Unique GEP Pseudoscalar Found, Physical Chiral Anisotropy Not Yet Derived

Abstract

Granular Entropic Physics (GEP) is being tested through the Stone-2 program as a sequence of bounded, pre-registered questions concerning the microscopic origin of chiral quantum matter. Stone 2A established a faithful Q8-linked proxy with a gapped irreducible Chern bulk and matched chiral boundary flow. Stone 2B derived its canonical four-state carrier K = W tensor M from the local binary-tetrahedral representation, and Stone 2C derived a canonical fusion selector and a Bell-type identity wire for the two-dimensional multiplicity factor M. This paper asks whether the enriched channel-rewiring algebra already contains a distinguished orientation-odd operator and whether canonical fusion preferentially couples that direction. The active operator algebra End(M) = M2(C) decomposes under the S3 channel-relabeling action as 1 + 1_sgn + 2. The operator Omega = P0 (R - R^-1) P0 / (i sqrt(3)) transforms as Ad_g(Omega) = sgn(g) Omega and therefore spans the unique local S3 pseudoscalar line, up to normalization and the unavoidable local convention Omega -> -Omega. The most general simultaneous-S3-scalar traceless two-carrier bilinear contains two independent coefficients, V = -J_Omega C_Omega - J_E C_E, where C_Omega is the covariantly transported pseudoscalar channel and C_E is the nonchiral Pauli-doublet channel. The relevant measure of pseudoscalar preference is therefore kappa_Omega = J_Omega - J_E. For the exact Stone-2C Bell compatibility wire, the unit parent penalty is h_wire = (3/4) I - (1/4) C_E - (1/4) C_Omega. Consequently, J_Omega_wire = J_E_wire = 1/4,kappa_Omega_wire = 0. Canonical fusion thus provides nonzero covariant orientation stiffness but gives the pseudoscalar exactly the same component weight as the nonchiral doublet. It transports orientation information without selecting physical handedness. The paper also proves that the sign assigned to an isolated untransported bond is not convention free. The invariant sign data require a derived bond transport tau and closed-loop products W_Omega(C). Central Q8 holonomy -I cannot determine this anisotropy or orientation-line holonomy by itself because Q8 and Omega act on commuting tensor factors of the carrier. All results are exact finite-dimensional algebra; no code or numerical calculation is used. The established conclusion is a refinement of the missing microscopic target from a single coupling J_Omega to the tuple (kappa_Omega, tau, W_Omega), together with a physical bond operator, energy scale, and branched carrier graph. The paper does not derive a physical GEP Hamiltonian, a nonzero chiral anisotropy, an ordered many-body phase, QWZ spatial dynamics, a Kaplan-type higher-dimensional wall, a Weyl boundary mode, doubler control, or anomaly cancellation. It identifies the unique local pseudoscalar and the exact point at which canonical fusion remains insufficient.