The Boundary Defect Is Invariant Under Chain-Homotopy Changes
Epistemic-graph event: 1344.
For Omega=D_H S-SD_G, any ordinary chain-homotopy change
S'=S+D_H K+K D_G
leaves Omega unchanged. The square-zero boundary identities cancel every
correction term. Target cocycle pairings on source cycles are unchanged as
well.
Therefore a nonzero physical boundary defect cannot be repaired by choosing
a different representative in the same chain-homotopy class. A genuine
repair requires an additional graded correction C satisfying
D_H C-CD_G=-Omega; under perfect-pairing uniqueness, such a correction
normally changes the forced adjunction and demands new physical data.
Future five-site endpoint or overlap homotopies can compare presentations, but they cannot erase a nonzero commutator of the forced Betti map.
Research note:
research/grothendieck/boundary-defect-chain-homotopy-rigidity.md.