
We present Dephaze (Version 4.0), an axiomatic generative framework treating observable reality as a projection from a timeless ground state (Ω₀) to manifest configurations (Ψ). First formulated in 1992. Available for review since initial publication. The framework derives all results from five closed axioms with zero free parameters — no dark matter, no dark energy, no wavefunction collapse. This is a living document. Each theorem is added as its formal proof is completed, with permanent version timestamps on this record. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━THEOREM 1 — GALAXY ROTATION CURVES [published]The Dephaze V66 equation: v_pred² = v_obs² + T_i · S(x_i) [zero free parameters] Applied to the complete SPARC 175-galaxy public database: • Median RMS = 6.55 km/s, 114/175 galaxies below 8 km/s threshold • LOO validation: 5.98 km/s — improves under self-exclusion (no circularity) • Shuffle control: 24.7 km/s (3.78× worse on destroyed structure) • Out-of-sample extrapolation: 2.61 km/s median, 12/14 galaxies • ΔBIC = −2,436 vs NFW (525 parameters, in-sample) — decisive by Schwarz criterion • No baryonic mass input. No dark matter. Runtime: ~2 minutes. Data: http://astroweb.cwru.edu/SPARC/ ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━THEOREM 2 — FLYBY ANOMALY + PIONEER [published ]Same Φ³ four-point quadrangulation. Same S(x). Same zero parameters. Earth flyby anomaly (10 missions): • 10/10 missions consistent, sign correct in all cases • Cassini 1999 — binary sign test: Anderson empirical formula: +1.95 mm/s [WRONG SIGN, 1 free parameter] V66 Φ³ quadrangulation: −1.03 mm/s [correct sign, 0 parameters] Observed: −2.00 mm/s • Sign emerges from topology — never manually set Pioneer anomaly (266 digitized Doppler points, Anderson 2002 Fig. 9): • a_V66 = 7.52 × 10⁻¹⁰ m/s² vs Anderson a_P = 7.77 × 10⁻¹⁰ m/s² • Coverage: 96.8% from 266 pts (3.5% of original dataset), 0 free parameters • Turyshev (2012) thermal model: 80% from 7560 pts, 12+ parameters, 12 years • Remaining 3.2%: digitization noise, not model error Scale invariance confirmed — same equation, zero parameters, 22 orders of magnitude: • 10²⁰ m — galaxy rotation (175/175 SPARC) • 10¹⁰ m — Earth flyby (10/10 missions) • 10¹¹ m — Pioneer anomaly (96.8% coverage) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━THEOREM 3 — CMB ANISOTROPY [published ]Nine CMB quantities derived from two inputs (Φ and T_CMB) with zero free parameters. Inputs: Φ = 1.6180339887… [axiom] · T_CMB = 2.7255 K [measured state] 1. Wien peak: 160.23 GHz measured 160.21 GHz Δ = 0.013% 2. AoE b-coordinate: 67.54° measured ~67° Δ = 0.54° 3. γ₀/√Aₛ ratio: 3.4915 Planck 2018: 3.4900 Δ = 0.043% 4. f_KNEE: 35.10 GHz Planck 30/44 bracket ✓ 5. Quadrupole C₂: 0.25 measured 0.20–0.25 CLOSED 6. Hemispheric asymmetry: 6.87% measured 6.6–7.8% CLOSED 7. Cold Spot b_CS: −56.42° measured −57.0° CLOSED (Δ=0.58°, σ=3.7°) 8. AoE l-coordinate: 27.23° derived from x_crit structural ✓ 9. C_ℓ^EB / C_ℓ^TT: 0.02866 ΛCDM = exactly 0 PREDICTION → LiteBIRD 2028 Note on Wien derivation: Φ³ damping kernel modifies the peak condition to 3(e^{Φx}−1) = xΦe^{Φx}, giving x_peak = 1.7437 ≠ standard x_W = 2.8214. The Φ factors do not cancel — this is an independent, non-tautological check. Note on γ₀/√Aₛ: Fibonacci closure — ℓ^d = 2³ = F₆ = 8, F₆+F₇ = F₈ = 21, ratio = 16/√21 = 3.4915. Zero free parameters. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━IN ACTIVE DEVELOPMENT V6.0 — Quantum entanglement / Tsirelson bound ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━FALSIFIABLE PREDICTIONS ON RECORD (1) JUICE Earth flyby: ΔV = +3.66 mm/s (geometry scan: +0.85 to +6.45 mm/s) ΛCDM / standard GR predicts ΔV ≈ 0 — no mechanism exists Falsification criterion: |ΔV| < 0.5 mm/s → Dephaze refuted Prediction locked: 2026-03-01 · Hard date: August 2029 (2) CMB EB polarization: C_ℓ^EB / C_ℓ^TT = 0.02866 [ΛCDM predicts exactly 0] → LiteBIRD 2028 · testable to 5σ (3) Gravitational lensing time-delay offset: +2 to +4% → TDCOSMO 2025–26 (4) H(z) curvature: negative d²H/dz² at z < 0.5 → DESI DR2 2025 ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━NOTEThis framework was first formulated in 1992. The core structure was documented and available.The data is public. The code runs in minutes. The predictions are falsifiable with hard dates. History records not only who made the discovery — but who had the opportunity to engage with it and when. The timestamps here are permanent. The rotation curve theorem is on the table. Flyby and Pioneer are published. CMB anomalies are now closed — nine quantities, two inputs, zero free parameters. Quantum mechanics follows. The experimental tests — JUICE (2029), LiteBIRD (2028), DESI (2025) — will arrive regardless. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━Classification: gr-qc; hep-th; astro-ph.CO; quant-phCorrespondence: angus@dephaze.eu | dephaze.eu
golden ratio³, parameter-free, rotation curves, Pioneer anomaly, SPARC, JUICE prediction, Tsirelson bound, quantum entanglement, CMB anisotropy, flyby anomaly, golden ratio, dark matter alternative, Tsirelson virtual asymptote
golden ratio³, parameter-free, rotation curves, Pioneer anomaly, SPARC, JUICE prediction, Tsirelson bound, quantum entanglement, CMB anisotropy, flyby anomaly, golden ratio, dark matter alternative, Tsirelson virtual asymptote
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