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 0.8.0 Version 0.8.0 is a claim-scoping revision built from published v0.7.0 (DOI 10.5281/zenodo.21987914). No central four-sector taxonomy is withdrawn, and no new result is added. The visible title drops and Reconstructing; the subtitle remains A One-Source W-Phase Flow Taxonomy, and an Established Obstruction to Its Closed-System Reading. The changes are: the Conclusion's concentration family is admissible for the parent functional, while membership in Csep(d) is not established; a short status note on the open H1 route (research notes, not canonical); two-branch displays are a conditional toy realization; a claim-status table is added after the Introduction; falsifiability is split into derivational-closure and empirical sections; the H1 section opens by locating its audit scope; and data-availability wording is narrowed to analytic reproducibility. Before deposit, the text was further corrected without adding results. The closed-system reading named in the subtitle is now defined: the reading in which configurations are compared by minimizing the configuration functional. The negative curvature of the homogeneous potential at the baseline is stated to be a property of that variational problem, not a decay rate. The correspondence with the neutron-star merger analysis now maps that paper's contact depth to the overlap depth, and its critical depth to a derived crossing, rather than to the polarity thickness. The envelope-mass monotonicity is written as a derivative along a family of states within a body class. H1 and H2 conditionality is made explicit in the polarity figure, the configuration table, the exchange chain, and the two-branch heading. The apparent-gravity steps 1–5 are labelled a structural articulation rather than a derivation, and the claim-status table gains a cross-sector row for the closed functional. The reserved version DOI replaces the placeholder in Data availability. Main results (unchanged from 0.7.0) 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 reading, that incompatibility is established: a finite constrained branch energy cannot be presupposed. The open, throughput-limited form remains unresolved and is recorded as a derivational target, not as a demonstrated main result. 2. A2 fallback on constrained coverage. The parent functional is globally unbounded below; whether the stated separated constraint removes all concentration directions has not been proved. Hypothesis H1 is therefore not yet well posed as a statement about a finite closed constrained infimum. The paper does not claim that the constrained infimum is −∞. 3. Topology / winding / two-envelope preservation is an assumption. Under the XYZ-only concentration prescription with fixed W-profile, retention of topology, winding number, and the two-envelope condition is labelled as an assumption of the construction, not a proof. 4. Open/closed mismatch demoted from main result. The mismatch between the open brane balance law and the closed configuration functional motivates an open-system H1 target (six explicit requirements in §10). It is not sold as the established main result of the equations. 5. Mechanism and separation-of-kind material from v0.6.0 is retained. The eight-step apparent-gravity chain remains, with steps 1–5 as a structural articulation and steps 6–8 as targets; ordinary gravity and the co-exterior problem stay separated by kind, not merely by scale; the configuration functional remains exhibited as the parent of the Madelung stationarity conditions; a standalone rising variational upper bound still does not establish that a constrained infimum rises. 6. Sector status stays narrow. The σ width sector remains excluded at its original scope. No wider Madelung scalar-sector exclusion is claimed (rc1 no-go withdrawn). Open candidates include the quartic self-interaction of ψbulk, the brane-displacement sector, the W-mode / Contact-fiber sector, and a constraint-cost route that would bear on H1 alone. H2 remains independent. 7. Supplementary hygiene. The live derivation companion remains the v0.7.0 note unless a later packet names a replacement. The rc1 phase-overlap worknote is archived and must not be reused as current theory. The claim audit and Codex response files remain available. 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. All remain falsifiability and derivational targets. 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). A Qeios preprint deposit is planned after this Zenodo version (publication-order gate: Zenodo first); mutual DOI linking is completed once both DOIs exist. Versions 0.2.0 through 0.5.4 incorporated external review. Internal v0.6.0-rc2 corrected a vacuum-curvature sign error and withdrew the rc1 amplitude-gap / scalar-sector exclusion. Version 0.7.0 centres the R0/λ incompatibility and demotes open/closed mismatch from main result to a §10 goal. Version 0.8.0 narrows claim wording without adding new results; the closed-system obstruction claim is unchanged.