The Betti Boundary Obstruction Is Basis-Invariant
Epistemic-graph event: 1329.
For the pairing-forced Betti candidate, set
Omega_n=D_H,n S_n-S_(n-1)D_G,n.
Under invertible basis changes in the source and target relative complexes,
Omega'_n=P_H,n-1^(-1) Omega_n P_G,n.
Therefore vanishing, field rank, and integral Smith invariant factors are
intrinsic. Relabelling sheets, changing orientations coherently, or making
unimodular relative-stratum basis changes cannot erase a nonzero obstruction.
A single coordinate-free matrix coefficient lambda(Omega_n x) != 0 is a
complete falsifier.
This reduces the five-site acquisition burden: locally source-labelled strata and incidence data are enough; no globally preferred basis is needed. Reduction modulo a prime is a valid one-sided hostile test—nonzero reduction proves failure—but vanishing at one prime cannot certify integral vanishing.
Research note:
research/grothendieck/boundary-commutator-basis-invariance.md.