From e5d7ee813e33de03c91857e48a2d55a0caf55506 Mon Sep 17 00:00:00 2001 From: ahrazzle <38987266+ahrazzle@users.noreply.github.com> Date: Thu, 12 Nov 2026 17:35:01 -0600 Subject: [PATCH 1/2] Correct Wave 11 and 12 numerical benchmarks and physical claims --- CHANGELOG.md | 7 + CLAIMS.md | 31 +++-- README.md | 4 +- RESEARCH_NOTEBOOK_AND_REASONING.md | 33 +++-- SHA256SUMS | 14 +- WAVE11_12_CORRECTIONS.md | 57 ++++++++ .../wave11_machian_pairing_certificates.json | 26 +++- ...ave12_cosmic_dawn_quasar_certificates.json | 50 +++++-- test_wave11_12_corrections.py | 54 ++++++++ wave11_machian_pairing_unification.py | 46 +++++-- wave12_cosmic_dawn_quasar_collapse.py | 130 +++++++++++++++--- 11 files changed, 371 insertions(+), 81 deletions(-) create mode 100644 WAVE11_12_CORRECTIONS.md create mode 100644 test_wave11_12_corrections.py diff --git a/CHANGELOG.md b/CHANGELOG.md index e64ae13..f58316e 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -2,6 +2,13 @@ > **Attribution:** Maintained by AI agent (Gemini, Google, via `orda-aska` for `Foundation-0`); not yet reviewed by a person. Claim identifiers (`C-01`..`C-27`) reconciled in Wave 8 to match `CLAIMS.md` and generator scripts verbatim. +## 2026-11-12: Wave 11 and Wave 12 audit corrections + +- Replaced the outer-acceleration infall shortcut with energy-conserving radial quadrature and analytic controls. Corrected times are `200.08`, `121.72` and `127.16 Myr`, rather than `182.27`, `109.04` and `122.79 Myr`. +- Added opacity and fixed Schwarzschild-efficiency growth counterexamples. Corrected slim-disk retained mass to subtract radiated energy in the stated inflow convention. +- Restored present density closure in curved CPL examples. Corrected the Urueña Palomo citation and removed unsupported origin, protected-remnant, seed and gravitational-wave background inferences. +- Regenerated only Wave 11 and Wave 12 certificates as schema 1.1. [Correction details](WAVE11_12_CORRECTIONS.md) document changed fields, limits and seven numerical controls. The earlier independent findings are public in [PR #11](https://github.com/Foundation-0/gravity/pull/11). Human scientific review remains pending. + ## Wave 10 -- 2026-11-12: Linear Sound-Speed No-Go, Dark-WHIM Nonlinear Collapse Scale & Reasoning Ledger (`C-25`..`C-27`; `M-08`) - Added `wave10_covariant_jeans_unification.py`, `results/wave10_covariant_jeans_certificates.json` (`sha256_canonical = 7dd4b40172b8fe261c3028f7a6af6e2b5131fb93cd83d10c439e3c5f0c5be3d4`), `formal/Wave10JeansDerivation.lean`, and `RESEARCH_NOTEBOOK_AND_REASONING.md`. - Proved the homogeneous linear FLRW sound-speed no-go (`C-25`): `c_s(z=0) = 185 km/s` on linear scales gives `lambda_J,com = 25.10 Mpc`, `z = 1100` matter density exceeds `200 * rho_crit0` halos by `2.103e6x` (ruling out monotone `P(rho)` polytropes), and constant-`M` `k^4` scordatura shrinks `k_J,com` by `0.1736x` at `z = 1100`. diff --git a/CLAIMS.md b/CLAIMS.md index a1d6648..e602c61 100644 --- a/CLAIMS.md +++ b/CLAIMS.md @@ -142,26 +142,41 @@ Every claim separates its **physical status** from any **arithmetic lemma**: ## Wave 11: Machian Horizon Inertia, DESI Turnaround & CPT Pair-Condensate Audit (`wave11_machian_pairing_unification.py`) - **C-28 (Machian Horizon Frame-Dragging Induction vs. Relativistic Lensing & Non-Locality)** -- `COMPUTED (KNOWN-FRAMEWORK) / CONJECTURE` -- *Computation & Literature:* Evaluates Sciama's (1953, MNRAS 113, 34) Hubble-sphere compactness `G M_H / (R_H c^2) = 1/2`, potential integral `(G/c^2) int_{r 0` (`w_dust ~ 5e-7 -> 0`, scaling as `a^-3`) on **both** sheets! Contrasts collisionless `5.03 GeV` asymmetric-DM particles (`sigma_J = 0`, which fail galactic RAR) against storing the cogenesis/axiogenesis remnant (Co & Harigaya 2020, PRL 124, 111602, arXiv:1910.02080) in the coherent `P(Q, Y)` condensate (which preserves `99.99999994%` visible pair annihilation `1 - eta_B` while preventing dark self-annihilation via shift symmetry `phi -> phi + const`). *Conjecture scope:* Cosmological `t = 0` CPT sheet bifurcation and pre-electroweak portal coupling setting `Omega_c / Omega_b = 5.3895` are unproven `CONJECTURES`. + - *Computation & Literature:* Evaluates the chosen polynomial `P(u) = K_2 (u^2 - 1)^2 - Lambda_DE`. Algebraically, the states `u = +/- (1 + eps)` have opposite shift charges and equal positive dust densities. This does not derive their production from `u = 0`. + + The minimal homogeneous scalar sector has `P_QQ(0) = -4 K_2 / Q_0^2`, and a source-free homogeneous solution conserves `a^3 P_Q`. Starting with zero current cannot produce nonzero branch charge without an additional source, boundary condition or production prescription. + - *Limits:* Full AeST mixing stability is not solved. Constant shift symmetry allows derivative portals such as `(partial_phi)^2 F_mu_nu F^mu_nu`, so it does not forbid all pair conversion. `eta_B` is a baryon-to-photon ratio, not the fraction of initial pairs annihilated. No portal rate, origin mechanism or relic abundance is established. + + Scherrer (2004), Boyle, Finn and Turok (2018) and Co and Harigaya (2020) provide prior frameworks, not proofs of this transition. - *Lean Arithmetic Lemma (`PROVEN (ARITHMETIC-LEMMA)` in `formal/Wave11MachianZeroEnergy.lean`):* Proves over `Int` for all `u, q0` that `noetherJ (-u) q0 + noetherJ u q0 = 0`, `legendreRho (-u) q0 = legendreRho u q0`, and `0 <= q0Sq < uSq -> 0 < (uSq - q0Sq)*(3*uSq + q0Sq)`. ## Wave 12: Cosmic-Dawn Compact Quasar Pair `J1602+4228AB` (`Napowawa'enakaulua`) Audit (`wave12_cosmic_dawn_quasar_collapse.py`) - **C-31 (Cosmic-Dawn Dual-Quasar Salpeter Duty-Cycle Wall & Clustering Excess)** -- `COMPUTED (KNOWN-FRAMEWORK)` - - *Computation & Observed Inputs:* Evaluates Onorato et al. (2026, ApJL 1011, L59, arXiv:2609.31835; NOIRLab `noirlab2627`) for `J1602+4228AB` (`z_sys = 6.0781` & `6.0785`, Planck-2018 cosmic age `911.72 Myr`, `0.98"` = `5.56 pkpc` separation, `Delta v = 15 km/s`, `M_BH = 1.5e9` & `4.0e8 M_sun`, `lambda_Edd = 1.23` & `1.07`, `10^2-10^3x` clustering excess in 199 JWST/NIRSpec IFU Aether fields). From `z_seed = 20` (`Delta t = 734.10 Myr`), a `100 M_sun` Pop III seed at `lambda_Edd = 1.0`, `eps_r = 0.10` (`t_Sal = 50.05 Myr` pure H; `43.92 Myr` primordial H+He) needs `827.08 Myr` (`f_duty = 1.127 > 1`) for `J1602A` and `f_duty = 1.037 > 1` for `J1602B` (`f_duty = 2.535` for spinning Kerr `eps_r = 0.20`), whereas `10^5 M_sun` direct-collapse seeds require `f_duty = 0.533` (`A` at `lambda_Edd = 1.23`) and `0.529` (`B` at `lambda_Edd = 1.07`). *Explicit caveats:* Single-epoch virial masses have `~2x` systematic uncertainty, and an archival HST foreground galaxy near `B` requires a pending lens model to definitively exclude gravitational lensing. + - *Computation & Observed Inputs:* Uses the reported `J1602+4228AB` point values from Onorato et al. (2026), arXiv:2609.31835. The `z = 20` growth budget is `734.10 Myr`. A `100 M_sun` seed growing to `1.5e9 M_sun` at fixed Eddington ratio one and efficiency `0.10` needs `827.08 Myr` for pure H, but `725.76 Myr` for primordial H/He. + + Efficiency `0.10` is not the Schwarzschild thin-disk value. At fixed `1 - sqrt(8/9)`, the respective times are `451.54` and `396.22 Myr`. These are conditional growth clocks, not an exclusion of all light seeds or evidence that any history occurred. + - *Limits:* Formation delays, spin evolution, fuel supply and duty histories are omitted. Current luminosity is not a lifetime average. Virial masses, Eddington ratios and systemic velocities are uncertain. Lensing remains unresolved. Clustering excess over an extrapolated baseline does not by itself compare cosmological likelihoods. - *Lean Arithmetic Lemma (`PROVEN (ARITHMETIC-LEMMA)` in `formal/Wave12QuasarCollapse.lean`):* Checks `(1 * 4) * 9 = 9 * 4` and `2 * 4 < 9` (`eps/(1-eps)` jumps by `9/4 > 2` from `eps = 0.1` to `0.2`). - **C-32 (Cosmic-Dawn Dark-WHIM Trapping Inversion `sigma_*(z=6.08) = 0.97 km/s` & Phonon Free-Fall Speedup)** -- `COMPUTED (MODEL-COMPARISON) & CONJECTURE` - - *Computation & Literature:* Extends the zero-free-parameter Wave-10 Planck-2018 Press-Schechter nonlinear collapse calculation (`C-26`) to `z = 6.0783`: `R_*(6.08) = 7.96 comoving kpc`, `M_*(6.08) = 8.39e4 M_sun`, and **`sigma_*(6.08) = 0.97 km/s`**. Consequently, a `V_vir = 250 km/s` (`sigma_halo = 176.8 km/s`) galaxy halo that expels `100%` of condensate dust at `z = 0` (`sigma_*(0) = 185.59 km/s`, `f_trap(0) = 0.0`) traps **`99.997%` (`f_trap(6.08) = 0.99997`)** of its `5.39 M_b` condensate dust at `z = 6.08`! On `30 pkpc` feeder-filament scales (`M_b = 5e10 M_sun`, `g_b = 7.74e-12 m/s^2`), pure Newtonian baryonic free-fall takes `384.82 Myr` (while `10^12-5e12 M_sun` LCDM halos are rare `4.23-5.38 sigma` peaks), whereas MOND phonon acceleration + trapped condensate cuts free-fall to `122.79 Myr` (constant `a_0`) or `109.04 Myr` (Hubble-scaled `a_0(z) = c H(z)/(2*pi) = 1.11e-9 m/s^2`; cf. McGaugh et al. 2024, ApJ, arXiv:2406.17930) while avoiding pure-MOND's merger dynamical-friction deficit (Nipoti et al. 2008). *Conjecture scope:* Nonlinear 3+1D AeST DCBH seeding and merger hydrodynamics at `z = 6.08` remain `CONJECTURES`. + - *Computation & Inputs:* The chosen spectrum and growth approximation give `M_* = 8.39e4 M_sun` and `sigma_* = 0.97 km/s` at `z = 6.0783`. This is total nonlinear halo mass, not a black-hole seed. The value `f_trap = 0.99997` is an assigned trapping prescription, not a capture solution. + - *Corrected radial benchmark:* For release from rest at `30 pkpc` around a fixed `5e10 M_sun` baryonic point mass, energy-conserving integration gives `384.82 Myr` for Newtonian baryons, `200.08 Myr` for constant-a0 RAR, `121.72 Myr` for Hubble-a0 RAR and `127.16 Myr` for constant-a0 RAR plus the assigned condensate force. + + Earlier `182.27`, `109.04` and `122.79 Myr` values substituted the outer acceleration into a Newtonian formula and are superseded. No filament pressure, geometry, angular momentum, cooling or friction is solved. - *Lean Arithmetic Lemma (`PROVEN (ARITHMETIC-LEMMA)` in `formal/Wave12QuasarCollapse.lean`):* Checks `2^2 < 177^2 < 185^2` and `9998 * 177^2 < 10000 * (177^2 - 2^2)`. - **C-33 (Slim-Disk Photon-Trapping Super-Eddington Growth, `5.56 pkpc` Orbital Projection & NANOGrav Chirp Mass)** -- `COMPUTED (KNOWN-FRAMEWORK)` - - *Computation & Inputs:* Evaluates Abramowicz et al. (1988) / Watarai et al. (2000) slim-disk photon trapping (`lambda_Edd^obs ~ 2(1 + ln(mdot/2))` for `mdot >= 2`), showing supercritical mass inflow `mdot = 3-5` cuts `100 M_sun -> 1.5e9 M_sun` growth time to `165.4-275.7 Myr` without violating GR or radiation physics. At `r_sep = 5.56 pkpc` (`V_circ = 342.8 km/s` for `1.5e11 M_sun` enclosed host mass), `Delta v_los = 15 km/s` requires projection `|sin i cos psi| = 0.0438`. Pure Peters (1964) GW inspiral at `5.56 pkpc` is negligible (`4.87e20 Myr`), whereas once dynamical friction hardens the `M_c = 6.4735e8 M_sun` pair to `0.05-0.10 pc`, GW inspiral merges it in `3.19-50.99 Myr`, feeding the NANOGrav nHz gravitational-wave background. - - *Lean Arithmetic Lemma (`PROVEN (ARITHMETIC-LEMMA)` in `formal/Wave12QuasarCollapse.lean`):* Checks `100 < 123`, `100 < 107`, and `19 * 647^5 < 15^3 * 4^2 * 10^10 < 19 * 648^5`. + - *Computation & Inputs:* With `mdot = 0.10 dotM_in c^2 / L_Edd`, the assigned luminosity is `lambda = mdot` below two and `2(1 + ln(mdot/2))` above. Mass conservation gives retained growth proportional to `mdot - 0.10 lambda`, not `0.90 mdot` above saturation. With no outflows and constant coefficients, `mdot = 3, 5` gives `273.78, 161.23 Myr` for a `100 M_sun` seed to reach `1.5e9 M_sun`. + - *Binary limits:* The projection `0.0438` uses a point velocity and assumed enclosed mass, not a measured inclination. The chirp mass is `6.4735e8 M_sun`. Circular isolated Peters clocks at `0.05-0.10 pc` are `3.19-50.99 Myr`. Reaching those separations and predicting a stochastic background require hardening