Density Field Dynamics (DFD) is a scalar refractive-index theory of gravity defined by the postulate that spacetime is flat but permeated by a scalar field ψ (x, t) establishing an optical refractive index n = exp (ψ). Light propagates according to the eikonal of the optical metric ds̃² = −c²dt²/n² + dx², while matter responds to the effective potential Φ = −c²ψ/2. The optical scalar sector ψ governs clock rates, refraction, and quasi-static dynamics; a transverse-traceless radiative sector hTTij carries gravitational waves — both derived as irreducible components of the same zero-mode parent tensor on ℂP² × S³. DFD reproduces all classic weak-field tests of general relativity (γ = β = 1; all PPN preferred-frame parameters exactly zero as a theorem), gravitational waves at speed c with two tensor polarizations, and MOND-like galactic phenomenology with μ (x) = x/ (1+x) and a₀ = 2√α cH₀ derived from S³ topology. v4. 0 is the completed two-volume release: the main paper (348 pp: axioms, theorems with proofs, derived predictions, falsifiers, and a revision ledger), a companion volume of extended derivations (76 pp), and a full reproducibility package containing the complete LaTeX source and every verification script. Reproduce the headline numbers in one command. Unzip the package and run python3 reproduce. py from the package root (Python ≥ 3. 8; no installation — pure standard library; pip install camb optionally unlocks the live cosmology gate). In about one minute it recomputes live — not table-lookups — six headline results, each checked against the value printed in the paper, exiting 0 only if all pass: (0) the fine-structure constant itself — α⁻¹ = 137. 03599985 from the closed-form spectral truncation at kₘax = 60, 0. 0056 ppm from CODATA, with the neighboring truncations missing by ~1. 7%; (1) the χ dark-matter abundance Ω_χh² = 0. 1182 from finite SU (2) level-60 Chern–Simons modular data, through 8 internal gates including presentation-invariance and two rival-preparation exclusions; (2) H₀ = α28. 5/tP = 72. 0897 km/s/Mpc from CODATA constants alone, zero cosmological inputs; (3) the locked CKM chain |Vcb| = 0. 04033, |Vₜd/Vₜs| = 0. 2109, ΔMₛ/ΔMd = 33. 2; (4) the εK chain, reproducing the paper's honestly-booked −13% inherited-|Vcb| deficit — a tension the suite prints rather than hides; (5) with CAMB, a live forward computation of σ₈ = 0. 8194 / S₈ = 0. 7844 at the derived parameter set. The closing output maps the deeper layers: READMEVERIFICATION. md (a referee's guide to every script and every caveat), the CAMB-based cosmology engine (CMB TT, BAO, θ*, lensing, joint likelihoods), the DFD-vs-ΛCDM head-to-head likelihood pipeline, the complete look-elsewhere/trials-factor audit, and the lattice-QCD program with source and run logs. Both LaTeX volumes rebuild from the package. Principal results (each traces to a numbered theorem; discrete inputs and selections are labeled as such in the text): (1) Fine-structure constant: α⁻¹ = 137. 036 from the microsector spectral action on ℂP² × S³ with truncation kₘax = 60, matching experiment at the 5. 6×10⁻⁹ fractional level (0. 0056 ppm residual). New in v4. 0: a trials-factor audit (Appendix CE) enumerates the theory's entire admissible discrete choice space (8. 0×10⁹ addresses across 15 dimensions, hostile enlargements included) and proves the α-ladder infeasibility theorem: the expected number of false α matches as good as observed across the full space is ~0. 007 — landscape scanning cannot produce this match by chance. (2) Electroweak sector: sin²θW = 3/13 = 0. 2308 from the anomaly-constrained gauge partition (0. 2%) ; αₛ (MZ) = 0. 1187 (0. 8σ, PDG 2024) ; Higgs scale v = MP · α⁸ · √ (2π) = 246. 09 GeV (0. 05%) — with mₜ = (1−α) v/√2 = 172. 74 GeV (0. 57σ). (3) Dark sector, derived (headline change from v3. 3): the χ field — the Chern–Simons transgression mode of the same microsector — is a derived cold, collisionless component with mass 5. 09 eV and abundance Ω_χh² = 0. 1182 computed forward from finite modular data (−1. 5σ against Planck), with uniqueness theorems excluding rival preparations. Where ΛCDM inserts a fitted dark-matter density, DFD computes one. The CMB third acoustic peak, cluster lensing (including the Bullet), and structure growth run on this derived component; the acoustic scale θ* employs one explicitly-labeled fitted screen amplitude — the paper documents the exhaustive derivable-amplitude search that failed to force it. (4) Gravity and cosmology confrontations (all pipelines shipped): H₀ = 72. 09 km/s/Mpc from Gℏ H₀²/c⁵ = α⁵⁷ (0. 3σ from JWST/SH0ES; the 9. 4σ Planck discrepancy is interpreted as ψ-screen optical bias) ; the cosmological-constant hierarchy ρc/ρP = (3/8π) α⁵⁷ spans the 122. 7 orders with no tuning; S₈ = 0. 784 resolving the lensing tension; Planck CMB lensing passed at +2. 06σ; BOSS DR12 full-shape P (k) statistically indistinguishable from Planck-ΛCDM at k ≤ 0. 15 h/Mpc under a maximally frozen protocol (acceptable but disfavored, Δχ² = +21. 5, at k ≤ 0. 