Decomposing and Reconstructing the Four Fundamental Interactions in Hyperbrane Relativity: A One-Source W-Phase Flow Taxonomy

Overview. This standalone Hyperbrane Relativity (HBR) preprint proposes a one-source reconstruction of the conventional four fundamental interactions: gravity, electromagnetism, the strong interaction, and the weak interaction. The four sectors are not treated as primitive ontological forces. They are decomposed into brane-side readings of a single oriented W-phase flow: W− Generation → brane Stability / Contact → W+ Reduction. Vertical binding covers strong-like contact and gravity-like response as two scale regimes; lateral release covers electromagnetism and light; vertical dissipation is a candidate carrier for part of weak-like decay. W-thickness polarity. A massified body is not a scalar point source. It carries an inner W−-oriented pole and an outer envelope pole, so nested and co-exterior placements behave differently. The envelope is a functional of the source state — density profile, internal strain, boundary data — growing with mass within a fixed body class, which makes the classification mass-gated: sufficiently massified bodies meet envelope-first, while low-mass configurations can interpenetrate. What is claimed, and what is not The distinguishing feature of this paper is that its weakest link is marked rather than hidden. Hypothesis H1 (co-exterior overlap penalty) is posited, not derived. The obvious candidate mechanism — overlap of mass-induced width distortions in the σ sector — is examined and shown not to supply it, for four independent reasons. Its sector of origin is left open. Hypothesis H2 (existence of a shared branch) is stated separately, because H1 alone gives only a rising cost along the separated branch and implies neither the existence of a shared solution nor a crossing at finite separation. That the branches cross at finite separation, and that a dynamically accessible path connects them, is a derivational target beyond both hypotheses. What the comparison of two energies establishes is a branch exchange, not a bifurcation in the mathematical sense; the latter would require the stationarity equations and their second variation. Conjecture 1 places strong-like constituents on the shared branch in their observed physical sector, and states explicitly that this does not by itself yield confinement: a finite envelope-formation cost would still permit separation. The observational anchor for the strong sector is stated carefully: isolated colour-charged asymptotic states are not observed, and separation attempts produce reorganization into colour-neutral hadrons. An unbounded separation cost is not an anchor — in full QCD the static potential flattens through string breaking. The weak-like placement is narrowed to a candidate Reduction-side channel for part of weak-like decay. Weak processes include scattering, and decay occurs in other sectors, so the correspondence is not one-to-one in either direction. No monotone irreversibility functional is exhibited. Scope and limitations This draft does not derive the Standard Model gauge groups, colour labels, QCD confinement, electroweak chirality, neutrino channels, the interaction-strength hierarchy, PPN gravity coefficients, or full tensor brane-strain dynamics. Nor does it derive why the list of sectors should have exactly four entries. All are listed explicitly as falsifiability and derivational targets. The apparatus of the standard theories is not adopted as a starting point, nor as a baseline against which to measure deviation; a completed HBR sector must nonetheless reproduce structure observationally equivalent to what that apparatus accounts for. Relation to other HBR papers The paper continues the HBR gravity-sector scaffold (Zenodo 10.5281/zenodo.21201334) and connects explicitly to the HBR neutron-star merger analysis (Zenodo 10.5281/zenodo.21153991), identifying the two papers’ envelope quantities with each other and converting a possible hidden inconsistency into a two-directional joint calibration and falsification target. Versions 0.2.0 through 0.5.4 incorporated four rounds of external review. The final rounds corrected three overstatements: an undetermined mechanism presented as derived, a provisional variational template described as an obtained result, and an incorrect statement of the observational anchor for the strong sector.