[huashengshao]

Native tree preparation exposed coherent color coefficients and their norm but no evaluator for requested color insertions. This change binds a retained Arc<TreeProgram> to exact matrices for Identity, charge pairs, ordered dipole products, unnormalized anticommutators and distinct-leg structure-constant tripoles. Each matrix is an overlap with a complete transformed ket tensor; no Gram inversion or multiplication of overlap matrices is used.

Hermitian self-contractions use the existing exact real lowering before numerical instruction construction. Independent bra/ket components and non-Hermitian products retain their directed complex values. Fixed-helicity, streamed-helicity and explicit-component methods support runtime parameters and preserve native carriers, working bits, row identities and typed numerical failures. Numerical model support remains SU(3), TR=1/2, within TreeProgram's declared field/propagator domain; formal Nc matrices are diagnostic algebra. This is not an open-index spin tensor API. Numerical accuracy remains Unknown: this layer supplies no certified error bound and makes no complete NNLO prediction claim.

This PR is deliberately stacked on codex/native-tree-color-correlations-base at 4f57331e698e6033584c0f65b55dc2a5c0e9cf41, composed from the numerical-error/tree baseline c9bfd3d7474a5942000b2173e2ff8095682da787 (PR #21) and exact operator actions 54b6f821da6a4bc92041936bc70f7946d7c47525 (PR #19). The review diff contains only the new correlation module/tests and its public module export; prerequisite changes are excluded. Retargeting to the upstream integration branch waits for those prerequisites.

Validation on Rust 1.97.1 with locked dependencies:

• All 96 rusticol-loop-reduction library tests passed with one test thread, including 12 new correlation tests. The same prebuilt full suite passed with PATH=/nonexistent, so Python and external compilers were unavailable.
• Coverage includes exact product ordering/tripole signs, repeated factors, redundant complex bases, zero-overlap/nonzero-insertion cases, crossed quark and adjoint channels, color conservation/Casimirs, runtime parameters, independent complex bra/ket phases, malformed/empty metadata and typed overflow recovery.
• Forced carriers: binary64/53, double-double/106 and arbitrary 113, 137, 256, 512 and 1024 bits. A public directed-component test reconstructs 137-bit inputs and retains a phase difference of 2^-80. Independent source review found no remaining issues.