The Five-Site Boundary Commutator Is Specified but Not Yet Evaluable
Epistemic-graph event: 1326.
The physical branch-pushforward gate has a finite exact decision procedure. Given source-derived relative boundary matrices and the pairing-forced Betti matrices, compute in every degree
Omega_q^n = D_H^n S_q^n - S_q^(n-1) D_G^n.
All commutators must vanish; one nonzero entry falsifies the forced chain map.
An audit of the frozen five-site sheet census, branch-lift gate, deck-transfer
gate, Cayley--Menger contour family, marked A2 specialization, and physical
residue-link artifacts finds no source-derived pair D_G,D_H. Several of
those artifacts explicitly list the required boundary specialization,
relative trace, or physical normalization as missing. Therefore the
commutator is currently undefined from physical evidence, rather than zero
or nonzero.
The algebraic Mackey and norm conclusions remain valid. The smallest
decisive next input for the one-bit (C2)^5 -> (C2)^4 quotient is the pair of
adjacent based relative boundary matrices, together with the forced maps and
source-fixed basis/orientation comparison.
Research note:
research/grothendieck/five-site-boundary-matrix-availability-audit.md.