ramsey-karp-fpt

Ramsey, Erdős–Hajnal & Karp-21 FPT Engine (smart-tree v10.10.0+)

"Complete disorder is impossible." — Ramsey Theory (Paul Erdős, 1935–1989)

ramsey-karp-fpt (src/mem8/regularity/ramsey_erdos_hajnal.rs & salience_karp_manybody.rs) turns NP-complete graph problems into sub-millisecond static analysis over the 5-color AST symbol graph (Import, CallRef, TraitImpl, TypeBound, MutableShared) plus the 6th anti-color $c_\emptyset$.

1. 256-Bit Bitboard Bron–Kerbosch & Erdős–Hajnal Bi-Cliques

1. Matula–Beck Degeneracy Ordering ($d \ll n$): Computes $(v_1, \dots, v_n)$ in $O(|V| + |E|)$ bucket-queue time so every forward monochromatic neighborhood $N_c^+(v_i)$ has size $\le d \le 255$.
2. BitSet256([u64; 4]) Hardware Bitboard: Executes Tomita-pivoted Bron–Kerbosch set intersections ($P \cap N(u)$, $X \cap N(u)$) in four CPU AND + felix_popcnt_u64 / felix_tzcnt_u64 instructions with zero heap allocations inside the recursion.
3. Erdős–Moser Tournament vs. Cyclic Deadlock Knot (CliqueTopology):
   • TransitiveTournament ($\vec{T}_k^{(c)}$): Clean acyclic compilation/call pipeline.
   • CyclicDeadlockKnot: Mutual lock/call cycle; emits feedback_back_edges (Minimum Feedback Arc Set) and RefactorPrescription::BreakDeadlockCycle or FlattenCircularImports.
4. Fox–Sudakov / Rödl Pure & Almost-Pure Bi-Cliques (ErdosHajnalBiClique):
   • Pure Bi-Clique ($d_c(A, B) = 1.0$): $|A|$ structs all depend on the exact same $|B|$ targets $\rightarrow$ ExtractSharedTraitFacade.
   • Almost-Pure Bi-Clique ($1 - \delta \le d_c(A, B) < 1.0$): Pinpoints API Conformance Bugs via missing_anomaly_edges — the exact pair $(a^, b^)$ where struct $a^$ forgot to implement or call sibling method $b^$.

2. Taming Karp's 21 NP-Complete Problems in smart-tree