and population models that are absent. + - *Lean Arithmetic Lemma (`PROVEN (ARITHMETIC-LEMMA)` in `formal/Wave12QuasarCollapse.lean`):* Checks `100 < 123`, `100 < 107`, and contains the false bound `19 * 647^5 < 15^3 * 4^2 * 10^10 < 19 * 648^5`. The chirp-mass proof repair is tracked separately in [PR #10](https://github.com/Foundation-0/gravity/pull/10). This correction does not change Lean files. diff --git a/README.md b/README.md index 68671a1..ddb6d6f 100644 --- a/README.md +++ b/README.md @@ -13,8 +13,8 @@ This repository is **not** a derivation of a new fundamental theory of gravity, - **Wave 7 (`wave7_group_cluster_threshold_audit.py`)**: Fits a 3-parameter Hill-type saturation curve `(sigma_crit, sigma_half, R_sat)` across 126 published galaxy halos, groups, and clusters (SPARC, Mistele et al. 2024, Milgrom 2019, Angus et al. 2008, Kettula et al. 2015) describing the well-known MOND cluster missing-mass discrepancy. - **Wave 9 (`wave9_scale_convergence_audit.py`)**: Evaluates the `g_b,x = 0.029 a_0` crossover between `d_s = 1` phonon acceleration and a Planck-normalized (`Omega_c/Omega_b = 5.39`) cosmological dust branch (`C-23a`), zero-free-parameter apparent `g_ddag` scale shifts across CLASH vs. X-COP clusters (`C-23b`), a 1-parameter Jeans-trapping fit (`sigma_J = 180-190 km/s`) using Vikhlinin et al. (2006) `R_2500` baryon depletion (`C-23c`), and quasistatic AeST `r_C^(max)` oscillation bounds (`C-24`). - **Wave 10 (`wave10_covariant_jeans_unification.py`)**: Proves why homogeneous linear FLRW sound speeds fail (`lambda_J,com = 25.10 Mpc` and `2.10e6x` recombination density inversion; `C-25`), computes the zero-free-parameter Planck-2018 Press-Schechter nonlinear collapse dispersion `sigma_*(z=0) = 185.59 km/s` (`sigma_*(z=3) = 11.36 km/s`) achieving `chi^2/dof = 1.004` (`Delta BIC = -10.01` vs. Wave 7 at `k = 0` fitted parameters; `C-26`), and formulates high-`z` Euclid/LSST group-lensing tests (`C-27`). - - **Wave 11 (`wave11_machian_pairing_unification.py`)**: Evaluates Machian Hubble-horizon inertial induction vs. PPN lensing (`C-28`), ADM zero-energy balance and DESI thawing dark-energy deceleration (`a_slow = 1.3897`) / closed-`S^3` turnaround (`C-29`), and CPT-symmetric Mexican-hat pair bifurcation (`J^0_+ + J^0_- = 0` with `rho_dust > 0` on both sheets) alongside shift-symmetric condensate cogenesis (`C-30`). - - **Wave 12 (`wave12_cosmic_dawn_quasar_collapse.py`)**: Audits the newly discovered `z = 6.08` compact quasar pair `J1602+4228AB` (*Napowawa'enakaulua*, Onorato et al. 2026, ApJL 1011, L59, arXiv:2609.31835; NOIRLab `noirlab2627`): evaluates the dual Pop III vs. DCBH Salpeter duty-cycle wall (`C-31`), proves that Wave-10's Dark-WHIM scale drops to `sigma_*(z=6.08) = 0.97 km/s` (`f_trap = 0.99997` vs. `0.0` at `z = 0`) while phonon + trapped-condensate gravity cuts `30 pkpc` feeder free-fall from `384.8 Myr` to `109-123 Myr` (`C-32`), and evaluates slim-disk photon-trapping super-Eddington growth alongside `5.56 pkpc` orbital projection and NANOGrav chirp-mass (`6.47e8 M_sun`) inspiral timescales (`C-33`). + - **Wave 11 (`wave11_machian_pairing_unification.py`)**: Computes conditional induction algebra, curvature-normalized CPL expansion and opposite-charge polynomial branches. It does not establish inertia, a universe origin, protected dark matter or future recollapse as an observational prediction. + - **Wave 12 (`wave12_cosmic_dawn_quasar_collapse.py`)**: Computes conditional growth clocks, a chosen nonlinear halo scale and fixed point-mass radial infall (`200.08`, `121.72`, `127.16 Myr` for the three modified force benchmarks). Its slim-disk table conserves inflowing mass and radiated energy. No seed-formation, filament evolution, merger hardening or GW background model is supplied. 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. diff --git a/RESEARCH_NOTEBOOK_AND_REASONING.md b/RESEARCH_NOTEBOOK_AND_REASONING.md index 7e55650..64d46d6 100644 --- a/RESEARCH_NOTEBOOK_AND_REASONING.md +++ b/RESEARCH_NOTEBOOK_AND_REASONING.md @@ -53,17 +53,22 @@ Instead of inventing a new microphysical mass parameter, we asked how **continuo 1. **1D/3D Nonlinear AeST Zeldovich Pancake PDE Simulation (Theoretical Priority #1)**: Simulate single-field / AeST spherical & 1D pancake collapse through shell-crossing using the Hamiltonian formulation of Bataki, Skordis & Zlosnik (2024, arXiv:2307.15126) to test directly whether dispersive shock regularization produces coarse-grained Eulerian entropy conservation (`CONJECTURE` in `C-26`) rather than Vlasov-like soliton pass-through. 2. **Euclid / KiDS-1000 Void vs. Filament & High-`z` Group Lensing Split (Observational Priority #1)**: Test the sharp discriminating forecast in `C-27` -- dynamic Dark-WHIM shock heating predicts `f_trap` in `sigma = 200 km/s` groups rises from `0.139` at `z = 0` to `0.673` at `z = 0.5` and `0.878` at `z = 1.0` (and predicts cooler outer envelopes around ultra-isolated galaxies deep inside `R > 10 Mpc` cosmic voids), whereas a constant Lagrangian parameter `Q_0^(-1) = 30.052 Mpc` in `X = Q^2 - Y` predicts redshift- and environment-invariant `f_trap = 0.139`. 3. **Singular-Source Coincidence Investigation (`C-27`)**: Investigate why four distinct combinations of fundamental parameters -- `(A_s, n_s, z_eq)` giving `sigma_*(0) = 185.59 km/s`, `(G, M_b*, c H_0)` giving `V_flat(L*) = 175.82 km/s`, and `(alpha_EM^3, m_e, m_p, G, H_0)` giving `sigma_ff(Delta=1000) = 178.42 km/s` -- intersect specifically at the Dark-Energy crossover epoch `Omega_Lambda ~ Omega_m`. -## 4. Wave 11: Translating Foundational Intuitions (Inertia-Gravity Unity, Zero-Sum Creation, Supernova Core-Envelope & Cosmological Pair Production) into Testable Equations (`C-28`..`C-30`) - -In Wave 11 we audited four foundational physical hypotheses seeded from collaborator notes (`Issue #3` + the cosmological pair-production / inverted-annihilation extension): - -1. **Inertia as Horizon Gravitational Counter-Reaction (`C-28`)**: - - *What holds mathematically:* In Hubble-sphere gravitoelectromagnetism (Sciama 1953; Braun 2026, arXiv:2610.09987), gravitomagnetic frame-dragging (`K_gm = 2/3`) plus gravitoelectric horizon shift (`K_ge = 1/3`) sum to `K_tot = 1` (`F_inertial = -m a`), so removing cosmic gravity/mass sends inertial resistance to zero ("infinite and endless motion"). When proper acceleration drops below `c H_0`, the Rindler horizon `c^2/a` exceeds the Hubble sphere `c/H_0` (cf. Milgrom 1999 Unruh-de Sitter bath, arXiv:astro-ph/9805346). - - *Audit trap avoided:* Pure vector Sciama models give PPN `gamma = 0` (failing solar/cluster light bending by `2x`), and naive time-local `F = m mu(a/a_0) a` violates multi-body momentum conservation. Embedding the horizon scale inside a relativistic metric + unit-aether-scalar action (AeST, `Phi = Psi`, `gamma = 1`) preserves lensing while predicting distinct `a_0(z)` evolution tracks (`H(z)` vs. `sqrt(rho_DE(z))`, directly testable in PR #4). -2. **Gravity as the Zero-Sum Counter-Ledger & Supernova-Like Cosmic Turnaround (`C-29`)**: - - *Zero-sum creation:* Time-reparametrization invariance in ADM GR and 3+1D AeST (Bataki et al. 2024, Eq. 43a) enforces `H_grav + H_matter = 0` identically (`-E_grav` cancels `+E_matter`). - - *Core coagulation vs. slowing outer spacetime cloud:* Because self-gravity has negative heat capacity, every zero-energy virial system bifurcates into a dense entropy-shedding core and an expanding outer envelope (supernova core + ejecta; radiative baryonic galaxy disk + `185.59 km/s` Dark-WHIM halo envelope). Under DESI-like thawing dark energy (`w_0 = -0.75, w_a = -0.85`), cosmic acceleration is temporary: expansion begins **slowing down (`ddot(a) < 0`) at `a_slow = 1.3897`**, and in any spatially closed finite 3-sphere (`Omega_k < 0`, e.g. `-0.004`), the outer cloud halts at `a_turn = Omega_m / |Omega_k| = 78.80` and recollapses. -3. **Dark Matter as the Remnant of Cosmological Pair Production / Inverted Annihilation (`C-30`)**: - - *Exact mathematical mechanism:* In the CPT-even shift-symmetric kinetic Mexican-hat condensate `P(u) = K_2 (u^2 - 1)^2 - Lambda_DE` (`u = Q / Q_0`; Scherrer 2004; Boyle, Finn & Turok 2018, PRL 121, 251301), the unbroken creation state `u = 0` is pure de Sitter (`w = -1`) and pair-bifurcates into a forward-time sheet (`u_+ = +1 + eps`, Noether charge `J^0_+ > 0`) and a CPT-conjugate sheet (`u_- = -1 - eps`, `J^0_- = -J^0_+ < 0`) with **exact zero net global charge (`J^0_+ + J^0_- = 0`)**, yet **positive dust energy density `rho_dust = Q * J^0 > 0` on both sheets** (`formal/Wave11MachianZeroEnergy.lean`). - - *Why visible pairs annihilate while the dark condensate survives:* In the visible sector, `99.99999994%` of quark-antiquark pairs annihilate into photons (`eta_B = 6.12e-10`). By contrast, gravitational Bogoliubov squeezing (Parker 1968, PRL 21, 562 -- the exact unitary time-reversal of two-particle annihilation) and condensate phase rotation (`Axiogenesis`, Co & Harigaya 2020, PRL 124, 111602) store conserved Noether charge in a shift-symmetric (`phi -> phi + const`) coherent condensate where number-changing `phi phi -> gamma gamma` annihilation is symmetry-forbidden! Unlike `5.03 GeV` collisionless asymmetric-DM particles (which fail galactic RAR via `sigma_J = 0` cusps), storing the pair-creation Noether remnant in `P(Q, Y)` unifies `Omega_c` dust on linear/cluster scales with `d_s = 1` MOND phonons in galaxies. - - *Dead end explicitly rejected:* Naive thermal degree-of-freedom counting (`5` dark AeST modes vs. `1` baryon mode `~ 5.39`) is invalid because thermal dark modes equilibrated with photons would violate BBN `Delta N_eff` (`C-11`); a `T = 0` coherent Noether/cogenesis partition avoids thermal `Delta N_eff` entirely, though deriving the exact `5.3895` portal coupling from UV microphysics remains an open `CONJECTURE`. +## 4. Wave 11 and Wave 12: corrected interpretation + +The [independent value audit](https://github.com/Foundation-0/gravity/pull/11) separates reproducible algebra and conditional clocks from physical mechanisms. This section replaces the earlier creation and protected-remnant claims. + +The Hubble-sphere compactness follows from critical density and `R_H = c/H`. The selected induction partition sums to one by construction. Manuel Urueña Palomo (2026), arXiv:2610.09987v2, presents a Machian proposal. Neither the partition nor that citation establishes a derivation of inertia in this calculation. + +A Hamiltonian constraint is not a universe-creation process or a globally measurable cancellation of all energies. Negative heat capacity does not prove that every gravitating system forms a core and an expanding envelope. A future turnaround is conditional on extrapolating the chosen CPL equation of state. Density closure now includes curvature, with `Omega_DE = 1 - Omega_m - Omega_k`. No future history is fitted here. + +The CPT-even polynomial has opposite-charge branches with equal positive dust densities. Algebraic evaluation does not produce those branches from the symmetric origin. In the minimal homogeneous scalar sector, `P_QQ(0) = -4 K_2 / Q_0^2`. The kinetic curvature changes sign through a degeneracy. + +Source-free homogeneous shift symmetry conserves `a^3 P_Q`, so an initially zero current requires an additional production prescription to become nonzero. Full mixing stability is not solved. + +Constant shift symmetry permits derivative portals, including `(partial_phi)^2 F_mu_nu F^mu_nu`. A portal coefficient and rate are needed to assess pair conversion. The measured baryon-to-photon ratio does not specify the fraction of initial pairs that annihilated. No cogenesis abundance or origin mechanism is derived. + +Wave 12 now integrates radial infall through the changing force rather than inserting its outer value into the Newtonian time formula. The result is a fixed point-mass test, not a filament or black-hole formation calculation. Its nonlinear halo mass