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/H_0 yieldinga_0 = c·H_0/(2π) = 1.082 × 10^(-10) m/s² (within 10% of empirical MOND scale), and4D vortex quantization n_X ∈ 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·β_Madelung·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:β_Madelung ≈ 0.040 is fixed by the dimensional structure of the Madelung self-couplingRG running, intermediate between the electroweak (β_W ~ 0.01-0.02) and QCD (β_s ~ 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 (a_0 isfixed by H_0). 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.