Local collar audit; exact Laurent/tensor identities
Coefficient ring: Z[i,t^+-1,r^+-1]/(i^2+1), A=t^2
PASS: distinguished vertex and half-twist units have their exact inverses
PASS: half-twist squares to the full framing scalar
PASS: ordinary cup is h^-1 times symmetric cup
PASS: ordinary cap is h times symmetric cap
PASS: both ordinary snake identities
PASS: both symmetric snake identities
PASS: unweighted state flip is involutive
PASS: evaluation square including both mixed states after marking reversal
PASS: coevaluation square including both mixed states after marking reversal
PASS: same-state cut tensor is preserved, F I F^t=I
PASS: annular matrix-element counit is preserved for arbitrary states
PASS: weighted self-duality has nontrivial same-state splitting defect
PASS: weighted self-duality fails the unmodified standard annular counit
PASS: opposite endpoint weights cancel across a paired cut
PASS: arbitrary reciprocal endpoint gauge cancels without specializing it
PASS: the same nontrivial gauge on both cut sides does not cancel
PASS: unweighted flip sends both fixed corner characters exactly
PASS: the weighted map does not send the same fixed corner character
PASS: reversing cyclic triangle order reverses the cocycle form universally
PASS: anchored bare-edge dictionary is anti-symplectic on the full lattice
All local tensor checks passed.
The written proof must separately identify actual collars, ribbon framings,
corner ideals, and the underlying closed link. Matrices do not certify those.
No manifold, triangulation, slope, or skein-configuration enumeration.
