Scoped exclusion
Exactly two scalar extensions over D8, both of order two
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Precisely the given scalar character restricted to fixed D8 subnet. Other source-derived field dictionaries are not excluded.
Read the exact result, assumptions and evidence
Result
The canonical scalar torus character g_q on V_E8 has order2 and fixed VOA V_E7 tensor V_A1. Over fixed V_D8 exactly one further extension gamma g_q exists, with fixed VOA V_D8prime and order2. Their weight-one spectra136/0/112/0 and120/0/128/0 exclude identification with actual native Jhat with60/64/60/64, even under full field conjugacy.
Required assumptions
- Given scalar quarter twist and explicit charge chart
Compare the given eight complex current channels, q=(1/4)^8, standard D5+D3 lattice and F=I5+T with T(x,y,z)=(x+y+z,x-y-z,-x+y-z,-x-y+z)/2. Eight channels and their normalization are not derived here from P1. Distinguish a local charged field, scalar monodromy character, flux register and native clock.
- Full unitary E8 field conjugacy with transported marks
Start with the existing unitary E8 lattice VOA, original cocycle and actual chat,Jhat,sigmahat. Full inner unitary E8 automorphisms are allowed for this conjugacy comparison. Cartan, Gaussian V4, Y, P5 and other marks are transported rather than frozen. This category is explicitly larger than original sign lifts and implies neither a G31 splitting nor a preferred microscopic conjugator.
Original evidence
- SCALAR-QUARTER-REPRODUCTION.txt lines 81–150
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/SCALAR-QUARTER-REPRODUCTION.txt
16e123a72d0d65e48fc1777bbc0b3a10a7585114c3f82bad33c87e0794e15f94
- source_reproduction.py lines 83–172
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-source-reconstruction-20261024/source_reproduction.py
ba667dfb7cee7df999876a1da48128d1b86ebfb268b306be397eff59ddea765f
finding:scalar-quarter-two-involutive-e8-extensions