gravity

Open, machine-checkable exploration into unifying gravitation and apparent dark matter by extrapolating quantum-mechanical and quantum-condensate scaling laws across hierarchical levels of abstraction.

Disclosure & Attribution: Initial Wave-1 and Wave-2 derivations, zero-dependency verification solvers, and numerical certificates written on 2026-11-11 by an AI agent (Gemini, Google, operating via orda-aska for Foundation-0), building on Foundation-0/fractals and Foundation-0/physics0; not yet reviewed by a person.

License: Code under Apache-2.0; documentation, proofs, and certificates under CC-BY-4.0.

Quickstart (Zero External Dependencies)

Every algebraic scaling law, boundary-value ODE shoot, phase-space inequality, and 3D external-field quadrature in this repository runs in under 1 second using only the Python 3 standard library (math, json, hashlib):

python3 verify_all.py
python3 verify_all.py --check
python3 wave3_empirical_audit.py
python3 wave3_empirical_audit.py --check

Canonical certificate output: results/certificates.json (SHA-256: 040a757f5b4a01e735d1c4a55bca639e79bf8c64ef92588ce290d931f614320a).

Summary of Findings & Epistemic Ledger

Following Foundation-0 claim discipline (KNOWN, PROVEN, VERIFIED, NEW-COMPUTATION, CONJECTURE — full ledger in CLAIMS.md):

| ID | Result / Finding | Tag | Certified Metric / Invariant | Status & Empirical Meaning | | :— | :— | :— | :— | :— | | C-01 | Coordinate-Fractal vs. Field-Gradient Dichotomy | PROVEN / VERIFIED | Coord-fractal ($D_f = 2$): $\beta_{\text{BTFR}} = 2.0186$, RAR RMS $= 0.6234\text{ dex}$ | Rules out universal-length coordinate-fractal gravity against SPARC ($\beta \approx 3.9\text{–}4.0$); requires gradient-driven scaling. | | C-02 | Unique $d_s = 1$ ($q = 3/2$) Condensate Fixed Point | PROVEN / VERIFIED | At $d_s = 1$: $d\ln v/d\ln r = -0.0147$, $\beta_{\text{BTFR}} = 3.8945$, RAR RMS $= 0.0096\text{ dex}$ | Generalizing Son & Wingate (2006) to spectral dimension $d_s$ ($\mathcal{L} \propto |X|^{1+d_s/2}$) proves $d_s = 1$ uniquely locks flat $v(r)$ and $M_b \propto v^4$. | | C-03 | Gravitational-Atom Soliton Invariant & Outer Falloff | VERIFIED | $\hat{\varepsilon}0 = 0.64953399$, $M{\text{sol}} r_{1/2} = 3.9251\,\hbar^2/(G m_\psi^2)$, outer slope $-0.4994$ | Reproduces Hui et al. (2017) ground state; proves wave pressure alone resolves inner cusps, not outer flatness. | | C-04 | Single-Boson 1 Mpc vs. Bullet Cluster Phase-Space Inversion | PROVEN / NEW-COMPUTATION | $m_{\max}(1\text{ Mpc NFW}) = 1.0306\text{ eV} < m_{\max}(1\text{ Mpc iso}) = 1.9379\text{ eV} < m_{\min}(\text{Bullet}) = 2.3015\text{ eV}$ | Empty mass window for any single thermalized boson trying to stay condensed at $1\text{ Mpc}$ (Mistele et al. 2024) while melting in the Bullet Cluster (Clowe et al. 2006). | | C-05 | Two-Tier Hybrid Condensate + Normal Sector | NEW-COMPUTATION / CONJECTURE | $m_L = 0.05\text{ eV}$ ($2\%$ DM, $\mathcal{N}{1\text{Mpc}} = 9432.5$) + $m_H = 3.0\text{ eV}$ ($98\%$ DM, $\mathcal{N}{\text{Bullet}} = 0.8867$) | Resolves C-04: light mode sustains Mpc phonon coherence while heavy mode melts in clusters ($g_{\text{Bullet}} = 2.161\,a_0$ screens phonons). | | C-06 | Discrete Scale-Invariant Soliton Tower Smoothness Bound | NEW-COMPUTATION | Ripple $\pm 0.036\%$ ($b=2$), $\pm 4.561\%$ ($b=6$), $\pm 6.084\%$ ($b=7$) | Self-similar mass towers $m_k = m_0 b^{-k}$ (Arvanitaki et al. 2010) must satisfy $b \le 6.2$ to avoid $>5\%$ log-periodic rotation ripples. | | C-07 | External-Field Rollover & Wide-Binary UV-Crossover Test | VERIFIED / NEW-COMPUTATION | Cosmic EFE rollover $R_{\text{EFE}} = 834.8\text{ kpc}$ ($e=0.01$); Solar WB velocity boost $+18.31\%$ ($\mu_1$) vs. $+3.16\%$ ($\mu_2$) | Sharp UV crossover $\mu_2(x) = x/\sqrt{1+x^2}$ cuts Solar wide-binary velocity boost at $e_{\text{MW}} = 1.81\,a_0$ by $5.8\times$ toward Gaia DR3 bounds. | | C-08 | Empirical Scale-Flow Convergence onto d_s* = 1.00 | VERIFIED / NEW-COMPUTATION | 2,630 SPARC RAR points ($\hat{d}s = 0.94 \pm 0.02$) and 139,027 KiDS 1-Mpc lenses ($\hat{\beta} = 4.00 \iff d_s^{\text{IR}} = 1.00$, $\chi^2 = 0.634$) confirm scale-flow convergence onto $d_s^* = 1$, rejecting $D_f = 2$ ($\Delta\text{BIC} = +402.59$) and bounding cosmic EFE to $e{\text{cosmic}} \le 0.0160$. |

Triage on Scientific & Civilizational Significance

Repository Layout

Wave Discoveries Summary (C-01 through C-20)