Established in scope
Full G0 lift cocycle trivialized by explicit cochain
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Full cocycle and global trivialization on G0 only; no splitting decision for full G31 or W(E8).
Read the exact result, assumptions and evidence
Result
For actual G0=<J,R>=C4×C2 the full8×8factor table of the original ordered lattice lift is computed. Its Hom(L,F2) class vanishes: b=(0,86,6,80,136,223,142,217), ordered1,R,J,JR,J²,J²R,J³,J³R, satisfies b(g)+g.b(h)+c(g,h)=b(gh) on64pairs. All512cocycle triples checked.
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.
- Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
Original evidence
- THEORY.txt lines 252–284
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/marked-seam-monodromy-20261023/THEORY.txt
83f6f464aff89acb5cc4194244a5636d4a4ff62600cdf5ee3c33ded4410f963a
finding:native-clock-reflection-full-factor-cocycle-trivialization