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 : ℕ}
(F : SimpleGraph (Fin k))
(H : SimpleGraph (Fin 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.