Scale Rigidity Without Shape Selection: The Exact Identifiability Boundary of an Eight-Tick Carrier

An eight-tick discrete carrier admits two competing two-phase windows: the adjacent dipole g₁ = δ₀ − δ₁ and the gap-two dipole g₂ = δ₀ − δ₂. Both generate equivariant worldlines on the recognition three-cube, both have the same neutralized load N(g₁) = N(g₂) = 2, and each admits a unique positive rescaling at which the reciprocal load cost vanishes. Unique zero-cost scale therefore does not select shape. The auxiliary nearest-neighbor Dirichlet functional D orders the windows the wrong way: D(g₂) = 4 < 6 = D(g₁). Operational settlement, by contrast, forces every settle window into the cyclic orbit of g₁ and none into the orbit of g₂. Bare posting and photon data still admit the gap-two countermodel, and on stable patterns the mass equality M_rest = M_pred is logically identical to the load factorization it would be asked to justify. Three named physical interface inputs (zero load cost on realized matter, origin carried by settled run indexing, and photon readout identified with the settled anchor) then yield the conditional formulas M_rest = M_pred, a² = M_pred/16, E_γ = M_pred/8, together with pairwise same-topology rigidity of pattern and amplitude. The interface is inhabited. The paper states an assumption-complete boundary, not a jointly minimal triple: the first and third inputs have formal underdetermination evidence; the second is carried indexing and presently lacks a deletion countermodel. No measured particle-mass comparison is claimed.