Hyperbrane Relativity V41.4: Universe Objects, OCS Geometry, and the Unified Geometric Origin of Gravity, Dark Matter, and the Cosmological Constant — Main Paper

Hyperbrane Relativity (HBR) is a geometric extension of general relativity in which theobservable universe is modelled as a dynamical 3-brane uniformly translating along a fourthspatial axis (W) of a 4-dimensional Euclidean bulk. This V41. 4 main paper presents thecomplete framework with Madelung quantum-fluid foundation (Why Madelung? Four HBR-specificrequirements), four-axis OCS structure (W-distance / cognitive / scale / time), branegeodesic principle (Proposition T2 with mass-independent equation of motion), 120-decadecosmological-constant pseudo-problem articulation, scale lensing and aggregate vortexmechanism for galaxy rotation, Hubble-scale brane thickness L_* = c/H₀ yieldinga₀ = c·H₀/ (2π) = 1. 082 × 10^ (-10) m/s² (within 10% of empirical MOND scale), and4D vortex quantization nX ∈ ℤ as the mathematical content of "one-thing one-universe" (一物一宇宙, ichi-mon'ichi-uchuu). The V41. 4 RG-running articulation of the BTFR sub-leading correction yields the SPARC-measured slope α = 4 - 4·βMadelung·log (M/M_*) = 4 - 4· (0. 040) · (2. 78) = 3. 56 in agreementwith the V32 Paper A LOCKED value α = 3. 56 ± 0. 11 at the 0. 1% level. This is not a fit: βMadelung ≈ 0. 040 is fixed by the dimensional structure of the Madelung self-couplingRG running, intermediate between the electroweak (βW ~ 0. 01-0. 02) and QCD (βₛ ~ 0. 1) gauge couplings. A 10-galaxy SPARC representative sample yields HBR-native single-galaxy predictionswithin ±15% of observation for 7 of 10 galaxies, without any free parameter (a₀ isfixed by H₀). NGC 3198 HBR-native prediction v_∞ = 159. 5 km/s deviates by +6% fromthe canonical Begeman 1989 value ~150 km/s and is within 1σ of the V32 Paper A fit152 ± 22 km/s. The four reviewer critical issues identified in V40 (Euclidean-vs-null connection, T2 equivalence-principle algebra, T7 MOND sign reversal, free function over-fitting) are all resolved. The cosmological-constant 120-decade hierarchy is articulated asa category mistake (QFT vacuum density vs Madelung bulk fluid density are independentphysical quantities, not a fine-tuning relocation). The Bullet Cluster lensing-vs-X-rayoffset is qualitatively articulated as the Contact-regime gas (ram-pressure decelerated) versus Observation-regime aggregate-vortex coherence (cross-W, ram-pressure unimpeded) distinction. The Yamamoto-internal terminology ontology (Birth Energy / バースエネルギー, EternalGeneration / エターナル生成, one-thing one-universe / 一物一宇宙, no-attractive-force /引力なし, etc. ) is preserved in bilingual notation with a complete Glossary (Appendix N). The Flow-Memory-Self trinity ontology articulates kinship with process philosophy (Whitehead 1929), autopoiesis (Maturana & Varela 1980), dissipative structures (Prigogine), and causal sets (Sorkin 1991). The mathematical foundation (V35 Madelung Tier 1-6 integration) is articulated in aseparate Mathematical Companion paper (Yamamoto 2026 Companion). V41. 4 is at the revise-and-resubmit preparation level for PRD / JCAP / CQG.