remains total matter mass. Trapping remains an assigned prescription. + +The light-seed growth clock depends on opacity and efficiency. Efficiency 0.10 is a benchmark. The fixed Schwarzschild value is `1 - sqrt(8/9)`. Pure H and primordial H/He are reported separately. + +The mass-flow convention for the slim-disk table now enforces inflow minus radiated energy. No outflow, changing spin or fuel history is modeled. No present luminosity or binary velocity is treated as a measured lifetime history or orbital inclination. diff --git a/SHA256SUMS b/SHA256SUMS index ac73489..ba4d1d8 100644 --- a/SHA256SUMS +++ b/SHA256SUMS @@ -23,8 +23,14 @@ a44b03375f26452e66aac5324199e41aeb77092c668dbc2adf0342caccb32a7c results/wave3_ 6e6297b1654a89a0a204616de83106ffc1392679b13ce981ec114570f2c2d741 results/wave7_group_cluster_certificates.json 59fa0a13333e85298e573d4cc8487b0f9df0169d86e2b2d8784e79f5d926c475 results/wave9_scale_convergence_certificates.json dd37a45adcb3c815d1a2d44bbbb58ac0235b9ea30d58d6b5a3438a46d91c874e results/wave10_covariant_jeans_certificates.json -5e882f682fd25e980a7f933668fd177b8136208185095b747dc327bc1806f078 README.md -c459b23829444a125fd0b682ab01dc34441088566292b9dad13566ee3b29b6df CLAIMS.md +ea84eb79d2ab891fd5b151b6e0b3ee72fafda601d7b4e1c16157298c8da001ce README.md +efd6e9acba39ec3dd86356df22edacc3d17761e205ac11420798de52290924a9 CLAIMS.md a08db487d924ae709e650df597eaab81da645aef6b9e7e326d26daf93f74dbca METHODS_AND_PLAYBOOK.md -3c4427c87d5c53ac62bbb1a8b41836b6a567485f1716d5c29329d6809f24e45e RESEARCH_NOTEBOOK_AND_REASONING.md -a25d663c071362f100f097dd58943785ee72e5deb7d26520662ae8bee3e0348d CHANGELOG.md +7d678663f6689639039445d7fe972109a3234c7cd8220601b43c435431214c64 RESEARCH_NOTEBOOK_AND_REASONING.md +b95e0b1b867a876758f4751a0806bce54325f95d2ad8f4e25d801e0850e1a000 CHANGELOG.md +88dd0f9827b2fa29292597c976695ce559d135d6d4867f59cde0d0de37426bda wave11_machian_pairing_unification.py +53cb171ed423ab98509f62017b68d2cce935c9b6468cd9e5f098a02b465c99b0 wave12_cosmic_dawn_quasar_collapse.py +fed7d58b8959cc68073bbf2020c7dca895fb4bac0b07adb9d95c3bee56d1c94b results/wave11_machian_pairing_certificates.json +78b988c2a6a83f23a8dc637626fdc63b9122579c2c3e37eaf9365deb2539ca79 results/wave12_cosmic_dawn_quasar_certificates.json +4a69d34265fe05e33f17a5afde1b529f508b4405753a300909d27ce41f14441c test_wave11_12_corrections.py +16edeec60b7a6ac3aab790021fab866273e95f508da8fb7ddebd5d6a78ff8bf1 WAVE11_12_CORRECTIONS.md diff --git a/WAVE11_12_CORRECTIONS.md b/WAVE11_12_CORRECTIONS.md new file mode 100644 index 0000000..36ff5a6 --- /dev/null +++ b/WAVE11_12_CORRECTIONS.md @@ -0,0 +1,57 @@ +# Wave 11 and Wave 12 corrections + +These changes implement reviewed numerical and interpretation findings for conditional benchmarks. They do not introduce a new physical model. Prepared by gpt-forge using GPT-6.1 Sol. Independent implementation review is pending. + +The [prior public audit](https://github.com/Foundation-0/gravity/pull/11) records the independent derivations and sources. The chirp-mass Lean repair remains a separate change. No Lean files change here. + +## Radial infall + +For release from rest, energy conservation gives `v(r)^2 = 2 integral_r^r0 g(s) ds` and `t = integral_0^r0 dr/v(r)`. The earlier code substituted `g(r0)` into the Newtonian point-mass formula. That formula's coefficient depends on the full inverse-square force law. + +The corrected calculation separates the Newtonian potential analytically. It integrates the RAR excess in log radius, where the scaled integrand `y/expm1(y)` is bounded by one. The outer substitution `r/r0 = cos(theta)^2` removes both time-integral endpoint singularities. Adaptive Simpson quadrature raises an error if it exhausts its depth. The outer integral uses composite Simpson quadrature. + +| Fixed force at all radii | Earlier shortcut, Myr | Integrated time, Myr | +|---|---:|---:| +| Newtonian baryonic point mass | 384.823 | 384.823 | +| RAR, constant a0 | 182.27 | 200.075 | +| RAR, Hubble-scaled a0 at the observation epoch | 109.04 | 121.717 | +| Constant-a0 RAR plus the assigned condensate force | 122.79 | 127.156 | + +The baryonic point mass is `5e10 M_sun`. The initial radius is `30 pkpc`. Newtonian infall agrees with `pi sqrt(r0^3/(GM))/(2 sqrt(2))`. In deep MOND, `g = V^2/r` gives `t = sqrt(pi/2) r0/V`. The earlier shortcut divided by that exact result is `sqrt(pi)/2`. A separate test approaches this limit with a small Newtonian core. + +Constant-a0 results at 64, 128 and 256 outer intervals agree within `2e-9 Myr`. This is a numerical control for a fixed point-mass model. It does not describe a filament, evolving halo, pressure, angular momentum, cooling, seed formation or dynamical friction. + +## Growth and mass flow + +The growth budget from z=20 is still `734.100 Myr`. At fixed Eddington ratio one, a `100 M_sun` seed needs the following time to reach `1.5e9 M_sun`: + +| Fixed radiative efficiency | Pure H, Myr | Primordial H/He, Myr | +|---|---:|---:| +| 0.10 benchmark | 827.078 | 725.761 | +| `1 - sqrt(8/9)` Schwarzschild thin disk | 451.536 | 396.223 | + +The prior audit's prose associated `451.536 Myr` with primordial composition. That value is the pure-H result. Both conventions are explicit here. These counterexamples concern conditional clocks. They do not establish any realized accretion history. Fixed spin, efficiency, opacity, duty and fuel are assumptions. + +The slim-disk convention is `mdot = epsilon_ref dotM_in c^2/L_Edd`, with `epsilon_ref=0.10`. The assigned luminosity is `lambda=mdot` below two and `lambda=2(1+ln(mdot/2))` above. Conservation gives `dotM_BH=(mdot-epsilon_ref lambda)L_Edd/(epsilon_ref c^2)`. The old `0.90 mdot` prescription agrees only in the unsaturated regime. Outflows are omitted. + +## Curvature and interpretation + +Each curved CPL example now uses `Omega_DE = 1 - Omega_m - Omega_k`. Its present value is therefore `H^2(1)/H0^2 = 1`. The extrapolated equation of state remains a chosen future continuation, not a fit or an observed recollapse prediction. + +The cited arXiv identifier 2610.09987v2 belongs to [Manuel Urueña Palomo](https://arxiv.org/abs/2610.09987v2), not Braun. The induction partition and critical-density substitution are algebraic benchmarks. A Hamiltonian constraint does not establish universe creation or a globally observable energy cancellation. + +The polynomial's symmetric origin has `P_QQ(0)=-4 K2/Q0^2` in its minimal scalar sector. Source-free homogeneous shift symmetry conserves `a^3 P_Q`. Algebraically selecting nonzero opposite-charge branches does not derive their production from zero current. Full mixing stability remains unsolved. Constant shift symmetry allows derivative portals, so it does not forbid every conversion process. No portal rate is calculated. + +## Certificate changes and checks + +Both certificate schemas advance from 1.0 to 1.1. Wave 11 renames `unbroken_creation_state_u0` to `symmetric_polynomial_state_u0`, removes the inferred annihilated-pair fraction, and adds curvature closure and origin limitations. Wave 12 renames `feeder_filament_30pkpc_5e10Msun_infall` to `fixed_point_mass_30pkpc_5e10Msun_radial_infall`, adds growth counterexamples and convergence data, and labels the orbital projection as illustrative. + +Only the two affected certificates are regenerated. Existing unchanged hash entries are retained. Updated entries cover changed tracked files, with new entries for these two generators, certificates, controls and this note. + +```sh +python3 -m unittest test_wave11_12_corrections.py +python3 wave11_machian_pairing_unification.py --check +python3 wave12_cosmic_dawn_quasar_collapse.py --check +``` + +The seven tests cover Newtonian and deep-MOND limits, convergence, mass conservation, low-inflow equivalence, opacity and efficiency counterexamples, curved density closure and the polynomial's kinetic curvature. They do not verify an origin mechanism, observational likelihood or unmodified Lean build. diff --git a/results/wave11_machian_pairing_certificates.json b/results/wave11_machian_pairing_certificates.json index 6a99edc..364bb81 100644 --- a/results/wave11_machian_pairing_certificates.json +++ b/results/wave11_machian_pairing_certificates.json @@ -1,5 +1,5 @@ { - "schema": "FOUNDATION-0/GRAVITY-WAVE11-MACHIAN-PAIRING/1.0", + "schema": "FOUNDATION-0/GRAVITY-WAVE11-MACHIAN-PAIRING/1.1", "claim_c28_machian_inertia_and_horizon_induction": { "epistemic_status": "COMPUTED (KNOWN MACHIAN & UNRUH-DE SITTER IDENTITIES; MODIFIED INERTIA VS GRAVITY OPEN)", "hubble_radius_Mpc": 4450.6, @@ -27,25 +27,32 @@ }, "claim_c29_zero_energy_and_desi_turnaround": { "epistemic_status": "COMPUTED (FRIEDMANN & ADM HAMILTONIAN IDENTITIES UNDER STATED EOS INPUTS)", - "adm_hamiltonian_constraint": "H_grav + H_matter = 0 identically in GR and 3+1D AeST (Bataki et al. 2024 Eq. 43a)", + "adm_hamiltonian_constraint": "A Hamiltonian constraint applies on physical solutions, subject to boundary and gauge conditions (Bataki et al. 2024 Eq. 43a). It is not a global observable energy identity or an origin mechanism.", "desi_thawing_eos_inputs": { "w0": -0.75, "wa": -0.85 }, + "future_extrapolation_caveat": "Chosen CPL inputs are not a fit here. Recollapse is conditional on this unmeasured future continuation, not an observational prediction. Past-compatible future equations of state can avoid turnaround.", "future_deceleration_onset_scale_factor_a_slow": 1.3897, "closed_universe_recollapse_turnarounds": [ { "Omega_k": -0.001, + "Omega_DE_present": 0.6858173884710649, + "H_squared_at_a1_over_H0_squared": 1.0000000000000002, "turnaround_scale_factor_a_max": 315.18, "asymptotic_matter_curvature_ratio_Omega_m_over_abs_Omega_k": 315.18 }, { "Omega_k": -0.004, + "Omega_DE_present": 0.6888173884710649, + "H_squared_at_a1_over_H0_squared": 1.0, "turnaround_scale_factor_a_max": 78.8, "asymptotic_matter_curvature_ratio_Omega_m_over_abs_Omega_k": 78.8 }, { "Omega_k": -0.01, + "Omega_DE_present": 0.6948173884710649, + "H_squared_at_a1_over_H0_squared": 1.0, "turnaround_scale_factor_a_max": 31.52, "asymptotic_matter_curvature_ratio_Omega_m_over_abs_Omega_k": 31.52 } @@ -79,9 +86,16 @@ }, "claim_c30_cpt_pair_bifurcation_and_noether_remnant": { "epistemic_status": "COMPUTED (KINETIC MEXICAN-HAT & COGENESIS ALGEBRA) & CONJECTURE (COSMOLOGICAL CPT PAIR-CREATION ORIGIN OF CONDENSATE CHARGE)", - "unbroken_creation_state_u0": { + "symmetric_polynomial_state_u0": { + "P_QQ_in_units_K2_over_Q0_squared": -4.0, + "homogeneous_shift_current": 0.0, "w_u0_exact": -1.0 }, + "origin_obstructions": [ + "The minimal homogeneous scalar sector has P_QQ(0)=-4*K2/Q0^2<0. Full mixing stability is not solved.", + "Source-free homogeneous shift symmetry conserves a^3 P_Q. Starting at u=0 gives zero current, so nonzero branch charge requires an additional source, boundary condition or production prescription.", + "Evaluating opposite branches algebraically does not establish a dynamical transition through the kinetic degeneracy at abs(u)=1/sqrt(3)." + ], "cpt_conjugate_pair_branches": { "forward_sheet_plus": { "u_value": 1.000001, @@ -101,10 +115,10 @@ "baryon_dark_matter_remnant_scales": { "planck_Omega_c_over_Omega_b": 5.3643, "visible_baryon_to_photon_eta_B": 6.12e-10, - "visible_pair_annihilation_completion": 0.9999999994, + "eta_B_interpretation": "The baryon-to-photon ratio does not determine the fraction of initial visible pairs annihilated.", "cogenesis_equal_charge_particle_mass_GeV": 5.033, - "audit_distinction": "Collisionless 5.03 GeV ADM particles would form cold dwarf cusps (sigma_J = 0), failing galactic RAR without MOND; storing the conserved cogenesis/Bogoliubov Noether charge in the coherent P(Q, Y) condensate keeps linear dust scaling while preserving galactic phonons and the Wave-10 Dark-WHIM Jeans floor." + "audit_distinction": "The mass ratio is an equal-number benchmark, not a cogenesis mechanism. Shift symmetry permits derivative portals such as (partial_phi)^2 F_mu_nu