Test galactic acceleration evolution against published observations

.github/workflows/acceleration-evolution.yml

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+name: Acceleration evolution
+on:
+  pull_request:
+    paths:
+      - 'acceleration-evolution/**'
+      - '.github/workflows/acceleration-evolution.yml'
+  push:
+    branches: [main]
+    paths:
+      - 'acceleration-evolution/**'
+      - '.github/workflows/acceleration-evolution.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  numerical-checks:
+    runs-on: ubuntu-latest
+    timeout-minutes: 5
+    strategy:
+      matrix:
+        python: ['3.12', '3.14']
+    steps:
+      - uses: actions/checkout@v7
+      - uses: actions/setup-python@v7
+        with:
+          python-version: ${{ matrix.python }}
+      - name: Analytic and failure checks
+        run: python -B -m unittest discover -s acceleration-evolution -p 'test_*.py' -v
+      - name: Verify prediction artifact
+        run: python -B acceleration-evolution/model.py --output acceleration-evolution/results.json --check
+      - name: Verify source-bound comparison
+        run: python -B acceleration-evolution/compare.py --check

README.md

@@ -36,6 +36,8 @@ All Python scripts use only the Python 3 standard library. Each certificate file
 
 ## Documentation Index
 
+- [`acceleration-evolution/`](acceleration-evolution/README.md) -- Testable constant versus H-tracking acceleration scales, reproducible predictions, and a comparison with published MUSE-DARK fitted curves. No new raw-data fit or detection claim. Includes the known inverse of annihilation and requirements for a separate cosmological-collision conjecture.
+
 - `CLAIMS.md` -- Audited ledger of `C-01` through `C-27` with explicit inputs, literature precedence, Lean lemma scope, and downgraded epistemic status tags.
 - `METHODS_AND_PLAYBOOK.md` -- Numerical methods, parameter assumptions, error-model caveats (`M-01`..`M-08`), and canonical checksum table.
 - `RESEARCH_NOTEBOOK_AND_REASONING.md` -- Complete reasoning trail, rejected operator dead ends, tangential WHIM/entropy-floor realizations, and next-agent handoff queue.

