Hyperbrane Relativity: A Geometric Extension of General Relativity — Master Edition V29.2

Summary V29.2 is the second peer-review hardening of the V29 cycle (V29 → V29.1 → V29.2), applying 14 editorial patches (12 planned + P13 emergency gate-c framing restoration + P14 cover-version bump) surfaced by a 4-reviewer external-review synthesis (Gemini + Grok + ChatGPT + Claude) of V29.1. No physics changes; physics is identical to V29.1. The principal scientific addition (inherited from V29) is a substantive measurement of source-dependent partial BBP saturation in M87* and Sgr A*, both confidence intervals excluding the kinematic ceiling Phi_min/Phi_inf = 1 and being mutually non-overlapping — a quantitative HBR-specific prediction at falsifier-grade precision. What's new in V29.2 vs V29.1 P1: All ?? cross-references resolved (3-pass compile, 0 undefined refs in EN+JP). P2: V28 narrative residue swept → "V28-V29.1 synthesis" wording. P3: SPARC MCMC text canonicalized to 15000-step Paper-A locked values (≥64 walkers, 15000 steps, ≥1000 burn-in). P4: Bibliography rebuilt — Issaoun2019 added; JP citations aligned with -jp suffix bibitems. P5: Abstract toned — G_munu+beta H_munu definite-equation claim weakened to "effective parameterization at weak field"; "one-scale theory" weakened to "candidate one-scale theory"; Delta w SI-determination disclaimer added. P6: "No event horizons" expression unified → "no Phi=0 stagnation surface in matter-sustained regions" / "horizon formation is disfavored within the present effective Phi-model". P7: Lorentz framing reframed — new section in Part XIV positions HBR's 4D Euclidean form as a Euclidean-embedding interpretation of Lorentz kinematics, recovered via Wick rotation theta → i phi (NOT a literal SO(4) replacement of SO(3,1)). Numerical example u=0.9c, v=0.5c → 0.561c (literal Euclid) vs 0.727c (Einstein) included. P8: Theorem 2 reframed as conditional — renamed to "Positivity of Phi in matter-sustained regions (conditional)"; conditional footnote enumerates 3 logical gaps; rigorous PDE proof using Gilbarg-Trudinger Theorem 3.5 deferred to V30. P9: "Submitted to Physical Review D" → "prepared for submission to Physical Review D". P10: Strong-expression sweep (V29.1 patch 4 residue) — "dark matter is unnecessary" → "particle dark-matter halos are not required for the SPARC fits considered here"; "three-body problem is solved" → "three-body trajectories regularized in the tested regime". P11: Bibliography V29.2 entry added. P12: EN+JP recompile + Zenodo bundle (3-pass each, 0 undefined refs/cites). P13 (emergency): Gate-speed-c framing restored to V28 canon. V29.1 had reintroduced V28-prohibited expressions treating c as if derived from gate dynamics ("rate-converts to inflow at gate speed c", "(gate self-contraction, frame-independent)", JP "ゲート速度 c", "バルク視点ではゲート出力速度"). HBR canonical convention: c is an empirical invariant imported from measurement, NOT derived; the gate inflow rate is fixed at c via the Dirichlet boundary condition ẊW|Σ=c; the identity |Uinflow|² = c² is a kinematic consequence of this boundary condition, NOT a derivation of c's invariance. Fixed at 24 sites: EN 10 (front matter, Part 1, Part 13/14/15 V27 ontological notes) + JP 14 (front_jp, parts_jp/part1, part13/14/15, plus Hubble constant section). P14 (cover oversight): Edition string on cover/titlepage bumped V29.1 → V29.2 (4 sites: titlepage EN/JP + pdftitle EN/JP). Without this, the V29.2 PDFs would still display "V29.1" on page 1. Authoritative numerical values EHT forward fit (Phase B-1) Quantity M87* Sgr A* chi^2/dof at theta_lit 20.494 22.885 chi^2/dof at theta_best 5.233 5.870 improvement 3.92x 3.90x Phi_min/Phi_inf best 0.301 0.736 Phi_min/Phi_inf 95% CI (n=500) [0.272, 0.342] [0.666, 0.835] inclination best (lit) 21.7 deg (17 deg) 36.7 deg (30 deg) M_factor best (M) 0.892 (5.80e9 M_sun) 0.955 (3.92e6 M_sun) Both Phi_min/Phi_inf 95% CIs exclude the kinematic ceiling Phi=1; the two sources' CIs are mutually non-overlapping (M87* upper 0.342 << Sgr A* lower 0.666). SPARC rotation curves (15000-step MCMC LOCKED, Paper A) SPARC quantity Value Galaxies 171 median chi^2/nu 1.31 DeltaAIC(HBR-MOND) -147.3 DeltaAIC(HBR-NFW) -4.3 HBR preferred over MOND 89% (153/171) HBR preferred over NFW 74% (126/171) Versioning chain (Concept-DOI) V26 → V27 → V28 (10.5281/zenodo.19869381) → V29 (10.5281/zenodo.20021551, withdrawn) → V29.1 (10.5281/zenodo.20028176) → V29.2 (this record, 10.5281/zenodo.20031326).