Established in scope
Actual group comparison and central pushout exclusion
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
An explicit lattice isometry identifies Gaussian and standard E8roots and preservesJ. Gamma_sign projects to<J>inG31. Neither group embeds in the other; common quotients are precisely1,C2and cannot retain order4clock. Zero invariant lattice mod2space forbids a nonzero equivariant sign-kernel map to trivialZ4and that central pushout identification.
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 312–366
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/equivariant-monodromy-20261023/THEOREMS.txt
e96dab9d854b4fa6c4c93dd7792fa8769d0ee41abdafa0072817d44990ac3b85
- checker.py lines 83–144
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/equivariant-monodromy-20261023/checker.py
91927ca2d86a724b387285b8406880df9cca0a46c7931940e5f344a91c230973
finding:actual-sign-lift-g31-group-comparison