Microscopic Transport Underdetermined, Two Source Classes Ruled Out

Abstract

Stone 2E of the Granular Entropic Physics (GEP) program audits whether the currently specified tetrahedral geometry, the local binary-tetrahedral (2T) carrier algebra, and canonical fusion already fix the Stone-2 microscopic orientation tuple (κ_Ω, τ, 𝒲_Ω). Using only exact finite combinatorics and finite-dimensional algebra — no Python, no numerical enumeration, no parameter fitting, no floating-point tolerance — it establishes four results. First, the 24 rooted oriented chair traversals at a fixed site reduce to 12 unoriented geometric rings under reversal, a distinction invisible to the central spinor holonomy but essential to any carrier graph. Second, a physical overlap that fixes only one channel does not determine transport on the unique S₃ sign line: its two full-bijection completions have opposite parity, so a second matched channel is the minimum datum required. Third, every interaction factorizing as spinor-only transport tensored with the multiplicity identity — including non-Abelian Wilson products and the central holonomy W = −I_W — gives J_Ω = J_E = κ_Ω = 0 by Hilbert–Schmidt orthogonality. Fourth, the canonical Bell-wire fusion gives J_Ω = J_E = 1/4 and κ_Ω = 0. These two source classes are each proved insufficient to generate pseudoscalar anisotropy, but they do not exhaust the symmetry-allowed mixed spinor–multiplicity dynamics. The overall verdict is therefore genuine underdetermination (INCONCLUSIVE_MICROSCOPIC_TUPLE), not a global no-go. The missing microscopic input is a single rule that simultaneously fixes the physical carrier vertex, adjacency, full channel incidence, and a Hermitian bond operator with a derived energy scale. Part of the Stone-2 series. Continuation of Stone 2A–2D (Zenodo).