Erdős–Hajnal conjecture for every forbidden induced graph

For each fixed finite simple graph H, prove a polynomial lower bound on the largest clique or independent set in every H-free graph G. H-free means no induced copy, not merely no subgraph. The integer form asks for constants C ≥ 1 and k ≥ 1 depending only on H, with n ≤ C*s^k for a homogeneous set of size s in every n-vertex G. Graphs are Boolean adjacency functions on Fin n; symmetry, no loops, embeddings and homogeneous sets are all explicit. Results for particular H, including the recently settled five-vertex cases, leave the general quantification over H unresolved. Research status checked 8 October 2026: no accepted general proof identified in the cited literature. This is a proposed formal statement; independent correspondence review is requested. A successful statement check establishes well-formedness, not the conjecture.

∀ h : Nat, ∀ H : Fin h → Fin h → Bool,
  (∀ i, H i i = false) → (∀ i j, H i j = H j i) →
  ∃ C k : Nat, 1 ≤ C ∧ 1 ≤ k ∧
    ∀ n : Nat, ∀ G : Fin n → Fin n → Bool,
      (∀ i, G i i = false) → (∀ i j, G i j = G j i) →
      (∀ f : Fin h → Fin n, (∀ i j, f i = f j → i = j) → ¬ (∀ i j, H i j = G (f i) (f j))) →
      ∃ s : Nat, ∃ f : Fin s → Fin n,
        (∀ i j, f i = f j → i = j) ∧ n ≤ C * s ^ k ∧
        ((∀ i j, i ≠ j → G (f i) (f j) = true) ∨
         (∀ i j, i ≠ j → G (f i) (f j) = false))

OA_statement : Prop