Hyperbrane Relativity: A 4D Embedding Extension of General Relativity (Complete Master Edition, V42)

What if the universe is not expanding — and we, ruler and all, are shrinking instead? Hyperbrane Relativity (HBR) pursues this counterintuitive yet remarkably natural reinterpretation, and finds that one new ingredient — a fourth spatial axis, the scale axis — can be enough to bring the picture into clean focus. Our observable three-dimensional universe is modelled as a contracting 3-brane embedded in a four-dimensional Euclidean bulk whose fourth direction is that scale axis. What we read as cosmic expansion is then the contraction of the observer’s own measuring scale relative to a non-contracting bulk reference, and the persistent supply of mass–energy on the brane is inflow from the inner-universe (W−) direction. From this single geometric premise, a chain of established physics follows as geometry rather than as separate postulates: Lorentz invariance as an emergent brane-internal symmetry; the Newtonian limit of gravity; E = mc2 as a kinematic identity fixed by the gate boundary condition; galaxy rotation curves that reproduce the SPARC sample without dark-matter halos; horizonless compact objects. The same geometry offers a unified, single-framework reading of three puzzles usually treated apart — the dark-matter phenomenology, the magnitude of the cosmological constant, and the MOND acceleration scale — as facets of brane–bulk projection, with the quantitative tests carried by focused companion papers. An extension of general relativity, not a replacement. Wherever solar-system, binary-pulsar, and weak-field gravitational-wave tests have confirmed GR, HBR reproduces those results to the same precision, and single-parameter PPN consistency with the Cassini bound (β = 1. 0 ± 10−4) is maintained. HBR’s distinctive step is the explicit 4D Euclidean embedding that ties this reinterpretation to particle-scale phenomena. Falsifiable, and honest about what is open. The framework makes specific predictions for H0 (z), EHT shadow shapes, ringdown modes, and SPARC residual structure. Open problems are stated plainly — including the SI determination of the brane thickness Δw and the rigorous causal-structure treatment of the exhausted-regime no-horizon claim. Bilingual edition: English main paper (HBRMaster. pdf) with a Japanese mirror (HBRMasterJP. pdf). New in V42. The cover and abstract are reframed for a reader-first, narrative opening (the “scale-axis” reversal) without changing any physical content; front-matter development notes are consolidated and the abstract now follows the title page directly; terminology is unified to “universe-object layer”; and the V41. 4/V41. 5 articulations (Koide 45° cone, Hubble-tension parameter, Bullet-Cluster Item 4) are integrated into the master edition. The V32 SPARC results are preserved bit-for-bit (171/175 galaxies, χ2ν = 1. 29, αBTFR = 3. 56 ± 0. 11).