Established within the stated premises
Nontrivial central quotient class and all subgroup restrictions
finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions
Z(Gamma)=F2^5 and Gamma/Z=F2^5, with full central cocycle kappa((u,e),(a,f))=(ea,ef). Restriction vanishes exactly on subgroups in e=0; otherwise a nontrivial square obstructs an order2 lift.32central characters yield16marked U1 classes,15nonzero: pure clock carry is a U1 coboundary, other classes are distinguished by commutators.
Scope: Central quotient extension with trivial coefficient action, distinct from split noncentral extension over<J> and the G0 factor.16classes describe the Z-induced family, not all H2(F2^5,U1).
Required premises and original source excerpts
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension
- experiments/theory-contracts/marked-seam-monodromy-20261023/THEORY.txt, lines 117–168
Source SHA256: 83f6f464aff89acb5cc4194244a5636d4a4ff62600cdf5ee3c33ded4410f963a
bounded-excerpt · current-at-snapshot