[lsimon125]

Summary

Improve native correlated matrix elements for cancellation-prone phase-space points, without adding Python or Symbolica to the numerical SDK. These changes were motivated by integrating the tree-level provider into MadNkLO.

• Retain rounding residuals through coherent amplitude sums, rational colour weights and complex bilinear contractions using twofold arithmetic.
• Add explicit, opt-in binary128 rescue: Runtime.compile_correlated_rescue(...) generates a Linux GCC/quadmath companion from retained evaluators; two additive C ABI functions load it and evaluate correlated requests with the existing binary64 buffer layout.
• Cache exact closed colour overlaps during connected-correlator preparation. The bounded cache preserves the full Nc Laurent polynomial, does not identify reflected traces, and returns independent coefficient mappings.
• Preserve Symjit-only builds with an explicit rescue-buffer type.

The changes do not alter colour/crossing conventions, model rules, dependency manifests or build configuration. There are no process-specific colour-factor shortcuts. The cache is isolated in its own commit and is a performance improvement, not a prerequisite for the numerical fixes.

Validation

• 125 focused colour tests, 5 focused Rust correlation tests, 17 C ABI tests, and 2 native rescue compiler regressions passed during development.
• Release cargo check -p rusticol-core --offline --locked passed with both default features and --no-default-features --features f64-symjit at the final revision.
• Antiquark crossed-channel stress gate (u~ g > u~ g g): compensation alone left 528 failures in 750,060 checks; explicit rescue reduced this to zero with unchanged tolerances. The massive b g > b g g rescue gate also passed all 750,060 checks.
• External MadNkLO integration against a normally built and installed SDK wheel passed 8,850 pointwise comparisons across scoped e+ e- > j j NNLO tree channels, general spin/colour and quadruple-colour requests, and massive crossed g g > b b~ g. Real F2PY accessor workflows and missing/wrong-companion loader guards also passed. These integration fixtures live in MadNkLO, not this PR.
• Exact-colour cache benchmark: all 576 five-gluon matrix entries unchanged; preparation reduced from 3.54 s uncached to 0.55 s cold / 0.33 s warm.

The installed-wheel numerical campaigns used da9f175a; the final 3f6b3cbc commit only corrects declaration/initialization for Symjit-only compilation and was checked in both feature configurations. No duplicate numerical campaign was needed for that type-only fix.

Scope And Limitations

Rescue is explicit, not an automatic precision switch. Preparation needs retained evaluators, Symbolica, and Linux GCC/quadmath; execution needs quadmath but no Python or Symbolica. Inputs and result buffers remain binary64, while internal currents/amplitudes use binary128. Companion loading checks artifact identity and dimensions; unsupported programs fail explicitly, and small imaginary components are not clamped. Convenience-language wrappers do not yet expose the two new C ABI functions.