Adjoint Denominators Are Submultiplicative but Can Cancel in a Composite
Epistemic-graph event: 1355.
For composable rational adjoints, S_(r q)=S_rS_q. Their least denominator
indices satisfy
L_(r q) | L_r L_q,
so composite localization primes lie in the union of stagewise supports. The inclusion can be strict.
With rank-one pairings P_G=2, P_H=3, P_J=2 and identity coefficient
pullbacks, the stage adjoints are 2/3 and 3/2, while their composite is
the integral identity. Terminal integrality therefore does not certify
integral intermediate transfers.
Together with boundary-defect cancellation, this makes terminal multi-bit tests doubly blind. Each one-bit five-site specialization needs its own Smith divisibility and boundary-commutator audit.
Research note:
research/grothendieck/adjoint-denominator-composition-cancellation.md.