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Graphon.SubgraphDensityBlueprint

Blueprint node for the finite density triangle (#94) #

Annotation-only wrapper carrying the blueprint-graph node for the finite subgraph-density triangle. Housing the Architect dependency here keeps Graphon.SubgraphDensities a pure combinatorics module (it is an upstream/reuse candidate); the mathematical content lives there.

theorem finite_density_triangle_blueprint {k n : } (F : SimpleGraph (Fin k)) (H : SimpleGraph (Fin n)) :
F.tInj H = F' : SimpleGraph (Fin k) with F F', F'.tInd H F.tInd H = F' : SimpleGraph (Fin k) with F F', (-1) ^ (F'.edgeFinset \ F.edgeFinset).card * F'.tInj H |F.t H - F.tInj H| k ^ 2 / n

The finite density triangle (#94; Lovász §5.2.3, (5.19)–(5.21)): the zeta identity t_inj(F, ·) = ∑_{F' ⊇ F} t_ind(F', ·), its inverse Möbius form t_ind(F, ·) = ∑_{F' ⊇ F} (−1)^{|E(F') ∖ E(F)|} t_inj(F', ·), and the collision comparison |t − t_inj| ≤ k²/n — all unconditional under the small-host zero convention.