Exact packet
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Seven fronts regenerate under one semantic certificate.
Passes 3542–3548 turn the surviving 19:9 symmetry lane into a finite cyclic-difference problem, compute the complete Perkel commutant, and expose Hoffman–Singleton as the duad–syntheme–pentad outer action of S6.
Seven fronts regenerate under one semantic certificate.
Four action archetypes reduce to two low and ten high internal signatures for each orbit profile.
End_B(Q^57) ≅ Q ⊕ M3(Q(√−19)) ⊕ Q(√−3).
A point transposition becomes three transpositions on the six pentads.
All 20 triangle holonomies are 2³ and all 45 four-row holonomies are 3².
Unique pair intersections plus deranged 3- and 4-holonomies form a sufficient Moore construction branch.
The three orbit cells adjacent to the unique fixed vertex have disjoint 56-cell neighborhoods. This forces the remaining 168 cells into a literal 56+56+56 partition. Internal circulant degree can only be 0, 2, or 4, and stabilizer invariance restricts all internal edges to the eighteen regular Borel orbits.
The explicit algebra separates Q(√−19) for conductor-19 symmetry, Q(√−3) for the conductor-3 phase sector, and Q(√5) for the golden adjacency spectrum. The decomposition is exact algebra, not a physical identification.