TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/e-series-joint-source-20261023/THEOREMS.txt
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Inclusive original lines: 65-104
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000065 | 
000066 | Let A=Hom(L,F2) and let Gtilde be the FULL inverse image of W(E8) in the
000067 | original sign-preserving automorphisms of the epsilon lattice group:
000068 | 
000069 |   1 -> A -> Gtilde -> W(E8) -> 1.
000070 | 
000071 | It acts on the existing full lattice VOA by the original Heisenberg action
000072 | and lattice phases. This introduces no additional carrier. The restriction
000073 | to G31 is the previously proved nonsplit extension, so the full extension
000074 | cannot split either. Composition must retain its original character carry.
000075 | 
000076 | For a chosen actual lift ghat, transport every mark by conjugation:
000077 | 
000078 | [OMITTED: non-scientific conversation or execution metadata]
000079 | [OMITTED: non-scientific conversation or execution metadata]
000080 | [OMITTED: non-scientific conversation or execution metadata]
000081 | 
000082 | and likewise H,Y,V4,P5 and the erasure map. On the associated local systems
000083 | define the transition
000084 | 
000085 |   F_ghat:[p,v]_Jhat -> [p,ghat v]_Jhat_g.               (3.1)
000086 | 
000087 | The quotient relation is preserved because
000088 | 
000089 |   Jhat_g ghat v=ghat Jhat v.
000090 | 
000091 | The transition preserves every lattice-field product and the transported
000092 | quartic/erasure diagram because ghat is an automorphism of the original
000093 | VOA. Moreover F_ghat F_hhat=F_(ghat hhat) exactly. Choosing separately
000094 | normalized sections S_g would insert their known character cocycle; dropping
000095 | it would invalidate this equation. Thus the full groupoid of transported
000096 | marked sources is coherent without assuming a forbidden global section.
000097 | 
000098 | This proves sufficiency of the stated transition object. Minimality of its
000099 | projected closure follows from the generated-group equalities in Section2.
000100 | The fibre remains V_L throughout; transport does not build a new model.
000101 | 
000102 | 4. Complete cyclic compiler action on the peripheral source
000103 | 
000104 | For the fixed original Jhat=S_J the actual cyclic compiler lift is solved