Passes 3535–3541 · exact finite computation

Four Borel archetypes and a field of factorizations

The missing-Moore symmetry search is reduced to four conditional 19:9 forms, the Perkel 57-space gains exact integer Fourier projectors, and the Hoffman–Singleton control proves that Moore curvature cannot arise from one globally reused factorization.

PASS_7_FRONTS 34ea459ab6acea3a2b5624ba6523016cfb914ffb54220ed64230f74f78a1fb6b

Independent clique source
3,720

Exact reconstruction columns, exact compatibility graphs, bitset maximum cliques, witnesses, and proof digests. The full rerun remains artifact-gated.

Conditional M57 symmetry
4 archetypes

Two orbit profiles and two order-19 displacement values survive all fixed-set, character, girth, and power-balance tests.

Perkel projectors
1 + 2 + 18 + 36

Four orthogonal denominator-171 projectors split the rational vertex module; the 54-dimensional conductor-19 sector obeys x³−8x+3.

Global-factorization no-go
0 / 120

Every colour identification between one row and one symbol factorization fails all twenty Hoffman–Singleton triangles.

Complete K6 atlas
6 rows · 6 factorizations

The HS edge chart uses every labelled one-factorization of K6 exactly once. All twenty holonomies have cycle type 2³.

Polynomial transplantation
Q[x]/(x²+2x−8)

W33 and Gewirtz now share an executable full-graph functional compiler, while geometry-sensitive claims remain fail-closed.

Boundary. The degree-57 Moore graph remains open. The four Borel archetypes are necessary conditional forms, not realized actions. No independent full 3,720-instance clique histogram is claimed until its heavy workflow artifact is observed.

Exact sources

analysis/bt3535_3541_clique_borel_fourier_factorization_ports.py
analysis/bt3535_star_clique_recertify.py
data/PART_BT3535_BT3541_CLIQUE_BOREL_FOURIER_FACTORIZATION_PORTS_results.json