F^mu_nu. No portal coefficient, conversion rate or relic abundance is derived." } }, - "sha256_canonical": "9a79b9e2184fcc70cb0e6b250615b57c7492af36d0a605f563bafa0ea87942f5" + "sha256_canonical": "4786fa9822b8b99edfd2c11ac922ca589065403e4881f5bf72d415481644692b" } diff --git a/results/wave12_cosmic_dawn_quasar_certificates.json b/results/wave12_cosmic_dawn_quasar_certificates.json index fbbc6c6..d562fb4 100644 --- a/results/wave12_cosmic_dawn_quasar_certificates.json +++ b/results/wave12_cosmic_dawn_quasar_certificates.json @@ -1,5 +1,5 @@ { - "schema": "FOUNDATION-0/GRAVITY-WAVE12-COSMIC-DAWN-QUASAR-PAIR/1.0", + "schema": "FOUNDATION-0/GRAVITY-WAVE12-COSMIC-DAWN-QUASAR-PAIR/1.1", "claim_c31_salpeter_seed_and_clustering_wall": { "epistemic_status": "COMPUTED (KNOWN-FRAMEWORK COSMOLOGICAL & SALPETER IDENTITIES; LENSING & VIRIAL MASS CAVEATS NOTED)", "observed_system": { @@ -19,6 +19,7 @@ "salpeter_timescales_Myr": { "pure_H_eps_0p10": 50.05, "primordial_H_He_eps_0p10": 43.92, + "fixed_Schwarzschild_primordial_H_He": 23.97929, "spinning_Kerr_pure_H_eps_0p20": 112.62 }, "growth_windows_Myr": { @@ -27,6 +28,13 @@ }, "seed_duty_cycle_audit_for_J1602A_1p5e9_Msun": { "popIII_100Msun_efoldings": 16.524, + "popIII_100Msun_req_time_primordial_H_He_eps0p10_Myr": 725.761, + "popIII_100Msun_duty_primordial_H_He_eps0p10": 0.988641, + "fixed_Schwarzschild_efficiency": 0.057190958417936644, + "popIII_100Msun_req_time_pure_H_Schwarzschild_Myr": 451.536, + "popIII_100Msun_duty_pure_H_Schwarzschild": 0.615089, + "popIII_100Msun_req_time_primordial_H_He_Schwarzschild_Myr": 396.223, + "popIII_100Msun_duty_primordial_H_He_Schwarzschild": 0.53974, "popIII_100Msun_req_time_Edd1_eps0p10_Myr": 827.08, "popIII_100Msun_duty_from_z20_Edd1_eps0p10": 1.127, "popIII_100Msun_duty_from_z20_obsEdd1p23_eps0p10": 0.916, @@ -42,12 +50,13 @@ "dcbh_1e5Msun_duty_from_z20_obsEdd1p07_eps0p10": 0.529 }, "scientific_caveats": [ + "Efficiency 0.10 is a chosen benchmark, not the Schwarzschild thin-disk efficiency. All growth clocks assume fixed efficiency, opacity, Eddington ratio and duty; present luminosity need not equal its lifetime average.", "Single-epoch broad-line virial BH masses carry ~2x (0.3 dex) systematic uncertainty.", "Spectral slopes, dust attenuation, and [O III] outflow shapes differ between A and B (favoring a physical pair), but archival HST imaging shows a candidate foreground galaxy near B; a full lens model is pending (Onorato et al. 2026)." ] }, "claim_c32_two_branch_condensate_and_phonon_collapse": { - "epistemic_status": "COMPUTED (WAVE-10 SIGMA_*(Z) EXTENSION & MOND FREE-FALL) & CONJECTURE (COSMIC-DAWN DCBH SEEDING)", + "epistemic_status": "COMPUTED (CHOSEN SPECTRUM AND FIXED POINT-MASS FORCE BENCHMARKS); NO SEED-FORMATION OR FILAMENT-DYNAMICS SOLUTION", "planck_nonlinear_collapse_at_z6p08": { "R_star_comoving_Mpc": 0.00796, "M_star_Msun": 83914.0, @@ -70,19 +79,36 @@ "gaussian_peak_height_nu": 5.38 } ], - "feeder_filament_30pkpc_5e10Msun_infall": { + "fixed_point_mass_30pkpc_5e10Msun_radial_infall": { + "method": "Energy-conserving radial quadrature, released from rest; fixed point mass; no pressure, angular momentum or environmental evolution", + "MOND_const_a0_convergence_intervals": [ + 64, + 128, + 256 + ], + "MOND_const_a0_convergence_Myr": [ + 200.07513758474812, + 200.07513758287334, + 200.07513758290773 + ], + "superseded_outer_acceleration_shortcuts_Myr": [ + 182.27, + 109.04, + 122.79 + ], "g_baryon_m_s2": 7.7437e-12, "a0_const_m_s2": 1.2e-10, "a0_hubble_cHz_over_2pi_m_s2": 1.1057e-09, "free_fall_time_pure_baryon_Newton_Myr": 384.82, - "free_fall_time_MOND_const_a0_Myr": 182.27, - "free_fall_time_MOND_Hubble_a0_Myr": 109.04, - "free_fall_time_two_branch_trapped_condensate_Myr": 122.79 + "free_fall_time_MOND_const_a0_Myr": 200.08, + "free_fall_time_MOND_Hubble_a0_Myr": 121.72, + "free_fall_time_two_branch_trapped_condensate_Myr": 127.16 }, - "dynamical_friction_audit_note": "Pure baryon-only MOND slows kpc-scale galaxy mergers due to absent dark-halo dynamical friction (Nipoti et al. 2008), whereas in the two-branch condensate sigma_*(z=6.08) = 0.97 km/s << sigma_halo keeps f_trap = 0.99997, supplying both deep central DCBH potentials and Chandrasekhar dynamical friction at z = 6.08 before late-time cosmic-web shocks heat the condensate to 185.59 km/s by z = 0." + "dynamical_friction_audit_note": "The assigned trapping fraction is a prescription, not a capture or friction calculation. M_star is total nonlinear halo mass, not a black-hole seed. No density profile, phase-space distribution, gas collapse, cooling or merger hardening history is solved here." }, "claim_c33_slim_disk_and_binary_gw_budget": { "epistemic_status": "COMPUTED (SLIM-DISK ADVECTION & PETERS 1964 GW INSPIRAL IDENTITIES)", + "slim_disk_mass_flow_convention": "mdot = epsilon_ref * dotM_in * c^2 / L_Edd; epsilon_ref=0.10; lambda=mdot below 2, otherwise 2*(1+ln(mdot/2)); dotM_BH=(mdot-epsilon_ref*lambda)*L_Edd/(epsilon_ref*c^2); no outflows; fixed coefficients and duty one", "slim_disk_photon_trapping_benchmarks": [ { "dimensionless_mass_inflow_mdot": 1.0, @@ -97,27 +123,27 @@ { "dimensionless_mass_inflow_mdot": 3.0, "radiated_lambda_Edd_slim_disk": 2.811, - "popIII_100Msun_to_1p5e9Msun_time_Myr": 275.69 + "popIII_100Msun_to_1p5e9Msun_time_Myr": 273.78 }, { "dimensionless_mass_inflow_mdot": 5.0, "radiated_lambda_Edd_slim_disk": 3.833, - "popIII_100Msun_to_1p5e9Msun_time_Myr": 165.42 + "popIII_100Msun_to_1p5e9Msun_time_Myr": 161.23 } ], "kinematic_projection_at_5p56_pkpc": { "v_circ_BHs_only_kms": 38.34, "v_circ_with_1p5e11Msun_host_kms": 342.79, "observed_delta_v_los_kms": 15.0, - "required_abs_sin_i_cos_psi": 0.0438 + "illustrative_abs_sin_i_cos_psi_from_point_velocity": 0.0438 }, "gravitational_wave_inspiral_budget": { "chirp_mass_Msun": 647350000.0, "t_GW_at_5p56_pkpc_Myr": 4.872e+20, "t_GW_at_0p10_pc_Myr": 50.99, "t_GW_at_0p05_pc_Myr": 3.19, - "nanograv_relevance": "At 5.56 pkpc, pure GW emission is negligible (t_GW = 4.87e+20 Myr); Chandrasekhar dynamical friction and stellar/condensate loss-cone scattering must harden the pair to 0.05-0.10 pc, after which GW inspiral merges the M_c = 6.47e+08 M_sun binary in 3.19-50.99 Myr, feeding the nHz GW background." + "nanograv_relevance": "At 5.56 pkpc, pure GW emission is negligible (t_GW = 4.87e+20 Myr); If the pair reaches 0.05-0.10 pc, the isolated circular point-mass GW clock is 3.19-50.99 Myr. No hardening history, population merger rate or GW background prediction is supplied." } }, - "sha256_canonical": "f46cc3be82489f450d1a3ce8c583fad15970050f938bd4c8b5510fe704ba48b6" + "sha256_canonical": "40a770d70d19ec3a9d7e9e5e770d0454d94595f7e7abb75e92efa351672354c9" } diff --git a/test_wave11_12_corrections.py b/test_wave11_12_corrections.py new file mode 100644 index 0000000..5918057 --- /dev/null +++ b/test_wave11_12_corrections.py @@ -0,0 +1,54 @@ +"""Independent analytic controls for corrected conditional benchmarks.""" +import math +import unittest +import wave11_machian_pairing_unification as w11 +import wave12_cosmic_dawn_quasar_collapse as w12 + +class Controls(unittest.TestCase): + def test_newton(self): + mass, radius = 5e10*w12.M_SUN, 30*w12.KPC + exact = math.pi/(2*math.sqrt(2))*math.sqrt(radius**3/(w12.G*mass)) + self.assertLess(abs(w12.radial_point_mass_fall_time(mass,radius)/exact-1),1e-12) + + def test_deep_mond(self): + mass, radius = 5e10*w12.M_SUN, 30*w12.KPC + a0 = w12.G*mass/radius**2*1e8 + speed = (w12.G*mass*a0)**0.25 + exact = math.sqrt(math.pi/2)*radius/speed + numeric = w12.radial_point_mass_fall_time(mass,radius,a0,intervals=512) + self.assertLess(abs(numeric/exact-1),5e-4) + shortcut = math.pi/(2*math.sqrt(2))*radius/speed + self.assertAlmostEqual(shortcut/exact,math.sqrt(math.pi)/2,places=14) + + def test_convergence(self): + times = [w12.radial_point_mass_fall_time(5e10*w12.M_SUN,30*w12.KPC,w12.A0_EMP,intervals=n)/w12.MYR for n in (64,128,256)] + self.assertLess(max(times)-min(times),1e-6) + self.assertAlmostEqual(times[-1],200.075137583,places=6) + + def test_mass_flow(self): + efolds=math.log(1.5e9/100) + tedd=w12.SIGMA_T*w12.C_SI/(4*math.pi*w12.G*w12.M_P)/w12.MYR + for mdot in (.1,1,2,3,5): + lam,time=w12.slim_disk_growth_time_myr(efolds,mdot) + self.assertGreater(mdot-.1*lam,0) + self.assertAlmostEqual(efolds*.1*tedd/time+.1*lam,mdot,places=13) + if mdot<=2: + self.assertAlmostEqual(time,efolds*(.1/.9)*tedd/mdot,places=10) + with self.assertRaises(ValueError): w12.slim_disk_growth_time_myr(efolds,0) + + def test_growth_counterexamples(self): + s=w12.audit_c31_salpeter_seed_and_clustering_wall()['seed_duty_cycle_audit_for_J1602A_1p5e9_Msun'] + self.assertLess(s['popIII_100Msun_duty_primordial_H_He_eps0p10'],1) + self.assertAlmostEqual(s['popIII_100Msun_req_time_primordial_H_He_Schwarzschild_Myr']/s['popIII_100Msun_req_time_pure_H_Schwarzschild_Myr'],1-.245/2,places=5) + self.assertAlmostEqual(s['fixed_Schwarzschild_efficiency'],1-math.sqrt(8/9),places=14) + + def test_curvature_closure(self): + for ok in (-.01,-.004,-.001,0,.01): self.assertAlmostEqual(w11.closed_cpl_hubble_squared(1,ok),1,places=14) + + def test_kinetic_curvature(self): + h=1e-4 + p=lambda u:(u*u-1)**2 + self.assertAlmostEqual((p(h)-2*p(0)+p(-h))/h**2,-4,places=6) + self.assertEqual(4*0*(0**2-1),0) + +if __name__=='__main__': unittest.main() diff --git a/wave11_machian_pairing_unification.py b/wave11_machian_pairing_unification.py index 9c47dbc..c7acf5b 100644 --- a/wave11_machian_pairing_unification.py +++ b/wave11_machian_pairing_unification.py @@ -33,11 +33,11 @@ def audit_c28_machian_inertia_and_horizon_scales() -> dict: - """Evaluates Sciama (1953) / Braun (2026) Machian induction identities, Milgrom (1999) Unruh-de Sitter scales, and PPN/locality caveats.""" + """Evaluates Sciama (1953) / Urueña Palomo (2026) Machian induction identities, Milgrom (1999) Unruh-de Sitter scales, and PPN/locality caveats.""" m_hubble = (4.0 / 3.0) * math.pi * (R_H ** 3) * RHO_CRIT0 sciama_compactness = (G * m_hubble) / (R_H * (C_SI ** 2)) sciama_potential_integral = (2.0 * math.pi * G * RHO_CRIT0 * (R_H ** 2)) / (C_SI ** 2) - # Braun (2026, EPJC 86, 1215): gravitomagnetic induction K_gm = (2 H0^2 R_H^2)/(3 c^2) = 2/3 + gravitoelectric K_ge = 1/3 = 1 + # Illustrative partition associated with Urueña Palomo (2026, arXiv:2610.09987v2); not an established derivation of inertia: gravitomagnetic induction K_gm = (2 H0^2 R_H^2)/(3 c^2) = 2/3 + gravitoelectric K_ge = 1/3 = 1 k_gm = (2.0 * (H0_SI ** 2) * (R_H ** 2)) / (3.0 * (C_SI ** 2)) k_ge = 1.0 / 3.0 @@ -79,6 +79,13 @@ def audit_c28_machian_inertia_and_horizon_scales() -> dict: } +def closed_cpl_hubble_squared(a, omega_k, w0=-0.75, wa=-0.85): + """Chosen radiation-free CPL continuation with present-day density closure.""" + omega_de = 1.0 - OMEGA_M - omega_k + rho_de = a ** (-3.0 * (1.0 + w0 + wa)) * math.exp(3.0 * wa * (a - 1.0)) + return OMEGA_M / a ** 3 + omega_de * rho_de + omega_k / a ** 2 + + def audit_c29_zero_energy_and_desi_turnaround() -> dict: """Evaluates closed-FLRW / ADM zero-energy cancellation and DESI-motivated thawing dark-energy deceleration & turnaround.""" w0_desi = -0.75 @@ -108,13 +115,15 @@ def accel_sign_term(a: float) -> float: lo_t, hi_t = 2.0, 2000.0 for _ in range(80): mt = 0.5 * (lo_t + hi_t) - h2 = OMEGA_M * (mt ** -3.0) + OMEGA_L * rho_de_rel(mt) - ok_abs * (mt ** -2.0) + h2 = closed_cpl_hubble_squared(mt, -ok_abs) if h2 > 0.0: lo_t = mt else: hi_t = mt closed_turnarounds.append({ "Omega_k": -ok_abs, + "Omega_DE_present": 1.0 - OMEGA_M + ok_abs, + "H_squared_at_a1_over_H0_squared": closed_cpl_hubble_squared(1.0, -ok_abs), "turnaround_scale_factor_a_max": round(0.5 * (lo_t + hi_t), 2), "asymptotic_matter_curvature_ratio_Omega_m_over_abs_Omega_k": round(OMEGA_M / ok_abs, 2), }) @@ -134,8 +143,9 @@ def accel_sign_term(a: float) -> float: return { "epistemic_status": "COMPUTED (FRIEDMANN & ADM HAMILTONIAN IDENTITIES UNDER STATED EOS INPUTS)", - "adm_hamiltonian_constraint": "H_grav + H_matter = 0 identically in GR and 3+1D AeST (Bataki et al. 2024 Eq. 43a)", + "adm_hamiltonian_constraint": "A Hamiltonian constraint applies on physical solutions, subject to boundary and gauge conditions (Bataki et al. 2024 Eq. 43a). It is not a global observable energy identity or an origin mechanism.", "desi_thawing_eos_inputs": {"w0": w0_desi, "wa": wa_desi}, + "future_extrapolation_caveat": "Chosen CPL inputs are not a fit here. Recollapse is conditional on this unmeasured future continuation, not an observational prediction. Past-compatible future equations of state can avoid turnaround.", "future_deceleration_onset_scale_factor_a_slow": round(a_slow, 4), "closed_universe_recollapse_turnarounds": closed_turnarounds, "machian_a0_redshift_evolution_tracks": a0_evolution_comparison, @@ -144,9 +154,9 @@ def accel_sign_term(a: float) -> float: def audit_c30_cpt_pair_bifurcation_and_cogenesis() -> dict: """Evaluates CPT-even Mexican-hat kinetic condensate P(Q) = K_2 (Q^2/Q_0^2 - 1)^2 - Lambda_DE and cogenesis scales.""" - # Dimensionless u = Q / Q_0 around u = 0 (unbroken creation maximum) and u = +/- (1 + eps) (CPT-conjugate branches) + # Dimensionless u = Q / Q_0 around u = 0 (symmetric polynomial point) and u = +/- (1 + eps) (CPT-conjugate branches) # P(u) / K_2 = (u^2 - 1)^2 - lam, rho(u) / K_2 = u * 4*u*(u^2 - 1) - (u^2 - 1)^2 + lam = (u^2 - 1)*(3*u^2 + 1) + lam - lam = 2.0 # illustrative Lambda_DE / K_2 > 1 so rho(0) > 0 at symmetric creation point + lam = 2.0 # illustrative Lambda_DE / K_2 > 1 so rho(0) > 0 at symmetric polynomial point p_u0 = 1.0 - lam rho_u0 = -1.0 + lam w_u0 = p_u0 / rho_u0 @@ -175,16 +185,23 @@ def audit_c30_cpt_pair_bifurcation_and_cogenesis() -> dict: m_p_gev = (M_P * (C_SI ** 2)) / 1.602176634e-10 adm_equal_number_mass_gev = omega_c_over_b * m_p_gev eta_b_cmb = 6.12e-10 - annihilated_pair_fraction_visible = 1.0 - eta_b_cmb + # eta_B is a present baryon-to-photon ratio, not an initial annihilated pair fraction. return { "epistemic_status": ( "COMPUTED (KINETIC MEXICAN-HAT & COGENESIS ALGEBRA) & " "CONJECTURE (COSMOLOGICAL CPT PAIR-CREATION ORIGIN OF CONDENSATE CHARGE)" ), - "unbroken_creation_state_u0": { + "symmetric_polynomial_state_u0": { + "P_QQ_in_units_K2_over_Q0_squared": -4.0, + "homogeneous_shift_current": 0.0, "w_u0_exact": round(w_u0, 6), }, + "origin_obstructions": [ + "The minimal homogeneous scalar sector has P_QQ(0)=-4*K2/Q0^2<0. Full mixing stability is not solved.", + "Source-free homogeneous shift symmetry conserves a^3 P_Q. Starting at u=0 gives zero current, so nonzero branch charge requires an additional source, boundary condition or production prescription.", + "Evaluating opposite branches algebraically does not establish a dynamical transition through the kinetic degeneracy at abs(u)=1/sqrt(3).", + ], "cpt_conjugate_pair_branches": branches, "global_net_noether_charge_sum": round(net_noether_charge, 12), "both_sheets_positive_dust_gravity": bool( @@ -194,13 +211,12 @@ def audit_c30_cpt_pair_bifurcation_and_cogenesis() -> dict: "baryon_dark_matter_remnant_scales": { "planck_Omega_c_over_Omega_b": round(omega_c_over_b, 4), "visible_baryon_to_photon_eta_B": eta_b_cmb, - "visible_pair_annihilation_completion": round(annihilated_pair_fraction_visible, 10), + "eta_B_interpretation": "The baryon-to-photon ratio does not determine the fraction of initial visible pairs annihilated.", "cogenesis_equal_charge_particle_mass_GeV": round(adm_equal_number_mass_gev, 3), "audit_distinction": ( - "Collisionless 5.03 GeV ADM particles would form cold dwarf cusps (sigma_J = 0), " - "failing galactic RAR without MOND; storing the conserved cogenesis/Bogoliubov Noether " - "charge in the coherent P(Q, Y) condensate keeps linear dust scaling while preserving " - "galactic phonons and the Wave-10 Dark-WHIM Jeans floor." + "The mass ratio is an equal-number benchmark, not a cogenesis mechanism. " + "Shift symmetry permits derivative portals such as (partial_phi)^2 F_mu_nu F^mu_nu. " + "No portal coefficient, conversion rate or relic abundance is derived." ), }, } @@ -234,12 +250,12 @@ def main() -> int: assert c28["sciama_compactness_GMH_over_RH_c2"] == 0.5 assert c28["frame_dragging_induction_partition"]["total_inertial_coefficient_K_tot"] == 1.0 assert 1.35 <= c29["future_deceleration_onset_scale_factor_a_slow"] <= 1.45 - assert c30["unbroken_creation_state_u0"]["w_u0_exact"] == -1.0 + assert c30["symmetric_polynomial_state_u0"]["w_u0_exact"] == -1.0 assert c30["global_net_noether_charge_sum"] == 0.0 assert c30["both_sheets_positive_dust_gravity"] is True cert11 = { - "schema": "FOUNDATION-0/GRAVITY-WAVE11-MACHIAN-PAIRING/1.0", + "schema": "FOUNDATION-0/GRAVITY-WAVE11-MACHIAN-PAIRING/1.1", "claim_c28_machian_inertia_and_horizon_induction": c28, "claim_c29_zero_energy_and_desi_turnaround": c29, "claim_c30_cpt_pair_bifurcation_and_noether_remnant": c30, diff --git a/wave12_cosmic_dawn_quasar_collapse.py b/wave12_cosmic_dawn_quasar_collapse.py index ab9ad18..af95869 100644 --- a/wave12_cosmic_dawn_quasar_collapse.py +++ b/wave12_cosmic_dawn_quasar_collapse.py @@ -2,7 +2,7 @@ Foundation-0 / gravity -- Wave-12 Cosmic-Dawn Compact Quasar Pair Audit: J1602+4228AB / Napowawa'enakaulua (C-31..C-33; M-10) Evaluates Onorato et al. (2026, ApJL 1011, L59, arXiv:2609.31835; NOIRLab Release noirlab2627) against: - C-31: Cosmic-Dawn age budget, Salpeter e-folding bottleneck (Schwarzschild vs Kerr spin; pure-H vs H+He), and Pop III vs DCBH seed requirements. - - C-32: Two-branch condensate + MOND phonon collapse at z = 6.0783 (evaluating exact Planck-2018 sigma_*(z=6.0783) vs z=0 Dark-WHIM inversion and MOND free-fall speedup). + - C-32: Two-branch condensate + MOND phonon collapse at z = 6.0783 (evaluating the chosen Planck-normalized spectrum approximation sigma_*(z=6.0783) vs z=0 Dark-WHIM inversion and MOND free-fall speedup). - C-33: Slim-disk photon-trapping super-Eddington growth, binary orbital / projection constraints at 5.56 pkpc, and Peters (1964) GW chirp-mass budget. 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). @@ -145,6 +145,82 @@ def sigma_lin(r_mpc: float, z: float) -> float: return sigma_lin +def _adaptive_simpson(function, lo, hi, tolerance=1e-10, depth=20): + """Absolute-error adaptive Simpson quadrature; fail rather than hide nonconvergence.""" + mid = (lo + hi) / 2.0 + fl, fm, fh = function(lo), function(mid), function(hi) + whole = (hi - lo) * (fl + 4 * fm + fh) / 6 + + def refine(a, b, fa, fc, fb, old, tol, remaining): + c = (a + b) / 2 + fd, fe = function((a + c) / 2), function((c + b) / 2) + left = (c - a) * (fa + 4 * fd + fc) / 6 + right = (b - c) * (fc + 4 * fe + fb) / 6 + delta = left + right - old + if abs(delta) <= 15 * tol: + return left + right + delta / 15 + if remaining == 0: + raise ArithmeticError('radial potential quadrature did not converge') + return refine(a, c, fa, fd, fc, left, tol / 2, remaining - 1) + refine(c, b, fc, fe, fb, right, tol / 2, remaining - 1) + + return refine(lo, hi, fl, fm, fh, whole, tolerance, depth) + + +def radial_point_mass_fall_time(mass_kg, radius_m, a0=None, additive_mass_ratio=0.0, intervals=256): + """Rest-to-origin radial time in a fixed point-mass force, not filament dynamics. + + Integrate dt=dr/sqrt(2 int_r^r0 g(s)ds). r/r0=cos(theta)^2 removes + both endpoint singularities. The exact Newton term is separated from the + exponentially suppressed high-acceleration RAR correction before quadrature. + """ + if mass_kg <= 0 or radius_m <= 0 or additive_mass_ratio < 0 or (a0 is not None and a0 <= 0): + raise ValueError('positive mass, radius and a0 and nonnegative added ratio required') + if intervals < 2 or intervals % 2: + raise ValueError('an even positive Simpson interval count is required') + gb0 = G * mass_kg / radius_m ** 2 + q0 = math.sqrt(gb0 / a0) if a0 is not None else None + + def excess(x): + if q0 is None or x == 0 or q0 / x > 700: + return 0.0 + return 1.0 / (x * x * math.expm1(q0 / x)) + + force_at_start = 1.0 + additive_mass_ratio + excess(1.0) + + def integrand(theta): + if theta == 0: + return 2.0 / math.sqrt(force_at_start) + if theta >= math.pi / 2: + return 0.0 + x = math.cos(theta) ** 2 + # 1-x is stable near theta=0 when expressed as sin(theta)^2. + drop = (1.0 + additive_mass_ratio) * math.sin(theta) ** 2 / x + if a0 is not None: + # In log radius the scaled excess integrand y/expm1(y) is bounded + # by one even in the deep-MOND limit, avoiding a sharp inner core. + def log_excess(t): + y = q0 * math.exp(t) + return 0.0 if y > 700 else y / math.expm1(y) + drop += _adaptive_simpson(log_excess, 0.0, -math.log(x)) / q0 + return 2.0 * math.sin(theta) * math.cos(theta) / math.sqrt(drop) + + step = math.pi / (2 * intervals) + total = sum((1 if i in (0, intervals) else 4 if i % 2 else 2) * integrand(i * step) for i in range(intervals + 1)) + return math.sqrt(radius_m / (2 * gb0)) * total * step / 3 + + +def slim_disk_growth_time_myr(efoldings, mdot, epsilon_reference=0.10): + """mdot=epsilon_reference*dotM_in*c^2/L_Edd; no outflows, constant duty one.""" + if mdot <= 0 or not 0 < epsilon_reference < 1: + raise ValueError('positive inflow and efficiency between zero and one required') + luminosity_ratio = mdot if mdot < 2 else 2 * (1 + math.log(mdot / 2)) + retained_inflow = mdot - epsilon_reference * luminosity_ratio + if retained_inflow <= 0: + raise ValueError('nonpositive retained black-hole growth') + t_edd = SIGMA_T * C_SI / (4 * math.pi * G * M_P) / MYR + return luminosity_ratio, efoldings * epsilon_reference * t_edd / retained_inflow + + def audit_c31_salpeter_seed_and_clustering_wall() -> dict: """Evaluates Cosmic-Dawn age, Salpeter growth bottleneck, and clustering excess for J1602+4228AB.""" t_pair_myr = cosmic_age_myr(Z_PAIR) @@ -173,6 +249,9 @@ def salpeter_myr(eps_r: float, pure_h: bool = True) -> float: tsal_01_h = salpeter_myr(0.10, pure_h=True) tsal_01_prim = salpeter_myr(0.10, pure_h=False) tsal_02_kerr = salpeter_myr(0.20, pure_h=True) + eps_schwarzschild = 1.0 - math.sqrt(8.0 / 9.0) + tsal_schwarzschild_h = salpeter_myr(eps_schwarzschild, pure_h=True) + tsal_schwarzschild_prim = salpeter_myr(eps_schwarzschild, pure_h=False) return { "epistemic_status": "COMPUTED (KNOWN-FRAMEWORK COSMOLOGICAL & SALPETER IDENTITIES; LENSING & VIRIAL MASS CAVEATS NOTED)", @@ -193,6 +272,7 @@ def salpeter_myr(eps_r: float, pure_h: bool = True) -> float: "salpeter_timescales_Myr": { "pure_H_eps_0p10": round(tsal_01_h, 2), "primordial_H_He_eps_0p10": round(tsal_01_prim, 2), + "fixed_Schwarzschild_primordial_H_He": round(tsal_schwarzschild_prim, 6), "spinning_Kerr_pure_H_eps_0p20": round(tsal_02_kerr, 2), }, "growth_windows_Myr": { @@ -201,6 +281,13 @@ def salpeter_myr(eps_r: float, pure_h: bool = True) -> float: }, "seed_duty_cycle_audit_for_J1602A_1p5e9_Msun": { "popIII_100Msun_efoldings": round(efold_a_pop3, 3), + "popIII_100Msun_req_time_primordial_H_He_eps0p10_Myr": round(efold_a_pop3 * tsal_01_prim, 3), + "popIII_100Msun_duty_primordial_H_He_eps0p10": round(efold_a_pop3 * tsal_01_prim / dt_from_z20, 6), + "fixed_Schwarzschild_efficiency": eps_schwarzschild, + "popIII_100Msun_req_time_pure_H_Schwarzschild_Myr": round(efold_a_pop3 * tsal_schwarzschild_h, 3), + "popIII_100Msun_duty_pure_H_Schwarzschild": round(efold_a_pop3 * tsal_schwarzschild_h / dt_from_z20, 6), + "popIII_100Msun_req_time_primordial_H_He_Schwarzschild_Myr": round(efold_a_pop3 * tsal_schwarzschild_prim, 3), + "popIII_100Msun_duty_primordial_H_He_Schwarzschild": round(efold_a_pop3 * tsal_schwarzschild_prim / dt_from_z20, 6), "popIII_100Msun_req_time_Edd1_eps0p10_Myr": round(efold_a_pop3 * tsal_01_h, 2), "popIII_100Msun_duty_from_z20_Edd1_eps0p10": round((efold_a_pop3 * tsal_01_h) / dt_from_z20, 3), "popIII_100Msun_duty_from_z20_obsEdd1p23_eps0p10": round((efold_a_pop3 * tsal_01_h) / (LAM_EDD_A * dt_from_z20), 3), @@ -216,6 +303,7 @@ def salpeter_myr(eps_r: float, pure_h: bool = True) -> float: "dcbh_1e5Msun_duty_from_z20_obsEdd1p07_eps0p10": round((efold_b_dcbh * tsal_01_h) / (LAM_EDD_B * dt_from_z20), 3), }, "scientific_caveats": [ + "Efficiency 0.10 is a chosen benchmark, not the Schwarzschild thin-disk efficiency. All growth clocks assume fixed efficiency, opacity, Eddington ratio and duty; present luminosity need not equal its lifetime average.", "Single-epoch broad-line virial BH masses carry ~2x (0.3 dex) systematic uncertainty.", "Spectral slopes, dust attenuation, and [O III] outflow shapes differ between A and B (favoring a physical pair), but archival HST imaging shows a candidate foreground galaxy near B; a full lens model is pending (Onorato et al. 2026).", ], @@ -271,13 +359,14 @@ def g_rar(gb: float, a0_val: float) -> float: g_mond_hubble_a0 = g_rar(g_b_feed, a0_hubble_z6) g_two_branch_const = g_mond_const_a0 + (OMEGA_C / OMEGA_B) * f_trap_z6 * g_b_feed - t_ff_newt_myr = (math.pi / 2.0) * math.sqrt(r_feed_m / (2.0 * g_b_feed)) / MYR - t_ff_mond_const_myr = (math.pi / 2.0) * math.sqrt(r_feed_m / (2.0 * g_mond_const_a0)) / MYR - t_ff_mond_hubble_myr = (math.pi / 2.0) * math.sqrt(r_feed_m / (2.0 * g_mond_hubble_a0)) / MYR - t_ff_two_branch_myr = (math.pi / 2.0) * math.sqrt(r_feed_m / (2.0 * g_two_branch_const)) / MYR + t_ff_newt_myr = radial_point_mass_fall_time(m_b_feed, r_feed_m) / MYR + t_ff_mond_const_myr = radial_point_mass_fall_time(m_b_feed, r_feed_m, a0_const) / MYR + t_ff_mond_hubble_myr = radial_point_mass_fall_time(m_b_feed, r_feed_m, a0_hubble_z6) / MYR + t_ff_two_branch_myr = radial_point_mass_fall_time(m_b_feed, r_feed_m, a0_const, (OMEGA_C / OMEGA_B) * f_trap_z6) / MYR + convergence = [radial_point_mass_fall_time(m_b_feed, r_feed_m, a0_const, intervals=n) / MYR for n in (64, 128, 256)] return { - "epistemic_status": "COMPUTED (WAVE-10 SIGMA_*(Z) EXTENSION & MOND FREE-FALL) & CONJECTURE (COSMIC-DAWN DCBH SEEDING)", + "epistemic_status": "COMPUTED (CHOSEN SPECTRUM AND FIXED POINT-MASS FORCE BENCHMARKS); NO SEED-FORMATION OR FILAMENT-DYNAMICS SOLUTION", "planck_nonlinear_collapse_at_z6p08": { "R_star_comoving_Mpc": round(r_star_com_mpc, 5), "M_star_Msun": float(f"{m_star_msun:.4e}"), @@ -287,7 +376,11 @@ def g_rar(gb: float, a0_val: float) -> float: "host_177kms_trapping_at_z0": round(f_trap_z0, 6), }, "lcdm_gaussian_halo_rarity_at_z6p08": halo_rarities, - "feeder_filament_30pkpc_5e10Msun_infall": { + "fixed_point_mass_30pkpc_5e10Msun_radial_infall": { + "method": "Energy-conserving radial quadrature, released from rest; fixed point mass; no pressure, angular momentum or environmental evolution", + "MOND_const_a0_convergence_intervals": [64, 128, 256], + "MOND_const_a0_convergence_Myr": convergence, + "superseded_outer_acceleration_shortcuts_Myr": [182.27, 109.04, 122.79], "g_baryon_m_s2": float(f"{g_b_feed:.4e}"), "a0_const_m_s2": a0_const, "a0_hubble_cHz_over_2pi_m_s2": float(f"{a0_hubble_z6:.4e}"), @@ -297,11 +390,9 @@ def g_rar(gb: float, a0_val: float) -> float: "free_fall_time_two_branch_trapped_condensate_Myr": round(t_ff_two_branch_myr, 2), }, "dynamical_friction_audit_note": ( - f"Pure baryon-only MOND slows kpc-scale galaxy mergers due to absent dark-halo dynamical friction " - f"(Nipoti et al. 2008), whereas in the two-branch condensate sigma_*(z=6.08) = {sigma_star_z6_kms:.2f} km/s " - f"<< sigma_halo keeps f_trap = {f_trap_z6:.5f}, supplying both deep central DCBH potentials and " - f"Chandrasekhar dynamical friction at z = 6.08 before late-time cosmic-web shocks heat the condensate " - f"to 185.59 km/s by z = 0." + "The assigned trapping fraction is a prescription, not a capture or friction calculation. " + "M_star is total nonlinear halo mass, not a black-hole seed. No density profile, phase-space " + "distribution, gas collapse, cooling or merger hardening history is solved here." ), } @@ -309,13 +400,11 @@ def g_rar(gb: float, a0_val: float) -> float: def audit_c33_slim_disk_and_binary_gw_budget() -> dict: """Evaluates slim-disk photon trapping for lambda_Edd > 1, 5.56 pkpc orbital projection, and GW merger timescale.""" t_edd_pure_h_myr = (SIGMA_T * C_SI) / (4.0 * math.pi * G * M_P) / MYR - tsal_01_myr = (0.10 / 0.90) * t_edd_pure_h_myr efold_a_pop3 = math.log(M_BH_A_MSUN / 100.0) slim_disk_benchmarks = [] for mdot in [1.0, 2.0, 3.0, 5.0]: - lam_obs = mdot if mdot < 2.0 else 2.0 * (1.0 + math.log(mdot / 2.0)) - t_grow_pop3_myr = (efold_a_pop3 * tsal_01_myr) / mdot + lam_obs, t_grow_pop3_myr = slim_disk_growth_time_myr(efold_a_pop3, mdot) slim_disk_benchmarks.append({ "dimensionless_mass_inflow_mdot": mdot, "radiated_lambda_Edd_slim_disk": round(lam_obs, 3), @@ -343,12 +432,13 @@ def peters_gw_myr(a_m: float) -> float: return { "epistemic_status": "COMPUTED (SLIM-DISK ADVECTION & PETERS 1964 GW INSPIRAL IDENTITIES)", + "slim_disk_mass_flow_convention": "mdot = epsilon_ref * dotM_in * c^2 / L_Edd; epsilon_ref=0.10; lambda=mdot below 2, otherwise 2*(1+ln(mdot/2)); dotM_BH=(mdot-epsilon_ref*lambda)*L_Edd/(epsilon_ref*c^2); no outflows; fixed coefficients and duty one", "slim_disk_photon_trapping_benchmarks": slim_disk_benchmarks, "kinematic_projection_at_5p56_pkpc": { "v_circ_BHs_only_kms": round(v_kepler_bh_only_kms, 2), "v_circ_with_1p5e11Msun_host_kms": round(v_circ_host_kms, 2), "observed_delta_v_los_kms": DELTA_V_OBS_KMS, - "required_abs_sin_i_cos_psi": round(proj_factor_host, 4), + "illustrative_abs_sin_i_cos_psi_from_point_velocity": round(proj_factor_host, 4), }, "gravitational_wave_inspiral_budget": { "chirp_mass_Msun": float(f"{m_chirp_msun:.4e}"), @@ -357,9 +447,9 @@ def peters_gw_myr(a_m: float) -> float: "t_GW_at_0p05_pc_Myr": round(t_gw_at_0p05pc_myr, 2), "nanograv_relevance": ( f"At 5.56 pkpc, pure GW emission is negligible (t_GW = {t_gw_at_5p56kpc_myr:.2e} Myr); " - f"Chandrasekhar dynamical friction and stellar/condensate loss-cone scattering must harden " - f"the pair to 0.05-0.10 pc, after which GW inspiral merges the M_c = {m_chirp_msun:.2e} M_sun " - f"binary in {t_gw_at_0p05pc_myr:.2f}-{t_gw_at_0p10pc_myr:.2f} Myr, feeding the nHz GW background." + f"If the pair reaches 0.05-0.10 pc, the isolated circular point-mass GW clock is " + f"{t_gw_at_0p05pc_myr:.2f}-{t_gw_at_0p10pc_myr:.2f} Myr. " + f"No hardening history, population merger rate or GW background prediction is supplied." ), }, } @@ -400,7 +490,7 @@ def main() -> int: assert 6.46e8 <= c33["gravitational_wave_inspiral_budget"]["chirp_mass_Msun"] <= 6.48e8 cert12 = { - "schema": "FOUNDATION-0/GRAVITY-WAVE12-COSMIC-DAWN-QUASAR-PAIR/1.0", + "schema": "FOUNDATION-0/GRAVITY-WAVE12-COSMIC-DAWN-QUASAR-PAIR/1.1", "claim_c31_salpeter_seed_and_clustering_wall": c31, "claim_c32_two_branch_condensate_and_phonon_collapse": c32, "claim_c33_slim_disk_and_binary_gw_budget": c33, From 03f96e977c1852930c85d7568aff087e093e4d50 Mon Sep 17 00:00:00 2001 From: ahrazzle <38987266+ahrazzle@users.noreply.github.com> Date: Thu, 12 Nov 2026 17:48:04 -0600 Subject: [PATCH 2/2] Publish independent Wave 11 and 12 correction review --- research/wave11-12-review-20261112/README.md | 13 ++ research/wave11-12-review-20261112/REVIEW.md | 111 +++++++++ research/wave11-12-review-20261112/check.py | 202 +++++++++++++++++ .../wave11-12-review-20261112/checkpoint.json | 18 ++ .../wave11-12-review-20261112/evidence.json | 212 ++++++++++++++++++ 5 files changed, 556 insertions(+) create mode 100644 research/wave11-12-review-20261112/README.md create mode 100644 research/wave11-12-review-20261112/REVIEW.md create mode 100644 research/wave11-12-review-20261112/check.py create mode 100644 research/wave11-12-review-20261112/checkpoint.json create mode 100644 research/wave11-12-review-20261112/evidence.json diff --git a/research/wave11-12-review-20261112/README.md b/research/wave11-12-review-20261112/README.md new file mode 100644 index 0000000..2986cae --- /dev/null +++ b/research/wave11-12-review-20261112/README.md @@ -0,0 +1,13 @@ +# Independent correction review + +The [review](REVIEW.md) and [replay script](check.py) independently check gravity commit `e5d7ee813e33de03c91857e48a2d55a0caf55506`. The reviewed source hashes are frozen in [evidence.json](evidence.json). The script accepts later commits that preserve those source bytes. + +Run with NumPy, SciPy and SymPy installed: + +```sh +python3 research/wave11-12-review-20261112/check.py . +``` + +This reproduces numerical and source-level controls. It does not establish a physical seed-formation mechanism or validate the repository's wider claims. The nine inherited manifest discrepancies recorded in the review describe the reviewed commit, before the separate checksum repair. + +The wider [research synthesis](https://github.com/Foundation-0/physics0/pull/18) connects the field, mechanical and observational results and identifies what would justify further research. diff --git a/research/wave11-12-review-20261112/REVIEW.md b/research/wave11-12-review-20261112/REVIEW.md new file mode 100644 index 0000000..4775f1f --- /dev/null +++ b/research/wave11-12-review-20261112/REVIEW.md @@ -0,0 +1,111 @@ +# Independent review of the Wave 11 and Wave 12 corrections + +**Disposition: no blocking scientific or implementation issue found in the correction commit.** The revised radial times, growth conventions, curved-background normalization and qualified origin statements are supported. This review does not validate a seed population, filament-collapse solution, universe-creation mechanism or the repository's other research claims. + +Reviewed on 12 November 2026 by gpt-forge using gpt-6-astra, independently of the gpt-6.1-sol implementation author. The exact reviewed commit is [`e5d7ee813e33de03c91857e48a2d55a0caf55506`](https://github.com/Foundation-0/gravity/commit/e5d7ee813e33de03c91857e48a2d55a0caf55506). [evidence.json](evidence.json) records hashes of all 11 changed files. No author files were changed during review. + +The seven submitted controls pass. Both certificate generators reproduce their checked-in files byte for byte. Each of the ten changed files covered by `SHA256SUMS` matches its entry. A repository-wide hash check also exposes nine inherited mismatches, described below. The whole manifest is not certified as current. + +## Independent radial calculation + +The submitted force law is + +```text +g(r) = (GM/r^2) / [1-exp(-sqrt(GM/a0)/r)] + f GM/r^2. +``` + +The extra ratio `f` is a prescribed point-mass contribution. The RAR formula is being extended to a static spherical infall benchmark. Its empirical use for rotation-supported galaxies does not itself establish the dynamics of high-redshift filaments. The [original RAR paper](https://arxiv.org/abs/1609.05917) concerns galaxy rotation curves. + +An independent elementary integral removes the need for the author's numerical inner potential quadrature. Define `x=r/r0`, `q=sqrt(g_b(r0)/a0)` and the dimensionless potential drop `U=integral_x^1 g(r0 s)/g_b(r0) ds`. Then + +```text +U(x) = (1+f)(1/x-1) + + log[(1-exp(-q/x))/(1-exp(-q))]/q. +``` + +This follows by substituting `y=q/s` in the excess-force integral and using `integral dy/(exp(y)-1)=log(1-exp(-y))`. Differentiation returns the specified force exactly. The logarithm is evaluated with `log1p` and `expm1` in the review script. + +[check.py](check.py) integrates the remaining time integral with `x=1-u^2`, independently of the author's `x=cos(theta)^2` transformation and nested Simpson implementation. It also solves the radial acceleration equation directly, stopping at `r/r0=1e-7` before the point singularity. + +| Prescribed force | Analytic-potential quadrature, Myr | Submitted quadrature, Myr | Direct radial ODE, Myr | +|---|---:|---:|---:| +| Newtonian baryons | 384.823182090 | 384.823182090 | 384.823182084 | +| Constant-a0 RAR | 200.075137583 | 200.075137583 | 200.075137578 | +| Hubble-a0 RAR | 121.716676614 | 121.716676614 | 121.716676609 | +| Constant-a0 RAR plus assigned mass | 127.156204634 | 127.156204634 | 127.156204632 | + +The two quadrature methods differ by at most 4.33e-13 fractionally. The radial ODE differs by at most 4.25e-11, including its omitted final radial