Signed-Incidence Structure
A Structural Note on Compositional Verification
Signed-incidence row structure → totally unimodular → field-independent fee; pairwise endpoint coupling bounded by rank 2; partition-style typed repair structurally fails
A composition where the coboundary row structure violates the signed incidence property, or where a pairwise (edge, dimension) block in the witness Gram exceeds rank 2
Abstract
A short structural note supplying three facts used repeatedly in the Bulla corpus: (i) each row of the coboundary matrix has at most one +1 and one −1; (ii) the coherence fee is field-independent as a difference of two totally-unimodular ranks; and (iii) pairwise endpoint coupling is bounded by rank 2 on every (edge, dimension) block. A negative corollary records that any partition-style typed repair constraint is structurally wrong: enforcing it makes fee-zero repair impossible in 151 of 240 nonzero-fee compositions on the real-schema corpus.