Hyperbrane Relativity: A Geometric Extension of General Relativity with Born Rule and Observation-Contact Separation Appendices (HBR Complete Master Edition V27)

Hyperbrane Relativity (HBR) describes the observable universe as a dynamical 3-brane uniformly translating in the -W direction within a flat 4D Euclidean bulk. The empirical 3D light speed c is identified with the gate-inflow speed at the dimensional boundary Σ = {w = w_brane(t)} via a Dirichlet-type condition (dot X^W |_Σ = c); E = mc^2 then arises as a geometric identity from the self-contraction |U_inflow|^2 = c^2. Lorentz invariance is treated as an emergent brane symmetry, not a fundamental postulate. The framework yields a single-parameter modification β of general relativity through the field equation G_μν + β H_μν = 8π T_μν, with weak-field expansion Φ = 1 + Φ_N/c^2 + β Φ_N^2/c^4 and PPN metric g_00 = -1 + 2U - 2β U^2. Key observational results carried over from prior versions: PPN constraint |β - 1| < 10^-4 (Cassini), SPARC 171-galaxy MCMC fit with χ²/ν = 1.29 (V26), and falsifiable predictions including a sub-leading 1/r^3 phase correction detectable by Einstein Telescope / Cosmic Explorer at SNR > 30. V27 adds two new appendices that complement the dynamical Born rule derivation in the main text: (A) a Gleason-type structural origin of the Born rule via measure uniqueness on κ-space, using the bulk-induced inner product as the only non-trivial geometric input and deriving the quadratic probability measure through a Cauchy functional equation; and (B) a rigorous formulation of the Observation-Contact Separation (OCS) principle via harmonic analysis, separating qualitative suppression (Riemann-Lebesgue lemma) from the quantitative leading rate (sinc form for rectangular overlap, polynomial decay for C^k overlap), with a three-regime classification: contact (|Δκ| L ≪ 1), transition (|Δκ| L ~ 1), and observation (|Δκ| L ≫ 1). The κ-selection rule is grounded as the Noether consequence of bulk W-translation invariance, sampled by the brane through the OCS sinc resonance. Released under CC-BY-4.0. PDF includes both English and Japanese editions.