Sources, dependencies, and intellectual influences

Checked 8 September 2026.

1. Dimofte–Garoufalidis, The quantum content of the gluing equations, arXiv:1202.6268v2, 25 October 2012, §§2.6 and 4.6. Formal input: the fixed two-tetrahedron figure-eight edge, meridian, and longitude rows. The source’s geometric eigenvalue signs are not substituted for the native half-root character.
2. Local collar and named-action note. Retained formal input: six-root central elimination, convention dictionary, named-action comparison, and its cited GY, CK, and PP dependencies. The present finite calculation does not independently reprove those inputs.
3. Cyclic-polarization note. Formal input: exact cyclic map and convergent nonzero meridian unit functional. Intellectual starting point: its eight-relation all-plus vacuum certificate. The new squared-moment proof explains why that certificate lifts without choosing sign components.
4. Generic boundary reconstruction, Theorem 8.1. Formal input for the trace consequence: the boundary-balanced filling isomorphism and its Frohman–Gelca/excision dependencies. The module unit is not the filled vacuum.
5. Panitch–Romo, On the length conjecture for twist knots, arXiv:2609.02706v1, 2 September 2026, §7. External problem calibration: the literal conjecture asks for a nonzero quotient and commuting map. It does not explicitly demand nonzero trace. This distinction limits the result’s scope.
6. The intrinsic-object and exact-translation strategy was encouraged by Joshua’s Origami comparison. This is influence on the approach, not a formal proof dependency. The minimal-compatible-quotient exact sequence is elementary linear algebra, not claimed as a new general theorem.

Novelty and priority of the synthesis are unassessed. No researcher endorsement or external review is claimed.