Established in scope
Marked C4 glue determines one complete local E8 vacuum source
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Complete conditional mathematical reconstruction for the specified U module and local unitary conformal extension. No derivation of primitive P1 membership or physical time/state/spacetime identification. H3(C4,U1) is not asserted zero; the original nonsplit G31 character extension is not replaced by scalar coefficients.
Read the exact result, assumptions and evidence
Result
In exactly Ext_H(U) there is one VOA and normalized local Q system class over U, represented by V_E8. q_D5(s)=5/8 and q_A3(f)=3/8 make H Lagrangian; the full abelian associator/braiding class trivializes only on H. H2(C4,C*)=H2(C4,U1)=0 gives uniqueness, with residual automorphisms Hom(C4,U1)=C4. The actual weight1 branching is60+64+60+64=248. Lattice vacuum, Sugawara vector, L0=N+Norm(alpha)/2, all vacuum correlators, unitary structure over U and associated local conformal net are determined in this class.
Required assumptions
- Original D5+A3 compiler split and established seed
Retain the established P1/P2 compiler with cyclic C4 glue to E8, D5 on the first5 and A3=D3 on the last3 standard coordinates, c3=1/(8pi) and phi_base=(4/3)c3=1/(6pi). No replacement by an optional E7 readout. Cut equivalence is the actual W(D5)xW(A3) action in the fixed chart, without conjugating J.
- Exact local reconstruction class of the marked C4 glue
Mathematical object class Ext_H(U): U=V_D5 tensor V_A3 with fixed embedding and sector chart, H=<(s,f)>=C4. Objects are connected local unitary conformal VOA extensions with the same conformal vector and underlying labelled U module exactly the sum of M_h for h in H, each once. Isomorphisms fix U and sector labels. This is an explicit mathematical reconstruction class; membership of primitive P1 is neither assumed nor derived.
Original evidence
- THEOREMS.txt lines 1–196
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/THEOREMS.txt
5c0d7328c583cdbc0a8c358445b57821d5b5722540ca372c1d28052b900eb584
- THEOREMS.txt lines 197–386
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/THEOREMS.txt
5c0d7328c583cdbc0a8c358445b57821d5b5722540ca372c1d28052b900eb584
- THEOREMS.txt lines 503–517
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/THEOREMS.txt
5c0d7328c583cdbc0a8c358445b57821d5b5722540ca372c1d28052b900eb584
finding:marked-c4-glue-unique-local-e8-vacuum-source