Established in scope
All62original clock objects admit character-valued lifts
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Ordered punctures, clock order4, full lift conjugation. No extra meridian square relation; distinct from central Z4extension.
Read the exact result, assumptions and evidence
Result
All62original clock objects admit strict C4*C4 lifts into the inherited lattice extension. Full conjugation gives11356classes=6856+4272+228. Every normal form and automorphism order is stored; independent Burnside verifies all62counts. Clocks0/3and0/5 give212and176classes.
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.
- Ordered G31reflection quadruples and chosen quarterclock
U=P1minusmu4, four ordered positive meridians in the60reflection class with product1. Chosen clocks have exact order4and conjugate meridians cyclically. Equivalence is simultaneous inner conjugation; central relaxations are separately defined relation contracts.
Original evidence
- THEOREMS.txt lines 175–296
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/global-g31-lattice-lift-20261023/THEOREMS.txt
a5db41f218483476fe623f0fc7353df5bfabf5f79af4a3eda58d7e05e0715fc0
- CLOCK_LIFTS.tsv lines 1–63
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/global-g31-lattice-lift-20261023/CLOCK_LIFTS.tsv
ff039702142160b1aeab24d98499484fb9d70b2d4145bb32493d04c58cd0849d
finding:all62-original-character-clock-lifts-complete