Defect Annihilation Defines a Maximal Cocycle-Level Readout Space
Epistemic-graph event: 1340.
For a graded Betti candidate S, the space
A^n(S)=Z^n(H) intersect ker(Omega_(n+1)^*)
is exactly the maximal target-cocycle subspace whose selected pullbacks are
source cocycles. It equals all target cocycles when S is a chain map, but
may remain nonzero when the full boundary commutator fails.
This construction is generally representative-dependent. In the target
complex Z^2 --[1 0]--> Z, the exact cocycle [1 0] pulls back along the
defective assignment 1 -> (1,1) from Z -> 0 to the nonzero source class
1. Thus the zero target cohomology class can produce a nonzero source
readout unless stronger compatibility is imposed.
The five-site selector can therefore be tested in the maximal annihilator space only after its physical cocycle representative and regulator normalization are frozen. This does not define a cohomology functor or a physical Mackey correspondence.
Research note:
research/grothendieck/maximal-defect-annihilating-readout-space.md.