The Residual Mod-Two Norm Homology Has a Closed Hilbert Series
Epistemic-graph event: 1361.
For a collapsed branch set of size k, multiplication by the norm monomial
on the five-site mod-two deck algebra has homology Hilbert series
H_k(t)=(1+t)^(5-k)((1+t)^k-1-t^k).
A basis is indexed by proper nonempty subsets of the collapsed directions,
tensored with arbitrary monomials in the untouched directions. At t=1
this recovers the dimensions 0,16,24,28,30 from Ledger 1340.
The full five-bit collapse yields graded dimensions 5,10,10,5: the proper
nonempty Boolean subsets, with the unit and top norm class removed. This is
formal augmentation-filtered deck homology, not physical relative-chain
homology or a geometric branch-support claim.
Research note:
research/grothendieck/mod2-norm-homology-hilbert-series.md.