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 (HBR_Master.pdf) with a Japanese mirror (HBR_Master_JP.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).