acceleration-evolution/.gitignore

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+__pycache__/
+*.pyc

acceleration-evolution/INFERENCE.md

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+# A test that separates evolution from calibration
+
+This protocol is proposed. The raw-data fit has not been performed. Its purpose is to compare constant and H-tracking acceleration scales using the same data, nuisance parameters and selection model. See the [study](README.md) for the current published-summary result.
+
+## Required observations
+
+For every galaxy, retain a stable survey identifier, redshift, sample-membership decision and original selection cuts. For every accepted radial point, retain radius, observed velocity, baryonic components, errors and shared nuisance-parameter draws. Include inclination, distance, stellar mass-to-light ratio, gas normalization, beam smearing and pressure support.
+
+Prefer the velocity data cubes and their observational model when practical. A RAR extracted under a chosen halo profile is conditional on that profile. Refitting the extracted relation does not automatically provide a model-independent test of gravity. Retain alternate halo and MOND reconstructions as sensitivity analyses of the same sample.
+
+The MUSE release must identify the 79 selected galaxies, the r > 2 kpc cut, four bin definitions and original posterior samples or covariance. A table of marginal best fits is insufficient to restore correlations between radii or between the two acceleration axes. A global fit over a broad redshift range needs its actual galaxy redshifts, not an invented effective redshift.
+
+## A common likelihood
+
+For galaxy i and radius j, predict the total acceleration from the baryonic component and a₀(zi) = A E(zi)^q. In log space, model the measured acceleration vector around that prediction with intrinsic scatter and its full measurement covariance. Treat uncertain baryonic acceleration as a latent quantity, or propagate joint posterior draws through the observational model.
+
+Shared galaxy parameters must be sampled or marginalized together. Independent radial error bars are not a substitute. If the original posterior has already used the tested RAR as a prior, account for that prior explicitly or refit the original measurements to avoid circular inference.
+
+Compare q = 0 and q = 1 with identical positive-amplitude priors and nuisance terms. Then fit free q to test the fixed forms. Report likelihood or predictive scores only after validating the statistical model. A confidence or credible interval must be labelled with its definition. Do not change a 95% interval into a 1σ error merely because a plotting routine expects one.
+
+Two calibrations answer different questions:
+
+1. A floating A compares shapes. It does not test the absolute equality a₀(0) = cH₀/(2π).
+2. A local-anchor prior compares shape and normalization. Use the local calibration's systematic uncertainty and any covariance shared with the distant sample. A fixed canonical number with zero uncertainty is only a benchmark.
+
+The fiducial background is flat matter plus constant Λ. Propagate cosmological uncertainty and report alternate E(z) histories as named sensitivity analyses. An acceleration scale tied to a changing dark-energy component is a different hypothesis and needs its own equations. Equality to a Hubble-scale number at z = 0 does not identify which cosmic quantity is involved.
+
+## Controls before interpreting q
+
+- Refit with and without each galaxy. Resample galaxies, not individual radii, when using a bootstrap.
+- Match or model stellar mass, surface brightness, physical radial coverage, inclination and gas fraction across redshift. Redshift trends in sample composition can mimic a₀ evolution.
+- Repeat the fit under the documented alternate mass and kinematic models. Include common calibration shifts and redshift-dependent shifts separately.
+- Keep repeated analyses of MHUDF, KMOS and other parent surveys in the same dependence group. Cross-match identifiers before combining studies.
+- For a baryonic Tully–Fisher cross-check, use consistently defined total baryonic masses and asymptotic Vflat. A peak-velocity proxy needs a separately validated mapping, with its uncertainty propagated.
+- Recover injected q = 0 and q = 1 samples through the full observational and selection procedure. Quantify bias and interval coverage before interpreting real-data model selection.
+
+## Falsification and interpretation
+
+Before looking at the final fitted exponent, freeze the sample, likelihood, priors, covariance handling and sensitivity range in a versioned analysis record. Use a calibrated interval with a declared coverage level. A 95% interval excluding q = 1 is a conditional rejection of H tracking only if the recovery tests and specified systematic checks retain valid coverage.
+
+A disagreement that disappears after a plausible mass-calibration or selection correction does not robustly falsify the physical law. A constant scale rejected within one reconstruction is evidence against that constant reconstruction, without identifying the cause.
+
+An evolving baryon–halo relation can also produce an evolving empirical acceleration scale within ordinary gravity.
+
+Replication requires an independently selected galaxy sample or a justified independent observable. Reanalysing the same bins, or switching reconstruction methods for the same galaxies, tests robustness rather than replication.
+
+Agreement with q = 1 would support this parameterization over alternatives in its tested range. It would not establish a unique mechanism, a new fundamental theory, or a cosmic origin scenario.
+
+## Retrieval checkpoint
+
+The MUSE release index was accessible on 12 November 2026. Its linked data server timed out. The KMOS3D CDS table was also unavailable in bounded attempts. The indexed schema contains redshift, masses, peak circular speed and dispersion but no individual errors or covariance. The author HTML supplies only five example rows.
+
+The immediate next action is a read-only retry of the documented releases in [evidence.json](evidence.json), followed by a schema and sample-selection audit. If the required covariance or posterior products are absent, retain that limit. Author contact would be a separate action requiring authorization to send a message.

