Cross-Domain Compositional Schema: Future-Sufficient Interfaces, Load-Bearing Relations, and Preserve-or-Reopen Reuse

Abstract

Version 0.4 carries the previously open tetrahedral/Bell branch through an explicit mathematical formalisation. It separates a four-context indexing simplex and Boolean restriction lattice from the Bell-native tetrahedral CHSH facets in R^4, formalises sign-to-context semantic attachment, and derives the exact Facet-adapted Tetrahedral Bell Chart E = Vλ + (ν/4)c with 1ᵀλ = 1. The three independent λ coordinates carry the selected facet address and ν = S_c(E) − 2 supplies the fourth transverse correlator coordinate, resolving the prior four-versus-three degree-of-freedom objection without forcing a tetrahedron to encode unrestricted four-correlator data by itself. The paper further treats marginal-fibre reopening, exact one-correlator ablation/restoration, the local/Tsirelson/PR normal-ray benchmarks, and a natural four-volume candidate that collapses exactly to |S−2|/3. After subtraction of native Bell/Fine/Tsirelson-Landau-Masanes ownership and a reparameterisation test, no independent new Bell inequality, quantum boundary, or physical mechanism survives; the current physical residual is null.