20 — reported as computed, with a neutrino-consistency cross-check) ; galaxy–galaxy lensing theorem: ΔΣ = √ (Mb a₀/G) / (4R), equivalently a lensing radial-acceleration relation gₗens = √ (gbar a₀) at the same a₀ as rotation curves — passing the KiDS-1000 GAMA isolated-lens test at 0. 4σ (full covariance, zero parameters) ; cluster five-factor calibration: 14/16 systems within a ±10% window — 15/16 within 1σ and 16/16 within 2σ of published mass errors; deep-field deflection α̂ = 2π√ (GM a₀) /c² (v4. 0 corrects a factor-2 error in earlier drafts — the corrected value is the one KiDS data confirm). (5) Flavor and CP: nine charged-fermion mass exponents derived (texture prefactors partly fitted, labeled) ; CKM Wolfenstein integers (λ, A) = (31, 108) × α from ℂP² line-bundle cohomology with the apex fixed by the Euler-projection postulate — γ = 66. 31° (its own falsifier), sin2β = 0. 719, J = 2. 97×10⁻⁵ (−1. 2σ) ; honest pulls printed: λ +1. 8σ, |Vcb| −1. 75σ, εK −14. 7%, ΔMₛ/ΔMd −5. 2% (FLAG-ξ-limited). Strong CP theorem: θ̄ = 0 to all loop orders, no axion. Baryogenesis: |ηB| ≃ 0. 206 α⁴ = 5. 8×10⁻¹⁰ — the magnitude forced with no CP-odd source (4% from observation; the sign rides the same discrete orientation bit as the arrow of time). Neutrinos (TM1): Δm² spectrum matching NuFIT (p = 0. 99), Σm_ν = 61. 5 meV, m_β = 9. 15 meV, m_ββ ∈ 0. 13, 2. 33, 3. 26, 5. 45 meV. (6) Quantum sector: the single-particle Schrödinger equation is derived as an algebraic identity of the master equation (the fixed-N interacting form likewise), with the quantum phase i identified with the ℂP² Kähler structure; the imports are explicitly inventoried — the value of ℏ, the variable-N field-theoretic map, and the Cl (4, 0) enlargement supplying the Dirac β — with the Born rule conditional and single-outcome selection not derived (a residue shared by all interpretations). The derived Schrödinger–Newton nonlinearity is an experimental discriminator (levitated-optomechanics coherence). (7) Statistical accounting, adversarially audited (new in v4. 0): Appendix CE prints a four-tier no-coincidence ladder with the most hostile accounting first — not statistically significant under a full selection charge; ≈3. 7–4. 1σ (conservative) to ≈5. 0σ (moderate) under hostile menu accounting; ≈5. 0–5. 5σ conditional on the forcing theorems as stated — plus the unconditional α-ladder theorem above. An earlier 5. 5–7. 1σ headline is explicitly retired in the text, with the audit trail shipped in the package. Falsifiers (near-term, no rescaling freedom): Belle II |Vcb| ceiling; LISA zero tensor-memory; CMB-S4 Nₑff = 3. 044; KATRIN-II/Project-8 m_β = 9. 15 meV; the a₀ (z) sign (unique against both ΛCDM and MOND) ; 2PN solar light-bending c₂ = 4π = (16/15) × GR; Euclid-era lensing-RAR amplitude at ±0. 1 dex; proton-decay null; the γ = 66. 31° apex. DFD introduces no continuous fit parameters; every discrete selection is enumerated in the trials-factor audit; one scale measurement fixes all dimensionful quantities via α⁵⁷. Independent verification is invited: the package is designed to make every claim checkable, and discrepancy reports are welcome. What's New in v4. 0 Result v3. 3 Status v4. 0 Status Dark sector "CMB without dark matter": peak ratio from baryon loading, peak location from ψ-lensing Derived χ component: the Chern–Simons transgression mode of the same microsector is a cold, collisionless field of mass 5. 09 eV with abundance Ω_χh² = 0. 1182 computed forward from finite SU (2) level-60 modular data (−1. 5σ vs Planck), with uniqueness theorems excluding rival preparations. Third peak, cluster lensing, and structure growth run on the derived component — no fitted dark-matter density anywhere Statistical accounting (anti-numerology) Not present Trials-factor audit (App. CE): the full admissible discrete choice space enumerated (8. 0×10⁹ addresses, 15 dimensions, hostile enlargements included) ; α-ladder infeasibility theorem — expected false α matches as good as observed ≈ 0. 007 across the whole space; four-tier no-coincidence ladder printed worst-case-first; the earlier 5. 5–7. 1σ headline explicitly retired Quantum sector Not in abstract Schrödinger equation derived as an algebraic identity of the master equation; quantum phase i = ℂP² Kähler structure; imports explicitly inventoried (ℏ value, variable-N map, Cl (4, 0) β ansatz) ; Born rule conditional; single-outcome selection honestly not derived; Schrödinger–Newton nonlinearity flagged as an experimental discriminator Galaxy–galaxy lensing ESD shape test proposed Theorem: ΔΣ = √ (Mb a₀/G) / (4R), equivalently a lensing radial-acceleration relation gₗens = √ (gbar a₀) at the same a₀ as rotation curves; passes the KiDS-1000 GAMA isolated-lens test at 0. 4σ (full covariance, zero free parameters) Deep-field deflection α̂deep = 4π√ (GM a₀) /c² Corrected: α̂deep = 2π√ (GM a₀) /c² (a factor-2 error found by internal re-derivation audit; the corrected value is the one the lensing data confirm) CKM sector (λ, A,
Gary Alcock (Sat,) studied this question.