acceleration-evolution/README.md

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+# Does the galactic acceleration scale follow cosmic expansion?
+
+This study defines a testable evolution model and checks its predictions against published observational summaries. Existing MUSE-DARK work reports an increase in the radial acceleration relation's fitted scale. Whether that increase tracks the cosmic expansion rate remains unresolved by this audit.
+
+**Status: reproducible predictions and published-summary comparison. No new galaxy-data fit or discovery claim.** Prepared by gpt-forge with gpt-6.1-sol research assistance at A's request, 12 November 2026. Not reviewed by a person. Review evidence and next actions are in [STATUS.md](STATUS.md).
+
+## The model and what would distinguish it
+
+Let A be the present-day acceleration scale and q its evolution exponent:
+
+\[
+E(z)=H(z)/H_0=\sqrt{\Omega_m(1+z)^3+1-\Omega_m},\qquad a_0(z)=A E(z)^q.
+\]
+
+The benchmark uses A = 1.2 × 10⁻¹⁰ m s⁻² and Ωm = 0.315 in a flat matter-plus-constant-Λ background. Radiation is neglected. The code restricts z to 0–5. These background assumptions are inputs to the test, not consequences of the proposed acceleration law.
+
+| Model | q | Distinguishing behavior |
+| --- | --- | --- |
+| Constant scale | 0 | No evolution. Also describes a scale tied to a constant Λ after normalization |
+| Instantaneous H tracking | 1 | Scale grows in proportion to H(z) |
+| Free exponent | fitted in a future likelihood | Tests whether either fixed model describes the data |
+
+A must be treated identically when comparing q = 0 and q = 1. A fixed local calibration tests shape and normalization together. Allowing A to float tests the evolution shape. A numerical coincidence today, such as a₀ ≈ cH₀/(2π), does not choose between these models. The function computing cH/(2π) is kept separate from the calibrated A.
+
+For a forward prediction, the implementation uses the empirical RAR form of [McGaugh, Lelli and Schombert (2016)](https://arxiv.org/abs/1609.05917):
+
+\[
+g_{\rm tot}(g_{\rm bar},z)=\frac{g_{\rm bar}}{1-\exp[-\sqrt{g_{\rm bar}/a_0(z)}]}.
+\]
+
+It approaches Newtonian behavior at high acceleration and √(gbar a₀) at low acceleration. This is an empirical galaxy model. It supplies no covariant gravitational action, external-field treatment, cosmological perturbations, or derivation of the origin of inertia.
+
+For isolated galaxies in the asymptotic deep-MOND regime, Vflat⁴ = G Mbar a₀. The resulting slope-four baryonic Tully–Fisher relation predicts:
+
+\[
+\Delta\log_{10}M_{\rm bar}\big|_V=-q\log_{10}E(z),\qquad
+\Delta\log_{10}V\big|_{M_{\rm bar}}=\frac{q}{4}\log_{10}E(z).
+\]
+
+These translations require asymptotic flat velocities and consistently defined total baryonic mass. They cannot be applied unchanged to stellar-mass relations, peak velocities, or a different fitted slope.
+
+| Redshift | H tracking: a₀(z)/A | Predicted mass-intercept shift | Predicted velocity shift |
+| --- | --- | --- | --- |
+| 0.5 | 1.322 | −0.121 dex | +0.030 dex |
+| 1.0 | 1.790 | −0.253 dex | +0.063 dex |
+| 2.0 | 3.032 | −0.482 dex | +0.120 dex |
+| 3.0 | 4.566 | −0.660 dex | +0.165 dex |
+
+These are predictions, not measured evolution. The full grid is in [results.json](results.json).
+
+## Check against existing observations
+
+[Ciocan et al. (2026), MUSE-DARK III](https://arxiv.org/html/2604.22613v1), derive accelerations from modelled velocity components for 79 star-forming galaxies at 0.33 < z < 1.44. Their Eq. 4 gives a linear central curve, a₀(z) = (1.00 + 1.59z) × 10⁻¹⁰ m s⁻². Their alternative MOND reconstruction gives (1.03 + 1.20z) × 10⁻¹⁰ m s⁻² in Eq. 14.
+
+Evaluating those curves at the sample boundaries gives the following comparison. Boundary values are evaluations of fitted functions, not measurements of endpoint galaxies. Both reconstructions use the same underlying sample.
+
+| Description | a₀(1.44)/a₀(0.33) | Growth relative to H tracking |
+| --- | --- | --- |
+| Constant benchmark | 1.000 | 0.521 |
+| H-tracking benchmark | 1.921 | 1.000 |
+| Published DC14 reconstruction, Eq. 4 | 2.158 | 1.123 |
+| Published MOND reconstruction, Eq. 14 | 1.934 | 1.007 |
+
+The central trends favor an increasing scale over a flat curve descriptively. The model-dependent change between the two reconstructions is material to the comparison with H tracking. Neither agreement nor discrepancy in this table supplies a confidence level. [comparison.json](comparison.json) retains the calculations and their limits.
+
+![Predictions and published central curves. No fitted confidence bands](comparison.png)
+
+The left panel holds the benchmark's local normalization fixed. The right divides every curve by its value at z = 0.33 to compare shapes. The dotted continuation of a benchmark beyond the measured sample is a forecast. Published curves are drawn only inside the sample interval. No observational error band has been reconstructed.
+
+### Why this is not a new detection
+
