Hyperbrane Relativity: Universe Objects, OCS Geometry, Koide 45° Cone, Hubble Tension, and Bullet Cluster Item 4 (Main Paper, V41.5.1 patch revision 2026-05-11)

Hyperbrane Relativity (HBR) is a geometric extension of general relativity in which the observable universe is a uniformly translating three-brane embedded in a flat four-dimensional Euclidean bulk. Every physical entity is represented as a universe object — a four-tuple consisting of an anchored thread, Contact region, Observation region, and scale parameter. Lorentz invariance emerges as a brane symmetry, with the empirical speed of light c fixing the W-flux Dirichlet boundary condition. This document is the V41. 5. 1 patch revision (144 pages) of V41. 5 (DOI 10. 5281/zenodo. 20116019, 2026-05-11), introducing five submission-readiness modifications. The mathematical companion paper (DOI 10. 5281/zenodo. 20103309) is unchanged. The framework rests on a Madelung-fluid foundation ψbulk = √ρbulk · exp (i Sbulk / ℏ) for the bulk, which provides a common geometric language for dark-matter-like, cosmological-constant, and MOND-like phenomena: dark matter is read as the projection of ordinary matter on adjacent W-phases through the Observation envelope; the cosmological constant is read as the overflow above a finite brane absorption capacity Pbraneᵐax; and MOND-like flat rotation curves emerge as the cross-section of collective Madelung-fluid aggregate vortices. Within this framework the paper articulates three new results: (i) the Koide relation Q ≈ 2/3 reformulated as a geometric 45° cone identity on the family-internal R³ vector of the extended 5-tuple universe object; (ii) an explicit HBR-internal articulation of the Hubble tension through the W-extent saturation parameter α ≈ 0. 48; and (iii) a complete three-component decomposition of the Bullet Cluster (gas/galaxies/aggregate vortex) with four distinguishing predictions. The V32 SPARC ensemble fit (α = 3. 56 ± 0. 11, χ²_ν = 1. 29, 171 galaxies) is preserved bit-for-bit and re-interpreted as an aggregate-vortex phenomenon. Six falsifiable predictions (P1–P6) are presented. The framework extends rather than replaces general relativity in the regimes in which the latter has been tested. The five V41. 5. 1 modifications are: (1) Terminology tone-down — seven internally-developed terms (Birth Energy, Eternal Generation, Fountain Universe, Contracting Brane, seeing-vs-touching, no-attractive-force, HBR-presentism) are introduced on first body use with standard-physics translations, while the bilingual glossary preserves the original notation. (2) Meta-record consolidation — internal review records (sprint logs, redline inventories, partial-downgrade notes) are consolidated into a new Appendix C (Revision History) as archive, leaving the body focused on physics content. (3) Mathematical Companion reintegration — three new appendices (Mathematical Foundations / Push-Restore Force Balance and T2 Geodesic / T4 Poisson Reduction in the Newtonian Limit) bring the Madelung Tier-1, Tier-2, and Tier-4 derivations into the main paper verbatim; the companion paper itself is bit-for-bit preserved. (4) Abstract Item 8 micro-edit and Title update — the Hubble-tension wording is harmonized with the in-text honest framing of the partial downgrade of the structural-parameter claim; title and subtitle reflect the V41. 5. 1 designation. (5) Abstract and Introduction-Motivation compact rewrite — the verbose multi-paragraph Abstract is replaced by a four-paragraph compact form, and the Motivation subsection is simplified to a single paragraph listing the five open problems (galactic flat rotation curves, the cosmological-constant problem ~120 orders of magnitude, the MOND acceleration scale a₀, the gravity hierarchy, and the precise inertial/gravitational mass equivalence) with bibliographic citations preserved. V32 Paper A LOCKED numerics are preserved bit-for-bit throughout: αBTFR = 3. 56 ± 0. 11, χ²_ν = 1. 29, NGC 3198 v_∞ = 159. 5 km/s, 91. 9% pass rate on 171/175 SPARC galaxies, a₀ = 1. 082 × 10⁻¹⁰ m/s², Cassini PPN |β − 1| < 10⁻⁴. The Madelung tier-excerpt SHA-256 baselines are maintained for all six tier files. All sixteen ideological-redline constraints hold and all eleven compromise-warning criteria remain not triggered (the full audit inventory is included as Appendix C-2). The mathematical companion paper (DOI 10. 5281/zenodo. 20103309) remains bit-for-bit preserved — no companion modification in V41. 5. 1. 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, Koide formula, Bullet Cluster, Twistor preliminaries.