe + +These calculations test scaling assumptions and sensitivity in ideal models. The collapse calculation reuses the pinned approximate gravity power spectrum in `../../inputs/`, rather than independently validating that approximation. + +Run from the repository root: + +```sh +python3 research/convergences-20261112/probes/scales/scale_probes.py +``` + +This rewrites `results.json` beside the script. Use the bundle command `python3 research/convergences-20261112/check.py` to regenerate in a temporary directory and verify all saved numerical results. diff --git a/research/convergences-20261112/probes/scales/results.json b/research/convergences-20261112/probes/scales/results.json new file mode 100644 index 0000000..ca3519f --- /dev/null +++ b/research/convergences-20261112/probes/scales/results.json @@ -0,0 +1,211 @@ +{ + "status": "reproducible model calculations; no new observational evidence", + "source_dependency": { + "path": "inputs/wave10_covariant_jeans_unification.py", + "sha256": "af8a2459aa8f5885250ab6b5914c50cc852bcc691982c8ef5cf692603bece927", + "limitations": "Reuses wave10 approximate EH no-wiggle power spectrum and fixed cosmology. Not an independent Boltzmann-code verification." + }, + "rate_responses": { + "KZ_nu": 0.6717, + "KZ_z_dynamic": 1.5, + "KZ_length_exponent": 0.3345869343229309, + "KZ_quench_100x_slower_length_factor": 4.668462435641381, + "viscosity_100x_at_fixed_epsilon_eta_factor": 31.622776601683793, + "sonic_Mach_10x_at_fixed_L_cs_p_half_length_factor": 0.01, + "pressure_100x_W_equal_1_length_factor": 0.31622776601683794, + "pressure_100x_fixed_time_visibility_length_factor": 0.1, + "assumptions": "KZ linear quench in scaling regime; Kolmogorov ordinary-fluid estimate; sonic p=1/2 illustrative; Gamma=Lambda*dx^2 with Lambda proportional to pressure and negligible other decoherence." + }, + "homogeneity_toy": { + "gamma": 1.8, + "tolerance_scan": [ + { + "fractional_tolerance": 0.1, + "rH_over_r0": 4.06812652484231 + }, + { + "fractional_tolerance": 0.01, + "rH_over_r0": 16.0281890316679 + }, + { + "fractional_tolerance": 0.001, + "rH_over_r0": 58.088837320328956 + } + ], + "bias_scan_at_1percent": [ + { + "bias": 1, + "rH_over_r0": 16.0281890316679 + }, + { + "bias": 1.5, + "rH_over_r0": 25.150198101934926 + }, + { + "bias": 2, + "rH_over_r0": 34.622803320919516 + } + ], + "interpretation": "Threshold and tracer change the reported scale in an unchanged smooth model. These are not revised WiggleZ measurements." + }, + "galaxy_convergence": { + "baseline_repository_four_scales": { + "empirical_wave9_group_onset_clean60_full126": [ + 180.0, + 190.0 + ], + "planck2018_press_schechter_Mstar_z0": 185.58809666617304, + "milgrom_btfr_Lstar_vflat": 175.82, + "bremsstrahlung_hubble_cooling_Delta1000": 178.42 + }, + "baseline_recomputed": { + "z": 0.0, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 1.0, + "Rstar_Mpc": 3.348258287597056, + "Mstar_Msun": 6240495103799.016, + "Vc_kms": 262.4612033203109, + "sigma1D_isothermal_kms": 185.58809666617304 + }, + "vflat_converted_with_same_isothermal_rule_kms": 124.32351426821877, + "conversion_note": "Conditional comparison only: galaxy Vflat, halo V200 and observed group line-of-sight dispersion do not have one universal conversion.", + "cooling_density_scan": [ + { + "Delta": 200, + "sigma_ff_kms": 35.684 + }, + { + "Delta": 500, + "sigma_ff_kms": 89.21 + }, + { + "Delta": 1000, + "sigma_ff_kms": 178.42 + }, + { + "Delta": 2500, + "sigma_ff_kms": 446.04999999999995 + } + ], + "cooling_time_scan_Delta1000": [ + { + "t_available_in_Hubble_times": 0.1, + "sigma_ff_kms": 17.842 + }, + { + "t_available_in_Hubble_times": 0.5, + "sigma_ff_kms": 89.21 + }, + { + "t_available_in_Hubble_times": 1, + "sigma_ff_kms": 178.42 + } + ], + "cooling_note": "Same free-free-only local formula. Delta variation changes the gas environment; time variation changes the physical criterion. Neither is a statistical error bar or same-halo convention conversion. Low-T endpoints may invalidate free-free-only cooling.", + "halo_convention_scan_fixed_Mstar": [ + { + "z": 0.0, + "halo_Delta_relative_to_critical": 100, + "sigma8_factor": 1.0, + "Rstar_Mpc": 3.348258287597056, + "Mstar_Msun": 6240495103799.016, + "Vc_kms": 233.82634959963596, + "sigma1D_isothermal_kms": 165.34019742199894 + }, + { + "z": 0.0, + "halo_Delta_relative_to_critical": 200, + "sigma8_factor": 1.0, + "Rstar_Mpc": 3.348258287597056, + "Mstar_Msun": 6240495103799.016, + "Vc_kms": 