segment. These controls support the corrected values and reject the superseded outer-acceleration shortcut for the same force laws. + +The Newtonian limit agrees with `pi sqrt(r0^3/(GM))/(2 sqrt(2))`, including added mass ratios 0.1, 5.36 and 20. The high-acceleration RAR limit also agrees with Newtonian infall. Maximum fractional discrepancies are 2.23e-16 for these controls. + +In exact deep MOND, `g=V^2/r` gives `t=sqrt(pi/2) r0/V`. The old shortcut is smaller by the factor `sqrt(pi)/2=0.8862269255`. For RAR values `q=0.01,0.001,0.0001`, the exact-potential times divided by that deep-MOND limit are 0.9959942, 0.9995847 and 0.9999576. The submitted 512-interval quadrature agrees with the corresponding RAR times to better than 7.83e-8 fractionally. + +These are convergence and force-law controls. They do not test gas pressure, angular momentum, changing mass, an external field or cosmological evolution during infall. The corrected prose and certificate state the fixed-point-mass scope. + +## Growth and retained mass + +For fully ionized composition with helium mass fraction `Y`, the electron-scattering opacity relative to pure hydrogen is `1-Y/2`. At fixed Eddington ratio one, + +```text +t_growth = log(Mfinal/Minitial) [epsilon/(1-epsilon)] kappa c/(4 pi G). +``` + +For a Schwarzschild thin disk with the usual zero-torque inner-boundary benchmark, the circular-orbit energy at `r_ISCO=6GM/c^2` is `sqrt(8/9)`. Therefore `epsilon=1-sqrt(8/9)=0.0571909584`. Efficiency 0.10 is a distinct benchmark. Maintaining either efficiency throughout growth is an imposed history. + +The independently computed times for `100 M_sun` to `1.5e9 M_sun` are: + +| Efficiency | Pure H, Myr | Primordial H/He, Myr | +|---|---:|---:| +| 0.10 | 827.078411 | 725.761306 | +| `1-sqrt(8/9)` | 451.536466 | 396.223249 | + +The implementation correctly identifies 451.536 Myr as pure hydrogen. The earlier audit's prose had associated it with primordial composition. The new correction note explicitly fixes that labeling error. None of these conditional clocks establishes an available fuel supply, seed-formation time or realized spin and duty history. + +With `mdot=epsilon_ref dotM_in c^2/L_Edd`, energy conservation gives + +```text +dotM_BH = dotM_in - L/c^2 + = (mdot-epsilon_ref lambda) L_Edd/(epsilon_ref c^2). +``` + +The new denominator follows this convention. It reduces to the old `(1-epsilon_ref) mdot` expression where `lambda=mdot`. Above saturation the old expression no longer conserves the assigned inflow and radiative loss. For `mdot=3,5`, the corrected growth times are 273.775666 and 161.232877 Myr. Outflows remain omitted as stated. + +The [Onorato et al. source](https://arxiv.org/html/2609.31835v1) supports the reported point masses and luminosity ratios. It also reports about 0.3 dex virial-mass scatter, 0.36 dex Eddington-ratio scatter and a conservative 100 km/s systemic-velocity uncertainty. + +The revised claims avoid turning present luminosity into a lifetime history or the point velocity into an inclination measurement. Lensing and hardening remain unresolved. + +## Curvature, sources and origin statements + +The curved CPL helper now uses `Omega_DE=1-Omega_m-Omega_k` in its radiation-free approximation. Independent evaluations recover `H^2(1)/H0^2=1`. Direct root finding reproduces the quoted future turnaround scales. Those roots remain conditional on the chosen continuation of the equation of state. They are not fitted predictions of DESI. + +The corrected author attribution is verified against [arXiv:2610.09987v2](https://arxiv.org/abs/2610.09987v2): Manuel Urueña Palomo authored the cited Machian proposal. The new text presents the induction partition as algebra rather than a derived physical mechanism. + +The [AeST Hamiltonian paper](https://arxiv.org/html/2307.15126v3) gives a constraint that vanishes on the constraint surface in equation 43a. This supports the correction from an unconditional identity to a constraint on physical states. It supplies no universe-production dynamics or general global-energy observable. + +For `P=K2[(Q/Q0)^2-1]^2`, direct differentiation gives + +```text +P_QQ = (4 K2/Q0^2) [3(Q/Q0)^2-1]. +``` + +Thus the minimal homogeneous scalar kinetic curvature is negative at `Q=0` and degenerate at `abs(Q/Q0)=1/sqrt(3)`. This calculation alone does not settle stability after full AeST mixing. The correction retains that qualification. + +Varying the source-free homogeneous action `integral dt a^3 P(phidot)` gives conservation of `a^3 P_Q`. An initially zero current does not become the proposed nonzero branch charge through algebraic branch selection. A derivative-only operator such as `(partial phi)^2 F_mu_nu F^mu_nu` is invariant under constant scalar shifts. Shift symmetry therefore does not forbid every pair-conversion interaction, and no conversion rate follows from the allowed operator alone. + +The revised claims remove the inference from baryon-to-photon ratio to an initial annihilated-pair fraction. They also distinguish total nonlinear halo mass from black-hole seed mass, and isolated Peters inspiral clocks from a hardening history or stochastic gravitational-wave population prediction. + +## Provenance limit and reproduction + +No formal proof file changes in this commit. The existing false Wave12 chirp-mass bound and its separate PR #10 repair are explicitly identified. This review does not assert a Lean build pass. + +The global `SHA256SUMS` file has nine mismatches in files outside this change: `lakefile.toml`, `verify_all.py`, `wave5_unified_forces_stochastic_qm.py`, `formal/verify_exact_rational_proofs.py`, `formal/GravityClaims.lean`, `formal/Wave5StochasticForces.lean`, `formal/Wave6Convergence.lean`, `formal/Wave7ThresholdAudit.lean` and `results/wave4_unified_certificates.json`. + +For each mismatch, both the expected hash and actual file bytes are unchanged from the parent commit. They are inherited repository provenance debt, not a numerical defect introduced by these corrections. All ten changed-file entries match. Any broader claim that the entire manifest passes would be false. + +Reproduce this review with NumPy, SciPy and SymPy: + +```sh +python3 check.py /path/to/checkout-at-e5d7ee813e33de03c91857e48a2d55a0caf55506 +``` + +The script requires the changed source files to match the exact reviewed commit. Later commits may add the review bundle without changing those files. It runs the independent controls and replays the submitted tests and certificate checks. It writes only its own `evidence.json`. No new physical model or parameter search is needed to close this correction review. diff --git a/research/wave11-12-review-20261112/check.py b/research/wave11-12-review-20261112/check.py new file mode 100644 index 0000000..8bb773e --- /dev/null +++ b/research/wave11-12-review-20261112/check.py @@ -0,0 +1,202 @@ +#!/usr/bin/env python3 +"""Independent numerical and provenance controls for the frozen Wave corrections. + +Usage: python3 check.py /path/to/reviewed/gravity/checkout +Only the directory containing this reviewer script receives output. +""" +from pathlib import Path +import hashlib, importlib.util, json, math, re, subprocess, sys +import numpy as np +import sympy as sp +from scipy.integrate import quad, solve_ivp +from scipy.optimize import brentq + +HERE = Path(__file__).resolve().parent +ROOT = Path(sys.argv[1]).resolve() if len(sys.argv)>1 else Path.cwd() +EXPECTED_HEAD = 'e5d7ee813e33de03c91857e48a2d55a0caf55506' + +def git(*args): + return subprocess.check_output(['git', '-C', str(ROOT), *args]) + +def sha(data): + return hashlib.sha256(data).hexdigest() + +git('cat-file', '-e', EXPECTED_HEAD+'^{commit}') +changed = git('diff', '--name-only', EXPECTED_HEAD+'^', EXPECTED_HEAD).decode().splitlines() +assert not any(name.startswith('formal/') for name in changed) +source_hashes = {name: sha((ROOT/name).read_bytes()) for name in changed} +for name, actual in source_hashes.items(): + assert actual == sha(git('show', EXPECTED_HEAD+':'+name)), name + +def module(name): + spec = importlib.util.spec_from_file_location(name, ROOT/(name+'.py')) + result = importlib.util.module_from_spec(spec) + spec.loader.exec_module(result) + return result + +w11 = module('wave11_machian_pairing_unification') +w12 = module('wave12_cosmic_dawn_quasar_collapse') + +# Integrate an analytic potential using a different endpoint substitution from +# the submission. The RAR excess has an elementary antiderivative. +def exact_potential_time(mass, radius, a0=None, added=0.): + g0 = w12.G*mass/radius**2 + q = None if a0 is None else math.sqrt(g0/a0) + start_force = 1+added+(0. if q is None or q>700 else 1/math.expm1(q)) + def integrand(u): + if u == 0.: + return math.sqrt(2/start_force) + if u == 1.: + return 0. + x = 1-u*u + drop = (1+added)*u*u/x + if q is not None and q < 700: + drop += math.log1p(-math.expm1(-q*u*u/x)/math.expm1(q))/q + return 2*u/math.sqrt(2*drop) + value, err = quad(integrand, 0., 1., epsabs=2e-13, epsrel=2e-13, limit=500) + return math.sqrt(radius/g0)*value, err + +def radial_ode_time(mass, radius, a0=None, added=0.): + g0 = w12.G*mass/radius**2 + q = None if a0 is None else math.sqrt(g0/a0) + def derivative(t, state): + x, vel = state + enhancement = 1. if q is None else 1/(-math.expm1(-q/x)) + return [vel, -(enhancement+added)/(x*x)] + def stop(t, state): + return state[0]-1e-7 + stop.terminal = True + stop.direction = -1 + sol = solve_ivp(derivative, (0., 2.), [1., 0.], events=stop, method='DOP853', + rtol=2e-12, atol=2e-14, max_step=.001) + assert sol.success and len(sol.t_events[0]) == 1 + return math.sqrt(radius/g0)*sol.t_events[0][0] + +mass, radius = 5e10*w12.M_SUN, 30*w12.KPC +g0 = w12.G*mass/radius**2 +c32 = w12.audit_c32_two_branch_condensate_and_phonon_collapse() +# Reconstruct the unrounded trapping fraction from the submitted spectrum, +# because the certificate deliberately stores its rounded presentation value. +sigma = w12.build_sigma_r_evaluator() +scale = brentq(lambda r:sigma(r, w12.Z_PAIR)-1.686, 1e-4, 1., xtol=1e-15) +rho = w12.OMEGA_M*w12.RHO_CRIT0 +mstar = 4*math.pi/3*(scale*w12.MPC)**3*rho +hz = w12.H0_SI*w12.e_hubble(w12.Z_PAIR) +dispersion = (10*w12.G*mstar*hz)**(1/3)/1000/math.sqrt(2) +fraction = 1-(dispersion/(250/math.sqrt(2)))**2 +added = w12.OMEGA_C/w12.OMEGA_B*fraction +cases = [('Newton', None, 0.), ('constant_a0_RAR', w12.A0_EMP, 0.), + ('Hubble_a0_RAR', w12.C_SI*hz/(2*math.pi), 0.), + ('RAR_plus_assigned_mass', w12.A0_EMP, added)] +radial = [] +for label, a0, extra in cases: + exact, quadrature_error = exact_potential_time(mass, radius, a0, extra) + submitted = w12.radial_point_mass_fall_time(mass, radius, a0, extra) + ode = radial_ode_time(mass, radius, a0, extra) + assert abs(submitted/exact-1) < 2e-10 + assert abs(ode/exact-1) < 1e-9 + radial.append({'case':label, 'analytic_potential_Myr':exact/w12.MYR, + 'submitted_Myr':submitted/w12.MYR, 'radial_ODE_Myr':ode/w12.MYR, + 'submitted_relative_error':submitted/exact-1, + 'ODE_relative_error':ode/exact-1, + 'dimensionless_outer_quadrature_error_estimate':quadrature_error}) + +newton = math.pi/(2*math.sqrt(2))*math.sqrt(radius**3/(w12.G*mass)) +newton_controls=[] +for extra in (0., .1, 5.36, 20.): + exact = newton/math.sqrt(1+extra) + result = w12.radial_point_mass_fall_time(mass, radius, additive_mass_ratio=extra) + assert abs(result/exact-1) < 2e-14 + newton_controls.append({'added_mass_ratio':extra,'relative_error':result/exact-1}) +high_acceleration = w12.radial_point_mass_fall_time(mass, radius, g0/1e8) +assert abs(high_acceleration/newton-1) < 2e-14 +deep=[] +for q0 in (.01, .001, .0001): + a0 = g0/q0**2 + V = (w12.G*mass*a0)**.25 + deep_limit = math.sqrt(math.pi/2)*radius/V + exact, _ = exact_potential_time(mass, radius, a0) + numerical = w12.radial_point_mass_fall_time(mass, radius, a0, intervals=512) + deep.append({'q0':q0,'RAR_over_exact_deep_MOND':exact/deep_limit, + 'submitted_over_exact_RAR':numerical/exact, + 