36 ↔ 36
Every A6 chamber determines one unique W33 spread.
An exact, objectwise U4(2)-equivariant bridge—plus an executable certificate for the exceptional outer automorphism of S6.
Every A6 chamber determines one unique W33 spread.
The spread stabilizer is S6; its derived subgroup is the attached A6.
The complete construction is frozen under a semantic SHA-256 certificate.
For a chamber H ≅ A6, the normalizer has order 720, fixes exactly one spread ΣH, and equals its spread stabilizer:
NG(H) = StabG(ΣH)
Transport under the four explicit U4(2) generators is path-independent. Therefore H ↦ Σ_H is an actual equivariant bijection, not a 36=36 analogy.
| A6 chamber intersection | Spread intersection | Pairs | Relation |
|---|---|---|---|
| |H ∩ K| = 18 | 1 shared line | 360 | SRG(36,20,10,12) |
| |H ∩ K| = 12 | 4 shared lines | 270 | SRG(36,15,6,6) |
The two relations are complementary. The graph identity is carried by the explicit object map; parameters alone are not used as identification evidence.
The twelve A5 subgroups in one chamber split into the two global A5 classes.
Same-side pairs meet in A4; every cross-pair meets in D10, yielding K6,6.
The S6 stabilizer acts faithfully on both six-sets. The two actions exchange cycle types exactly as the exceptional outer automorphism requires:
(2,1,1,1,1) ↔ (2,2,2), (3,1,1,1) ↔ (3,3), and (6) ↔ (3,2,1).
The directed multiplicities are 15, 40, and 120 in each direction.
A concrete 5B-containing U4(2) embedding in the Monster would automatically transport the full 36-spread carrier, all 36 A6 chambers, both rank-three orbitals, and all local double-six charts. This sharply specifies what a future Monster-word certificate must preserve.
Evidence boundary. This packet does not serialize Monster words, choose a unique class fusion, prove an 81-dimensional restriction multiplicity, identify the distinct 36 magic-ray graph, or construct a Griess, VOA, Leech, or photonic multiplication law.
analysis/w33_pass3663_3669_monster_chamber_spread_bridge.py
data/PART_3663_3669_MONSTER_CHAMBER_SPREAD_BRIDGE_results.json
tests/test_w33_pass3663_3669_monster_chamber_spread_bridge.py
Semantic SHA-256: ea0d3d989c05d51dc1e60de05cb9fe9f3308d8c36f1e40749b915f7bc0aaefca