The S₃ Dijkgraaf–Witten invariant of Spec ℤ[1/S]

Stage 6 — Z_DW = |Hom(π₁ᵉᵗ, S₃)|/6, decomposed by image: 1 + 3(2ᵗ−1) + (3ᵏ−1) + 6c. The trivial/C₂/C₃ terms are our own machinery; the S₃ term 6c is refereed by cubic-field enumeration. Renders emitted JSON only.

|Hom(π₁, S₃)| decomposed by image, per prime set S

trivial (1) image C₂ — 3(2ᵗ−1) quadratic image C₃ — 3ᵏ−1 cyclic cubic image S₃ — 6c non-Galois cubic

N_S₃ (= c, cubic iso classes) vs number of ramified primes t

Each point is one prime set S; c is the count of non-Galois cubic fields with rad(disc) ⊆ S — all totally real (R3).

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