'old_shortcut_over_exact_deep_MOND':math.sqrt(math.pi)/2}) +assert abs(deep[-1]['RAR_over_exact_deep_MOND']-1) < 5e-4 +assert all(abs(row['submitted_over_exact_RAR']-1) < 5e-7 for row in deep) + +# Independent opacity and mass-energy derivation. kappa_HHe/kappa_H=1-Y/2. +tedd = w12.SIGMA_T*w12.C_SI/(4*math.pi*w12.G*w12.M_P)/w12.MYR +efolds = math.log(1.5e9/100) +growth=[] +for epsilon in (.1, 1-math.sqrt(8/9)): + for label, opacity_ratio in [('pure_H',1.),('primordial_H_He',1-.245/2)]: + time = efolds*epsilon/(1-epsilon)*tedd*opacity_ratio + growth.append({'epsilon':epsilon,'composition':label,'time_Myr':time}) +seed = w12.audit_c31_salpeter_seed_and_clustering_wall()['seed_duty_cycle_audit_for_J1602A_1p5e9_Msun'] +assert abs(seed['popIII_100Msun_req_time_primordial_H_He_eps0p10_Myr']-growth[1]['time_Myr'])<.0005 +assert abs(seed['popIII_100Msun_req_time_pure_H_Schwarzschild_Myr']-growth[2]['time_Myr'])<.0005 +assert abs(seed['popIII_100Msun_req_time_primordial_H_He_Schwarzschild_Myr']-growth[3]['time_Myr'])<.0005 +slim=[] +for mdot in (.1,1.,2.,3.,5.,10.): + lam = mdot if mdot<=2 else 2*(1+math.log(mdot/2)) + retained = mdot-.1*lam + exact = efolds*.1*tedd/retained + submitted_lam, submitted_time = w12.slim_disk_growth_time_myr(efolds,mdot) + assert abs(submitted_time/exact-1)<2e-15 and submitted_lam==lam + slim.append({'mdot':mdot,'lambda':lam,'retained_dimensionless_rate':retained,'time_Myr':exact}) + +curvature=[] +for ok in (-.01,-.004,-.001,0.,.01): + assert abs(w11.closed_cpl_hubble_squared(1.,ok)-1)<1e-14 + row={'Omega_k':ok,'H2_at_a1':w11.closed_cpl_hubble_squared(1.,ok)} + if ok<0: + turn=brentq(lambda aa:w11.closed_cpl_hubble_squared(aa,ok),2.,2000.) + row['turnaround_scale_factor']=turn + row['matter_curvature_limit']=w11.OMEGA_M/abs(ok) + curvature.append(row) + +u, K2, Q0, Q = sp.symbols('u K2 Q0 Q', positive=True) +P=K2*((Q/Q0)**2-1)**2 +current=sp.diff(P,Q) +curvature_polynomial=sp.diff(P,Q,2) +assert sp.simplify(curvature_polynomial.subs(Q,0)+4*K2/Q0**2)==0 +assert sp.simplify(curvature_polynomial.subs(Q,Q0/sp.sqrt(3)))==0 +assert current.subs(Q,0)==0 +assert sp.simplify(current.subs(Q,-Q)+current)==0 +# For L=a^3 P(phidot), Euler-Lagrange gives d(a^3 P_Q)/dt=0. +# Derivative-only portals are unchanged by a constant shift of phi. + +def manifest_map(data): + return {line.split(None,1)[1]:line.split(None,1)[0] for line in data.decode().splitlines() if line.strip()} +current_manifest=manifest_map((ROOT/'SHA256SUMS').read_bytes()) +parent_manifest=manifest_map(git('show',EXPECTED_HEAD+'^:SHA256SUMS')) +inherited_mismatches=[] +for name, expected in current_manifest.items(): + actual=sha((ROOT/name).read_bytes()) + if actual!=expected: + assert name not in changed + parent_actual=sha(git('show',EXPECTED_HEAD+'^:'+name)) + assert parent_actual==actual and parent_manifest[name]==expected + inherited_mismatches.append(name) +for name in changed: + if name!='SHA256SUMS': assert current_manifest[name]==source_hashes[name] + +checks=[] +for args in [['-m','unittest','test_wave11_12_corrections.py'], + ['wave11_machian_pairing_unification.py','--check'], + ['wave12_cosmic_dawn_quasar_collapse.py','--check']]: + result=subprocess.run([sys.executable,*args],cwd=ROOT,capture_output=True,text=True) + assert result.returncode==0 + stable_output = re.sub(r'Ran (\d+) tests? in [\d.]+s', + r'Ran \1 tests (elapsed time omitted)', result.stdout+result.stderr) + checks.append({'command':'python3 '+' '.join(args),'returncode':result.returncode, + 'output':stable_output}) +for name, expected in source_hashes.items():assert sha((ROOT/name).read_bytes())==expected +evidence={'reviewed_commit':EXPECTED_HEAD,'source_sha256':source_hashes, + 'radial_comparisons':radial,'newtonian_controls':newton_controls, + 'high_acceleration_relative_error':high_acceleration/newton-1, + 'deep_MOND_controls':deep,'growth_counterexamples':growth,'slim_disk':slim, + 'curvature_controls':curvature,'polynomial_curvature':str(curvature_polynomial), + 'formal_files_unchanged':True,'inherited_global_manifest_mismatches':inherited_mismatches, + 'all_changed_manifest_entries_match':True,'author_checks':checks} +(HERE/'evidence.json').write_text(json.dumps(evidence,indent=2)+'\n') +print(json.dumps({key:value for key,value in evidence.items() if key not in ('source_sha256','author_checks')},indent=2)) diff --git a/research/wave11-12-review-20261112/checkpoint.json b/research/wave11-12-review-20261112/checkpoint.json new file mode 100644 index 0000000..355b2ad --- /dev/null +++ b/research/wave11-12-review-20261112/checkpoint.json @@ -0,0 +1,18 @@ +{ + "status": "complete; no blocking issue in correction commit; inherited global manifest mismatches recorded", + "reviewed_commit": "e5d7ee813e33de03c91857e48a2d55a0caf55506", + "files": [ + { + "path": "REVIEW.md", + "sha256": "8aed8f4fbbbd8862bf29c70fe8f429d09c7c9c0897b77f431beabf30ea44d0a4" + }, + { + "path": "check.py", + "sha256": "eab27a99be552ffe9ea0db7cbcc9c54a7ed1fc9f17d88709ffba518b46085865" + }, + { + "path": "evidence.json", + "sha256": "691e9a7fbccaafc339db65a20b43b4dc655b92d94bc8591f1489ab8f9bcf99a4" + } + ] +} diff --git a/research/wave11-12-review-20261112/evidence.json b/research/wave11-12-review-20261112/evidence.json new file mode 100644 index 0000000..a7fff52 --- /dev/null +++ b/research/wave11-12-review-20261112/evidence.json @@ -0,0 +1,212 @@ +{ + "reviewed_commit": "e5d7ee813e33de03c91857e48a2d55a0caf55506", + "source_sha256": { + "CHANGELOG.md": "b95e0b1b867a876758f4751a0806bce54325f95d2ad8f4e25d801e0850e1a000", + "CLAIMS.md": "efd6e9acba39ec3dd86356df22edacc3d17761e205ac11420798de52290924a9", + "README.md": "ea84eb79d2ab891fd5b151b6e0b3ee72fafda601d7b4e1c16157298c8da001ce", + "RESEARCH_NOTEBOOK_AND_REASONING.md": "7d678663f6689639039445d7fe972109a3234c7cd8220601b43c435431214c64", + "SHA256SUMS": "45d6b2826527f882800f2e1fa51896693c8e84de413970e8675d778cd370aa57", + "WAVE11_12_CORRECTIONS.md": "16edeec60b7a6ac3aab790021fab866273e95f508da8fb7ddebd5d6a78ff8bf1", + "results/wave11_machian_pairing_certificates.json": "fed7d58b8959cc68073bbf2020c7dca895fb4bac0b07adb9d95c3bee56d1c94b", + "results/wave12_cosmic_dawn_quasar_certificates.json": "78b988c2a6a83f23a8dc637626fdc63b9122579c2c3e37eaf9365deb2539ca79", + "test_wave11_12_corrections.py": "4a69d34265fe05e33f17a5afde1b529f508b4405753a300909d27ce41f14441c", + "wave11_machian_pairing_unification.py": "88dd0f9827b2fa29292597c976695ce559d135d6d4867f59cde0d0de37426bda", + "wave12_cosmic_dawn_quasar_collapse.py": "53cb171ed423ab98509f62017b68d2cce935c9b6468cd9e5f098a02b465c99b0" + }, + "radial_comparisons": [ + { + "case": "Newton", + "analytic_potential_Myr": 384.8231820895629, + "submitted_Myr": 384.82318208956303, + "radial_ODE_Myr": 384.8231820843983, + "submitted_relative_error": 2.220446049250313e-16, + "ODE_relative_error": -1.342070898857628e-11, + "dimensionless_outer_quadrature_error_estimate": 3.774758283725532e-15 + }, + { + "case": "constant_a0_RAR", + "analytic_potential_Myr": 200.07513758299433, + "submitted_Myr": 200.07513758290773, + "radial_ODE_Myr": 200.07513757782954, + "submitted_relative_error": -4.3287595730134854e-13, + "ODE_relative_error": -2.5814350657071827e-11, + "dimensionless_outer_quadrature_error_estimate": 1.695310558602614e-13 + }, + { + "case": "Hubble_a0_RAR", + "analytic_potential_Myr": 121.7166766140901, + "submitted_Myr": 121.71667661408623, + "radial_ODE_Myr": 121.71667660892543, + "submitted_relative_error": -3.186340080674199e-14, + "ODE_relative_error": -4.243205786735871e-11, + "dimensionless_outer_quadrature_error_estimate": 1.9595436384634013e-14 + }, + { + "case": "RAR_plus_assigned_mass", + "analytic_potential_Myr": 127.15620463376732, + "submitted_Myr": 127.15620463374627, + "radial_ODE_Myr": 127.15620463172033, + "submitted_relative_error": -1.6542323066914832e-13, + "ODE_relative_error": -1.609823385706477e-11, + "dimensionless_outer_quadrature_error_estimate": 6.877831637552845e-14 + } + ], + "newtonian_controls": [ + { + "added_mass_ratio": 0.0, + "relative_error": 2.220446049250313e-16 + }, + { + "added_mass_ratio": 0.1, + "relative_error": 2.220446049250313e-16 + }, + { + "added_mass_ratio": 5.36, + "relative_error": 0.0 + }, + { + "added_mass_ratio": 20.0, + "relative_error": 2.220446049250313e-16 + } + ], + "high_acceleration_relative_error": 2.220446049250313e-16, + "deep_MOND_controls": [ + { + "q0": 0.01, + "RAR_over_exact_deep_MOND": 0.9959942052496246, + "submitted_over_exact_RAR": 1.000000000000037, + "old_shortcut_over_exact_deep_MOND": 0.8862269254527579 + }, + { + "q0": 0.001, + "RAR_over_exact_deep_MOND": 0.9995847463313614, + "submitted_over_exact_RAR": 1.000000000024938, + "old_shortcut_over_exact_deep_MOND": 0.8862269254527579 + }, + { + "q0": 0.0001, + "RAR_over_exact_deep_MOND": 0.9999575875686578, + "submitted_over_exact_RAR": 1.0000000782144847, + "old_shortcut_over_exact_deep_MOND": 0.8862269254527579 + } + ], + "growth_counterexamples": [ + { + "epsilon": 0.1, + "composition": "pure_H", + "time_Myr": 827.0784108740284 + }, + { + "epsilon": 0.1, + "composition": "primordial_H_He", + "time_Myr": 725.7613055419598 + }, + { + "epsilon": 0.057190958417936644, + "composition": "pure_H", + "time_Myr": 451.5364663110016 + }, + { + "epsilon": 0.057190958417936644, + "composition": "primordial_H_He", + "time_Myr": 396.2232491879039 + } + ], + "slim_disk": [ + { + "mdot": 0.1, + "lambda": 0.1, + "retained_dimensionless_rate": 0.09, + "time_Myr": 8270.784108740285 + }, + { + "mdot": 1.0, + "lambda": 1.0, + "retained_dimensionless_rate": 0.9, + "time_Myr": 827.0784108740284 + }, + { + "mdot": 2.0, + "lambda": 2.0, + "retained_dimensionless_rate": 1.8, + "time_Myr": 413.5392054370142 + }, + { + "mdot": 3.0, + "lambda": 2.8109302162163288, + "retained_dimensionless_rate": 2.7189069783783673, + "time_Myr": 273.775666363764 + }, + { + "mdot": 5.0, + "lambda": 3.83258146374831, + "retained_dimensionless_rate": 4.616741853625169, + "time_Myr": 161.2328766448419 + }, + { + "mdot": 10.0, + "lambda": 5.218875824868201, + "retained_dimensionless_rate": 9.47811241751318, + "time_Myr": 78.5357397123941 + } + ], + "curvature_controls": [ + { + "Omega_k": -0.01, + "H2_at_a1": 1.0, + "turnaround_scale_factor": 31.518261152893515, + "matter_curvature_limit": 31.518261152893515 + }, + { + "Omega_k": -0.004, + "H2_at_a1": 1.0, + "turnaround_scale_factor": 78.79565288223378, + "matter_curvature_limit": 78.7956528822338 + }, + { + "Omega_k": -0.001, + "H2_at_a1": 1.0000000000000002, + "turnaround_scale_factor": 315.1826115289351, + "matter_curvature_limit": 315.1826115289352 + }, + { + "Omega_k": 0.0, + "H2_at_a1": 1.0 + }, + { + "Omega_k": 0.01, + "H2_at_a1": 1.0 + } + ], + "polynomial_curvature": "4*K2*(3*Q**2/Q0**2 - 1)/Q0**2", + "formal_files_unchanged": true, + "inherited_global_manifest_mismatches": [ + "lakefile.toml", + "verify_all.py", + "wave5_unified_forces_stochastic_qm.py", + "formal/verify_exact_rational_proofs.py", + "formal/GravityClaims.lean", + "formal/Wave5StochasticForces.lean", + "formal/Wave6Convergence.lean", + "formal/Wave7ThresholdAudit.lean", + "results/wave4_unified_certificates.json" + ], + "all_changed_manifest_entries_match": true, + "author_checks": [ + { + "command": "python3 -m unittest test_wave11_12_corrections.py", + "returncode": 0, + "output": ".......\n----------------------------------------------------------------------\nRan 7 tests (elapsed time omitted)\n\nOK\n" + }, + { + "command": "python3 wave11_machian_pairing_unification.py --check", + "returncode": 0, + "output": "CHECK OK (byte-identical): wave11_machian_pairing_certificates.json sha256_canonical=4786fa9822b8b99edfd2c11ac922ca589065403e4881f5bf72d415481644692b\n" + }, + { + "command": "python3 wave12_cosmic_dawn_quasar_collapse.py --check", + "returncode": 0, + "output": "CHECK OK (byte-identical): wave12_cosmic_dawn_quasar_certificates.json sha256_canonical=40a770d70d19ec3a9d7e9e5e770d0454d94595f7e7abb75e92efa351672354c9\n" + } + ] +}