Foundation-0/gravity -- Reproducible MOND, Superfluid-DM & Group/Cluster Scaling Audits

Attribution & Review Disclosure: Written by an AI agent (Gemini, Google, via orda-aska for Foundation-0); not yet reviewed by a person. Remediated in Wave 8 following an independent external audit (0311496) by a Cursor / Grok 4.7 reviewer. Licenses: Code under Apache-2.0; documentation and numerical results under CC-BY-4.0.

Scope & Honest Scientific Framing

This repository is not a derivation of a new fundamental theory of gravity, dark matter, or quantum mechanics, and its scripts are not parameter-free. Its durable content consists of:

1. Reproducible textbook and model evaluations (COMPUTED (KNOWN-FRAMEWORK)): Zero-dependency Python 3 calculations of Milgrom's (1983) acceleration scale a_0 ~ c H_0 / (2*pi) and BTFR scaling, the Berezhiani & Khoury (2015) P(X) propto |X|^(3/2) superfluid-phonon scaling, the Hui et al. (2017) Schrodinger-Poisson ground-state soliton (M r_{1/2} = 3.925 hbar^2 / (G m^2)), 3D AQUAL external-field quadratures (Bekenstein & Milgrom 1984), a spherical Bogoliubov-p-Laplacian BVP solver at chosen xi_coh = 0.20 kpc, relativistic sterile-fermion freeze-out checks (including the 7/8 fermionic radiation factor, g_*S,dec, and non-relativistic transition redshift z_nr), and a seeded Nelson (1966) stochastic harmonic-oscillator check.
2. Empirical fits & astrophysical benchmark confrontations (EMPIRICAL-FIT / COMPUTED):
   • Wave 3 (wave3_empirical_audit.py): Fits to the 14 SPARC RAR bin means (RARbins.mrt, 2,630 rotation points; Lelli et al. 2017, where s/sqrt(N) bin errors prefer d_s = 0.94 +/- 0.02 when a_0 is profiled), 8 SPARC kinematic BTFR bins, and 4 stacked KiDS-1000 weak-lensing bins (129,027 isolated lenses using H_0 = 73 km/s/Mpc; Mistele et al. 2024, Delta BIC(free - beta=4) = -0.44 on the 12-bin combined fit).
   • 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): 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.

Cross-repository convergence research

The convergence research collection connects this repository with fractals, physics0 and astr0. It preserves nine exploratory reports, source ledgers, mathematical probes and independent agent reviews.

The collection includes a test specification for nonlinear AeST collapse, distinctions between interference and readable records, a lattice mechanics comparison and methods for combining astronomical evidence. Its scope and next tests are explicit. No nonlinear AeST simulation or new galaxy-data fit is claimed.

Cosmic dawn audit

The cosmic dawn research note distinguishes a quasar-pair observation from Wave 10 collapse-scale assumptions. A standard-library probe checks the native calculation, high-wavenumber sensitivity and failed root brackets. The note also states what an extra-dimension test would need to predict.

Repository Layout & Verification Commands

The root audit scripts use only the Python 3 standard library. The separate convergence research probes declare their NumPy and SymPy dependencies in their own reproduction instructions. The research value assessment pins its NumPy and SciPy dependencies in its own bundle requirements. Each certificate file in results/*.json embeds a sha256_canonical field equal to the sha256 checksum of json.dumps(payload_without_sha_field, sort_keys=True, separators=(",", ":")) computed by the generator script that writes it (this is a deterministic content checksum for reproducibility, not a cryptographic signature). Raw file digests are recorded in SHA256SUMS.

Script / Config	Output / Target	Verification Command
verify_all.py	results/certificates.json (C-01..C-07)	python3 verify_all.py --check
formal/verify_exact_rational_proofs.py	results/exact_rational_proof_certificates.json	python3 formal/verify_exact_rational_proofs.py
wave3_empirical_audit.py	results/wave3_empirical_certificates.json (C-08)	python3 wave3_empirical_audit.py --check
wave4_unified_field_solver.py	results/wave4_unified_certificates.json (C-09..C-11)	python3 wave4_unified_field_solver.py --check
wave5_unified_forces_stochastic_qm.py	results/wave5_forces_stochastic_certificates.json (C-12..C-17)	python3 wave5_unified_forces_stochastic_qm.py --check
wave6_convergence_unification.py	results/wave6_convergence_certificates.json (C-18..C-20)	python3 wave6_convergence_unification.py --check
wave7_group_cluster_threshold_audit.py	results/wave7_group_cluster_certificates.json (C-21..C-22)	python3 wave7_group_cluster_threshold_audit.py --check
wave9_scale_convergence_audit.py	results/wave9_scale_convergence_certificates.json (C-23..C-24)	python3 wave9_scale_convergence_audit.py --check
wave10_covariant_jeans_unification.py	results/wave10_covariant_jeans_certificates.json (C-25..C-27)	python3 wave10_covariant_jeans_unification.py --check
wave11_machian_pairing_unification.py	results/wave11_machian_pairing_certificates.json (C-28..C-30)	python3 wave11_machian_pairing_unification.py --check
wave12_cosmic_dawn_quasar_collapse.py	results/wave12_cosmic_dawn_quasar_certificates.json (C-31..C-33)	python3 wave12_cosmic_dawn_quasar_collapse.py --check
lakefile.toml + lean-toolchain	GravityClaims, Wave5StochasticForces, Wave6Convergence, Wave7ThresholdAudit, Wave10JeansDerivation, Wave11MachianZeroEnergy, Wave12QuasarCollapse	lake build
SHA256SUMS	Raw file SHA-256 digests of scripts, Lean files, and JSON outputs	sha256sum -c SHA256SUMS

Documentation Index

• acceleration-evolution/ -- Pending independent reproduction. Testable constant versus H-tracking acceleration scales, reproducible predictions, and a comparison with published MUSE-DARK fitted curves. No new raw-data fit or detection claim. Includes the known inverse of annihilation and requirements for a separate cosmological-collision conjecture.

• CLAIMS.md -- Audited ledger of C-01 through C-33 with explicit inputs, literature precedence, Lean lemma scope, and downgraded epistemic status tags.

• METHODS_AND_PLAYBOOK.md -- Numerical methods, parameter assumptions, error-model caveats (M-01..M-10), and canonical checksum table.

• RESEARCH_NOTEBOOK_AND_REASONING.md -- Complete reasoning trail, rejected operator dead ends, tangential WHIM/entropy-floor realizations, Cosmic-Dawn quasar confrontation, and next-agent handoff queue.

• CHANGELOG.md -- Reconciled chronological history across Waves 1-12 matching CLAIMS.md and code identifiers.

AeST response benchmark and independent checks

The AeST response benchmark constructs allowed field preparations on a specified expanding background and a flat-space control. It includes the canonical map, executable response checks and a bounded pressure-closure comparison.

A separate Astra agent reproduced the scalar constraint and kinetic structure from an independent ADM action. A separately declared slow-subspace test and its independent five-field replay are complete. The simple zero-pressure closure still fails for this specified benchmark.

Research value assessment

The 12 November assessment records the Wave 11/12 audit, bounded research directions, reproducible controls and stopping gates. Its separate NumPy/SciPy dependencies are pinned in the bundle requirements.