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 = wbrane (t) via a Dirichlet-type condition (dot XW |_Σ = c) ; E = mc² then arises as a geometric identity from the self-contraction |Uᵢnflow|² = c². 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 + ΦN/c² + β ΦN²/c⁴ and PPN metric g₀0 = -1 + 2U - 2β U². Key observational results carried over from prior versions: PPN constraint |β - 1| 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 Cᵏ 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.