262.4612033203109, + "sigma1D_isothermal_kms": 185.58809666617304 + }, + { + "z": 0.0, + "halo_Delta_relative_to_critical": 500, + "sigma8_factor": 1.0, + "Rstar_Mpc": 3.348258287597056, + "Mstar_Msun": 6240495103799.016, + "Vc_kms": 305.7654779598322, + "sigma1D_isothermal_kms": 216.20884291814318 + }, + { + "z": 0.0, + "halo_Delta_relative_to_critical": 2500, + "sigma8_factor": 1.0, + "Rstar_Mpc": 3.348258287597056, + "Mstar_Msun": 6240495103799.016, + "Vc_kms": 399.8374335145938, + "sigma1D_isothermal_kms": 282.72776061039457 + } + ], + "amplitude_stress_test": [ + { + "z": 0.0, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 0.95, + "Rstar_Mpc": 3.009529252330152, + "Mstar_Msun": 4531666031266.755, + "Vc_kms": 235.90912084656523, + "sigma1D_isothermal_kms": 166.81293909436297 + }, + { + "z": 0.0, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 1, + "Rstar_Mpc": 3.348258287597056, + "Mstar_Msun": 6240495103799.016, + "Vc_kms": 262.4612033203109, + "sigma1D_isothermal_kms": 185.58809666617304 + }, + { + "z": 0.0, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 1.05, + "Rstar_Mpc": 3.6964597916926376, + "Mstar_Msun": 8396922578379.905, + "Vc_kms": 289.75580783197654, + "sigma1D_isothermal_kms": 204.88829660617674 + } + ], + "redshift_trajectory": [ + { + "z": 0, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 1.0, + "Rstar_Mpc": 3.348258287597056, + "Mstar_Msun": 6240495103799.016, + "Vc_kms": 262.4612033203109, + "sigma1D_isothermal_kms": 185.58809666617304 + }, + { + "z": 0.5, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 1.0, + "Rstar_Mpc": 1.8798156664459702, + "Mstar_Msun": 1104353173415.9067, + "Vc_kms": 161.736533519577, + "sigma1D_isothermal_kms": 114.36499961729822 + }, + { + "z": 1, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 1.0, + "Rstar_Mpc": 1.0387541635342963, + "Mstar_Msun": 186337610481.2747, + "Vc_kms": 98.87636139831538, + "sigma1D_isothermal_kms": 69.91614564380059 + }, + { + "z": 3, + "halo_Delta_relative_to_critical": 200.0, + "sigma8_factor": 1.0, + "Rstar_Mpc": 0.12353583996062095, + "Mstar_Msun": 313430392.70742536, + "Vc_kms": 16.066183501118733, + "sigma1D_isothermal_kms": 11.360507301428482 + } + ] + } +} diff --git a/research/convergences-20261112/probes/scales/scale_probes.py b/research/convergences-20261112/probes/scales/scale_probes.py new file mode 100644 index 0000000..32a4f95 --- /dev/null +++ b/research/convergences-20261112/probes/scales/scale_probes.py @@ -0,0 +1,121 @@ +#!/usr/bin/env python3 +"""Small scale-selection probes. Existing research repositories remain read-only. + +No observational fit. Rate and homogeneity examples are analytic toy calculations. +The gravity baseline reuses the repository's transfer-function approximation. +Run: python3 scale_probes.py +""" +from __future__ import annotations + +import hashlib +import importlib.util +import json +import math +from pathlib import Path +import sys + +sys.dont_write_bytecode = True +HERE = Path(__file__).resolve().parent +GRAVITY = HERE.parents[1] / "inputs" +sys.path.insert(0, str(GRAVITY)) +spec = importlib.util.spec_from_file_location("scale_probe_wave10", GRAVITY / "wave10_covariant_jeans_unification.py") +wave10 = importlib.util.module_from_spec(spec) +spec.loader.exec_module(wave10) + + +def collapse(sigma_r, growth, redshift=0.0, halo_delta=200.0, sigma8_factor=1.0): + """Same PS threshold, variable halo definition or spectrum amplitude. + + Changing halo_delta at fixed mass compares conventions, not an NFW + remeasurement of the same halo. sigma8 factors are stress tests, not posteriors. + """ + target = wave10.DELTA_C_SPH / growth(redshift) + lo, hi = 1.0e-4, 25.0 + for _ in range(60): + mid = math.sqrt(lo * hi) + if sigma_r(mid) * sigma8_factor > target: + lo = mid + else: + hi = mid + radius = (lo + hi) / 2 + mass = 4 * math.pi / 3 * (radius * wave10.MPC) ** 3 * wave10.OMEGA_M * wave10.RHO_CRIT0 + ez2 = wave10.OMEGA_M * (1 + redshift) ** 3 + wave10.OMEGA_L + halo_radius = (3 * mass / (4 * math.pi * halo_delta * wave10.RHO_CRIT0 * ez2)) ** (1 / 3) + circular = math.sqrt(wave10.G * mass / halo_radius) / 1000 + return {"z": redshift, "halo_Delta_relative_to_critical": halo_delta, + "sigma8_factor": sigma8_factor, "Rstar_Mpc": radius, + "Mstar_Msun": mass / wave10.M_SUN, "Vc_kms": circular, + "sigma1D_isothermal_kms": circular / math.sqrt(2)} + + +def homogeneity_scale(gamma, tolerance_fraction, bias=1.0): + """xi(r)=b^2 (r0/r)^gamma toy, D2=3 within fractional tolerance. + + N(