The Terminal Anchor Proposition

Every mathematical framework has a moment where structure forces a unique choice. For Theorem 18, that moment is the closure of the Gray code Hamiltonian cycle on Q5. The Gray code traversal of Q5 closes at step 15, a defect bond connecting two specific vertices that completes the Hamiltonian cycle. That closure event is not orientation-neutral. It carries a nontrivial orientation-sign invariant, computed as the sign of a canonical reordering permutation on the odd-step axis sequence. Under the conventional labelling, this invariant equals σ_Γ = −1, verified by exhaustive enumeration over 1, 152 valid Hamiltonian cycles in the parity-aligned class, with zero counterexamples. Within the T17 active ladder, two slots share the defect-local support at the terminal position: Σ₄, which lies in the order-collapsed reduction and is therefore orientation-blind, and Λ₄, which lies in the order-retained reduction and can carry orientation-sign information. Since the Gray closure event carries σ_Γ = −1, it cannot land on Σ₄. The only remaining candidate is Λ₄. The result is a forced identification: Λ₄ = (F₇, F₆, F₂) is the canonical anchor slot of the T17 active ladder. This is not a choice or a convention; it is a structural consequence of the orientation-sign invariant combined with the two-slot constraint at the terminal locus. The paper also develops the cohomological perspective underlying the descent map, connecting the anchor identification to a signed transport potential on Q5 vertices and a Gray edge-orientation cocycle. A complete cohomological characterization of the Gray cycle in these terms is identified as a direction for future work. Dependencies: Theorems 14, 15, 16, 17.