Established in scope
No E6 vertex selection even with full clock-field phases
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Complete stabilizer test inside H preserving root factors setwise, with fixed J/compiler field lifts, Y and covariant quartic/erasure maps. No pointwise freezing of every individual quartic vector or separately chosen charged state. The full transported family is the exact object.
Read the exact result, assumptions and evidence
Result
C_H(J) has order64 and cyclic4 image on the four E6 vertices. Its Y stabilizer is{I,d}, d=diag(1,1,1,1,1,1,-1,-1), acting by two transpositions without a fixed vertex. d preserves sigma,c and the actual quartic/erasure diagram. With fixed full Jhat and chat=S_c D31, exactly four d field lifts126,127,128,129 commute with both;126 and127 are involutions. Thus genuine automorphisms of the same full associated object fix no E6 vertex. Character-gauge conjugation transfers this to all four cyclic lifts. The supplied field phases therefore select no vertex.
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.
- Joint category of original compiler flags and cover actions
Retain original E8 lattice VOA products, J/sigma/c/Y, D5+A3 root factors and quartic/erasure diagram. Transitions transport all marks through actual lifts in the original sign extension; they are not fixed-J stabilizers. The Burau peripheral comparison uses the associated local system induced from the existing marked C3 cover and its retained deck module. No independent geometric Gauss-Manin identification, added line correction or selected E6 vertex.
- Full original G31action and inherited lattice sign extension
The60actual original complex reflections act on the same original even E8lattice. Study exactly their full preimage in the automorphism group of the lattice group defined by unchanged eps_e8. Kernel A=Hom(E8,Z2), with g.a=a composed g^-1. No scalar replacement, enlarged coefficients or extra square relation for lifted puncture meridians.
Original evidence
- SELECTION.txt lines 1–110
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-joint-source-20261023/SELECTION.txt
eaf46bcdc3ae40faded8b33bb100e5a6625cc3f71bdc07a4d696e49bd6705e7d
finding:e6-vertex-nonselection-survives-full-field-clock-phases