+- The primary Eq. 2 and Eq. 4 errors are explicitly 95% intervals. They are preserved as reported. The Fig. 3 plotting convention needs verification before fitting its bins.
+- The Eq. 2 value, 2.38 × 10⁻¹⁰ m s⁻², describes a constant-RAR fit over the whole redshift sample. It is not a point measurement at z = 1.
+- Several radii within one galaxy share fitted parameters. The global fit, four bins and alternative reconstructions overlap. Combining them as independent evidence would count the same data repeatedly.
+- Both acceleration axes depend on disk and halo modelling. Redshift-dependent mass, gas, inclination, pressure-support and selection errors can resemble evolution.
+- A numeric joint covariance, the selected radial data and their modelling posteriors were not recovered. The advertised MUSE release server timed out during this session.
+
+[Alcock (September 2026)](https://arxiv.org/abs/2609.38796) already compares the same binned MUSE measurements with H tracking. This study therefore contributes reproducibility and an uncertainty audit, not the first proposal of that connection. Its abstract treats plotted errors as 1σ. We do not reuse its significance estimates without resolving the plotting convention and reconstructing the likelihood.
+
+Other observations are retained as context. [Übler et al. (2017)](https://arxiv.org/abs/1703.04321) report baryonic Tully–Fisher intercepts for 135 KMOS3D galaxies using slope 3.75, maximum pressure-corrected circular velocities and estimated molecular gas. [Puech et al. (2010)](https://arxiv.org/abs/0903.3961) use six distant rotating disks, with substantial gas and calibration uncertainties.
+
+Neither summary is inserted as a slope-four, asymptotic-velocity a₀ measurement. The accessible Übler HTML has five example catalogue rows followed by ellipses. The full machine-readable table was not retrieved, and its documented schema lacks individual measurement errors. [evidence.json](evidence.json) records values, definitions, overlap, source locations and retrieval limits.
+
+## What would test or falsify the model
+
+The [inference protocol](INFERENCE.md) defines the input requirements and a fair comparison of q = 0, q = 1 and free q. It keeps calibration and galaxy selection visible, uses galaxy-level covariance, and requires independent data before treating the trend as replicated. A robust exclusion of q = 1 would falsify this H-tracking parameterization under its stated background and galaxy assumptions.
+
+The next executable step is to recover the selected MUSE radial data and modelling posteriors, then fit A, q and intrinsic scatter using the same likelihood for each model. The published summaries support this investigation but do not replace that step. No new significance or fitted q is reported here.
+
+## The annihilation idea
+
+The reverse process, photon conversion into particle–antiparticle pairs, is known physics. [Annihilation and relics](annihilation-and-relics.md) connects it to early-universe balance and possible dark relics. It also states what a collision of universe-scale objects would have to predict. No collision model is solved, and no relation between that idea and a₀(z) has been derived.
+
+## Reproduce
+
+From the repository root, Python 3.11 or later is sufficient for all numerical checks:
+
+```sh
+python3 -B -m unittest discover -s acceleration-evolution -p 'test_*.py' -v
+python3 acceleration-evolution/model.py --output acceleration-evolution/results.json --check
+python3 acceleration-evolution/compare.py --check
+```
+
+Omit `--check` to regenerate a numerical artifact. Checks are read-only and reject missing or stale artifacts. They require the same schema and scalar types, allowing relative floating-point differences up to 10⁻¹² for platform rounding. The comparison embeds the SHA-256 digest of the source transcription.
+
+Tests check analytic limits, signs, units, numerical stability, source changes and stale-output rejection. They validate the calculation, not the physical hypothesis. The [validation record](VALIDATION.md) also records an unrelated failure in an unchanged baseline certificate.
+
+The optional figure uses `plot.py` and the pinned `plot-requirements.txt`. Numerical verification has no third-party dependency. All figures are generated from model predictions and the explicitly labelled published central curves.
+
+## Connections across Foundation0
+
+- [fractals](https://github.com/Foundation-0/fractals): distinguish measured scaling from visual resemblance, and state the scales and epochs over which a relation holds.
+- [physics0](https://github.com/Foundation-0/physics0): preserve model assumptions, known mechanisms, conjectures and falsification conditions.
+- [astr0](https://github.com/Foundation-0/astr0): identify observations, selection, calibration and covariance needed to adjudicate the models.
+
+This directory owns the equations, evidence transcription and generated results. The companion repositories link to it rather than copying a numerical implementation.