Hyperbrane Relativity V41.5.4: Universe Objects, OCS Geometry, Madelung Quantum-Fluid Foundation, Three-Reading Articulation of Cosmological Puzzles, Hubble Tension, Bullet Cluster Item 4, and Quantum-Gravity Smooth Connection (Main Paper)

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 of 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. 4 integrated edition (190 pages) of V41. 5. 1 (DOI 10. 5281/zenodo. 20123256, 2026-05-12), incorporating the V42 Foundational Insights articulation into the V41. 5. 1 baseline and adding the Decision B Hard Unlock declaration. The V41. 4 mathematical companion paper (DOI 10. 5281/zenodo. 20103309) is unchanged. The V41. 5. 4 main paper carries forward the V41. 5. 1 articulation of universe objects, OCS geometry, the Koide 45 degree cone identity, the Hubble tension via W-extent saturation, the Bullet Cluster three-component decomposition, and the SPARC ensemble analysis. It adds the V42 statement of (i) the central driving principle (P2) articulation chain from energy distribution to brane-section flow; (ii) the Madelung quantum-fluid foundation ₁ₔ₋₊ = R (x) e^i (x) with the quantum potential decomposition and the E = mc² geometric identity stated as a consequence of the Dirichlet boundary condition XW|_ = c; (iii) the two-stage gravity mechanism in which Stage 1 is W-thickening of the brane around energy concentrations and Stage 2 is the push-restore force balance recovering Newtonian gravity in the appropriate limit; (iv) the post-Newtonian articulation distinguishing the externally measured ₏₏₍ from the HBR-internal parameter ₇₁ₑ; (v) the SR derivation from thread-slice geometry, with the GPS operational test (+38. 6\, s/day) anchoring the framework empirically; (vi) the three-projection unification of cosmological puzzles, in which dark matter (Reading A: absorption overflow), the cosmological constant (Reading B: scale-lens / W-translation), and the MOND-like phenomenology (Reading C: aggregate vortex) are stated as three projections of one structural principle; and (vii) the quantum-gravity smooth connection, in which gravity emerges as the classical eikonal limit of Madelung dynamics rather than requiring a separate quantum-gravity theory. The V41. 5. 4 sprint also integrates the open-problem set of the V48 SPARC spin-off paper (O55f: cluster-scale extension; O55g: first-principle derivation of the saturation coefficient ₒ₀ₓ 0. 48; O55h: first-principle derivation of the Madelung running parameter ₌₀₃₄₋ₔ₍₆ 0. 040 and the kinematic projection exponent; O55i: closed-form O-mode projection kernel relating intra-Contact and externally observed kinematics; O55j: structural status of the c-calibration axiom). Three new V42 open problems are also recorded: O16 (Reading A/B/C structural relationship), O17 (Madelung field for matter formation), O18 (HBR quantum gravity, full closure). The V42 mathematical and conceptual statements appear as new sections, each accompanied by a "Relation to earlier sections" paragraph that explicitly positions the V42 articulation as a refinement of the V41. 5. 1 baseline rather than a replacement. The most significant programmatic addition of V41. 5. 4 is the Decision B Hard Unlock declaration (Section 20. 7-bis): the original V32 SPARC ensemble fit (alpha-BTFR = 3. 56 +/- 0. 11, chi-square-nu = 1. 29, 171 galaxies, v-infinity NGC 3198 = 159. 5 km/s, a-zero = 1. 082 x 10^-10 m/s², 91. 9 percent pass rate) is fully retired from any LOCKED-target or comparison-anchor obligation for new HBR work. The intermediate Soft Unlock (2026-05-22) reclassified the V32 fit from a reproduction target to a comparison baseline; the Hard Unlock (2026-05-25) removes even the comparison obligation. Subsequent HBR papers (V41. 5. 4, V48, V48. x, V49+, LLM-SR-driven analysis) are free to report numerical results that legitimately deviate from V32 without "tension" framing or post-hoc reverse-engineering of structural forms. The Madelung-running articulation alpha = 4 - 4 beta-Madelung * (exponent) approximately 3. 56 is reframed as a standalone HBR structural form, articulated independently of any V32 reproduction obligation. The V48 SPARC free-fit result xi-best = 0. 224 +/- 0. 022 is reported as observation rather than as a tension to be reconciled with the canonical Madelung phase normalisation 1/ (2 pi) = 0. 159. Foundational postulates (P12. 1, P18. 1, P26. 1, P27. 1, P30. 1, P31), forbidden-language guardrails, and the foreign-theory firewall remain LOCKED. The V32 published PDF (DOI 10. 5281/zenodo. 20060756) is unchanged on Zenodo; no published record is retracted or revised by the Hard Unlock. The motivation for the Hard Unlock is the structural observation, articulated repeatedly through the 2026-05 sprints, that the V32 LOCKED constraint had become a compromise-pattern source: subsequent HBR articulations were forced into post-hoc forms reverse-engineered to recover V32 numerics, restricting the articulation freedom released by the post-2026-05-07 articulation revisions (OCS-modulated gravity, universe-object-per-galaxy, W-axis longitudinal continuum, brane cross-structure dual reading). The Hard Unlock restores articulation freedom to the post-2026-05-07 state of the HBR programme. The V48 SPARC spin-off paper (DOI to be supplied at co-upload) is co-published as a sister record. The V48 paper applies the V41. 5. 4 framework to the SPARC distance-corrected subsample (135 galaxies), reports a 91. 9 percent pass rate within +/- 30 percent in velocity for the leading alpha-BTFR = 4 floor prediction with no per-galaxy fitted parameter, and analyses the xi offset structural diagnostic of the slope-4-vs-observed-slope tension. The acceleration scale a-zero = c H-zero / (2 pi) is shown to enter through the empirical c-invariant Dirichlet condition derived in V41. 5. 4; the V48 paper records the c-calibration axiom as Open Problem O55j with reference to the V41. 5. 4 geometric identity articulation. Per the Hard Unlock, the V48 numerical results are reported as data-driven free-fit values rather than as offsets from a V32 baseline. Compile and verification: lualatex 3-pass with bibtex; 0 errors, 0 undefined citations, 0 undefined references. HBR canonical guardrails verified: forbidden "modified gravity" affirmative self-adoption check passed (only negations present) ; forbidden "drift / 漂流" language for brane motion check passed (zero occurrences). The V42 mathematical companion paper (DOI 10. 5281/zenodo. 20103309) is referenced as a supplementary record; the V41. 4 main paper (DOI 10. 5281/zenodo. 20102858) is in the lineage chain.