Established in scope
One complete cyclic field-lift class and joint associated clock
In the question: Active mathematical program: marked seam monodromies and lattice lifts
All256 character candidates over the fixed cyclic compiler group; all-field equality from eight generators and unchanged cocycle, with all240 roots checked directly. No full G31/Weyl splitting or identification of different cover automorphisms.
Read the exact result, assumptions and evidence
Result
With original fixed Jhat=S_J, the ninth-power equation has F2 rank6. Exactly four compiler lifts S_c D_a with a=31,62,151,182 have ninth power Jhat; their sigmahat masks are63,30,183,150. The16 Jhat-preserving character gauges give one orbit with stabilizer4. No solution retains both separately generator-normalized J and sigma sections. On Vper=(C12 x V_L)/((Delta12 p,v)~(p,Jhat v)), Chat[p,v]=[R12 p,chat v] satisfies Chat4=sigmahat, Chat12=I and Jcomp=Chat9=Q12 Jper. The two J roles share the same fibre lift while retaining different base components.
Required assumptions
- 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.
- Existing marked cyclic covers and Burau lattice model
On B=P1 minus(mu4 union infinity), Cn:un^n=x^4-1 for n=2,3,4 are the existing marked covers with positive finite exponent1. Fix the mu3 deck orientation omega. Use the original J and sigma with c=J sigma, actual reduced Burau matrices at omega and their retained Z[omega]^3 basis and invariant Hermitian form. Do not identify this integral model and trace form with independently constructed geometric cycles or their intersection form.
- 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.
Original evidence
- JOINT-CLOCK.txt lines 1–190
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-joint-source-20261023/JOINT-CLOCK.txt
02a15050dc0d8f7ad69ad1d867318d7a9abfa4bee274e14f1f06a12cf16c9628
- JOINT-CLOCK.txt lines 191–281
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/e-series-joint-source-20261023/JOINT-CLOCK.txt
02a15050dc0d8f7ad69ad1d867318d7a9abfa4bee274e14f1f06a12cf16c9628
finding:complete-fixed-jhat-cyclic-field-lift-and-associated-clock