Established in scope
Equivariant lifting and divisibility by eight
In the question: Active mathematical program: marked seam monodromies and lattice lifts
Original60reflection class, ordered punctures, marked central generator and simultaneous inner conjugation. General theorems use their explicitly stated hypotheses.
Read the exact result, assumptions and evidence
Result
Central orbifold H2 decides lifting; based lifts form an H1torsor and unbased lifts require centralizer quotient. Cone power defects are complete on oriented punctured quotient surfaces. The existing determinant class on C_m*C_mwith opposite parity lifts exactly for8|m, then16lifts; an original order8matrix example is given.
Required assumptions
- Active purely mathematical marked-seam program
Within the stated mathematical scope, marked pairs, lattice transport systems, reflections, clocks and cohomology are independent mathematical objects. Earlier origin/completion tasks are historical, not active. Distinguish new definitions, derived theorems and optional markings.
- Original G31reflections and central determinant class
The60original reflections generate G31of order46080. Use exactly E=Z4xG31with determinant cocycle from original holonomy proof§4; distinguish E,effective diagonal quotient and noncentral lattice lifts. Mark z.
- 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 35–161
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/equivariant-monodromy-20261023/THEOREMS.txt
e96dab9d854b4fa6c4c93dd7792fa8769d0ee41abdafa0072817d44990ac3b85
finding:orbifold-lift-criterion-and-determinant-eight-divisibility