Decomposing the Four Fundamental Interactions in Hyperbrane Relativity: A One-Source W-Phase Flow Taxonomy, and an Established Obstruction to Its Closed-System Reading

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. What is new in version 0.8.1 Version 0.8.1 is a claim-scoping revision built from published v0.8.0 (DOI 10.5281/zenodo.23033153). No new result is added. Title and subtitle are unchanged. The changes are: the mass-gated classification is stated conditionally throughout, because the envelope scale must also grow relative to the body's inner scale, which is not established; the closed-reading obstruction is restated as an obstruction to treating the uniform baseline as a stable minimum of the closed functional, and the constrained-infimum reading of H1 is spelled out; calibration requirements are made explicit, including that the fate of the constrained branch (termination, loss of stability, saturation, or crossing to a shared branch) is not derived; the claim-status table is split into two tables without changing any cell wording; the self-stress ratio is written as ξA; the W-to-length conversion behind the δAB contraction is stated; a negative quadratic term is required to be paired with a positive stabilizing quartic; and the joint compact-object falsifier is written conditionally on calibration. σ width sector. The exclusion of the σ width sector at its original scope now rests on two closures specific to it: the +1 : −2 linear-response identity and the linear regime of ordinary matter. Two further closures given in earlier versions (the softening of an exact width potential and the resummation of its alternating quartic series), and one argument for the substrate origin of the restoring term, relied on a derivation of the width potential that confined energy in a W-bracket around the brane. They are withdrawn pending re-derivation. Main results (scope unchanged from 0.8.0) 1. Core claim: registered Lagrangian vs. presupposed baseline. A positive uniform baseline amplitude R0 exists only on the λ<0 branch, where the homogeneous potential is a maximum and the parent functional is unbounded below. As a closed variational reading, that obstruction is established: a finite constrained branch energy cannot be presupposed. The open, throughput-limited form remains unresolved and is recorded as a derivational target. 2. H1 is not yet well posed as a closed statement. Whether the separated constraint removes all concentration directions has not been proved. The paper does not claim that the constrained infimum is −∞, and a rising trial upper bound does not establish that a constrained infimum rises. 3. Sector status stays narrow. The σ width sector is excluded at its original scope by the two closures above. No wider scalar-sector exclusion is claimed. H2 remains independent. What is still not claimed H1 and H2 remain hypotheses and are kept independent. The paper does not derive the Standard Model gauge groups, colour labels, confinement, electroweak chirality, neutrino channels, the interaction-strength hierarchy, PPN coefficients, full tensor brane-strain dynamics, or why the sector list should have exactly four entries. GW170817 forbids an unbounded outward slope; it does not select among resolutions that meet that requirement. Relation to other HBR papers The paper continues the HBR gravity-sector scaffold (Zenodo 10.5281/zenodo.21201334) and connects to the HBR neutron-star merger analysis (Zenodo 10.5281/zenodo.21153991). Version 0.7.0 centred the R0/λ incompatibility. Version 0.8.0 narrowed claim wording without adding results. Version 0.8.1 makes the remaining conditional statements explicit and withdraws, pending re-derivation, the two σ-width closures that depended on a W-bracket derivation of the width potential.