Established in scope
Nontrivial central quotient class and all subgroup restrictions
In the question: Active mathematical program: marked seam monodromies and lattice lifts
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).
Read the exact result, assumptions and evidence
Result
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.
Required assumptions
- 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.
Original evidence
- THEORY.txt lines 117–168
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/marked-seam-monodromy-20261023/THEORY.txt
83f6f464aff89acb5cc4194244a5636d4a4ff62600cdf5ee3c33ded4410f963a
finding:quarter-lift-central-quotient-class-and-all-subgroup-restrictions