Hyperbrane Relativity: Universe Objects, OCS Geometry, Koide 45 degree Cone, Hubble Tension, and Bullet Cluster Item 4 (Main Paper, Revised 2026-05-11)

This is the revised version of the Hyperbrane Relativity (HBR) Master Edition main paper, building on the V41. 4 published baseline (DOI 10. 5281/zenodo. 20102858) with comprehensive reviewer-internal articulation patches. Hyperbrane Relativity is a geometric extension of General Relativity in which the observable universe is the W-axis 3D cross-section of a flat 4D Euclidean bulk, with the brane translating along the W-axis under a Dirichlet boundary condition. The present revision (130 pages) consolidates the V41. 4 articulations and adds the following structural contributions: (1) Target-internal mechanism for galactic flat rotation curves: a W-helical vortex line at the galactic core with push-restore balance (Madelung quantum potential and Gross-Pitaevskii pressure versus W-axis tension force) reproducing the V32 Paper A LOCKED tanh form on the SPARC 171/175 ensemble at the bit-for-bit level (αBTFR = 3. 56 ± 0. 11, χ²ν = 1. 29, NGC 3198 v_∞ = 159. 5 km/s). (2) Observer-side distance-pipeline scale-lens correction: a four-tier distance ladder (L1 Anchor f (0) ≡ 1 via Gaia parallax through L4 Cosmological f → fₘax ≈ 1. 25) with explicit operational connection to the OCS framework (incoming light as the Observation regime channel of the OCS Trichotomy CN12; observer location at OCS-axis 4 anchor convention). (3) Three-way re-evaluation of Newton, MOND, and HBR on the SPARC 175 ensemble: HBR-full (target-internal mechanism plus observer-side distance correction) attains 91. 9% pass rate within ±30% with zero per-galaxy free parameters, while the MOND universal-a₀ claim is directly falsified by a non-zero log a₀ᵃpparent versus log D slope (+0. 0335 to +0. 0448 dex/dex). The HBR-derived geometric acceleration a₀ = cH₀/ (2π) = 1. 082 × 10^-10 m/s² is 90. 2% of the MOND canonical value (Milgrom 1983) and 71. 0% of the SPARC empirical median; the ~30-40% systematic offset is recorded as an open structural diagnosis. (4) Foundational driving principle (P2 articulation): energy distribution on the bulk's W-axis 3D cross-section sources the brane-section flow that drives matter dynamics, with the W⁻ Birth Energy inflow (supply side) and the brane-section vortex flow (response side) as two aspects of the same single mechanism. The hyperbrane is identified as the bulk's W-axis 3D cross-section itself. (5) HBR-Virial theorem reformulation without gravitational attraction (Open Problem O12): 2⟨T⟩ = ⟨Uₚush-restore⟩ replacing the standard 2⟨T⟩ = -⟨Ugrav⟩, with implications for the Zwicky 1933 cluster mass estimate that historically motivated the dark-matter hypothesis. The revision also incorporates explicit honest framing of three reviewer-internal critiques: (i) the linear log-running βMadelung sub-leading correction degrades on the SPARC 175 ensemble (Open Problem O14, new) ; (ii) the relationship between the target-internal and observer-side articulations is structurally unresolved at the present layer (Open Problem O15, new) ; (iii) the a₀ systematic offset diagnosis (Open Problem O13, new). The two articulation-layer constraints (βMadelung ≈ 0. 040, α ≈ 0. 48) are partially downgraded from "structural parameters" to "articulation-layer constraints pending V42 first-principle derivation". Strategic compatibility: V32 Paper A LOCKED numerics preserved bit-for-bit (RL-7) ; V35 mathematical tier excerpts preserved bit-for-bit; sixteen ideological-redline (RL) constraints holding and eleven compromise-warning (W) criteria not triggered. The mathematical foundation in the V35 Tier 1-6 framework is preserved as a companion paper (DOI 10. 5281/zenodo. 20103309). Subjects: General Relativity, Modified Gravity, Galactic Dynamics, Dark Matter, Dark Energy, Hubble Tension, Madelung Quantum Hydrodynamics, Bulk-Brane Cosmology, MOND comparison, SPARC galaxy rotation curves.