From the deep-research math validation (docs/research/2026-06-11-math-validation.md):
1. Excess conflict compared a magnitude-WEIGHTED mismatch ratio
(min(|a|,|b|) weights) against the UNWEIGHTED arccos(rho)/pi
expectation (Sheppard / degree-0 arc-cosine kernel). The two are not
the same statistic (Cho & Saul: J1 != J0 angular dependence), and for
correlated LoRAs mismatches concentrate on small-magnitude positions,
so the weighted ratio sat systematically below the baseline — real
conflict was under-detected (excess clamped to 0), biasing decisions
away from TIES. Now: unweighted mismatch fraction AND correlation
computed on the same noise-floored position set, baseline
arccos(rho_strong)/pi. Weighted ratio kept as a separate metric.
2. slerp mode for N>=3 diffs replaced iterative pairwise SLERP with a
weighted Karcher (Frechet) mean on the unit hypersphere (chordal-mean
init, log/exp-map iteration, existing norm correction). Iterative
multi-SLERP is order-dependent and collapses empirically (scores
below plain linear averaging at m=5; Karcher 0.610 vs multi-SLERP
0.239). N=2 keeps standard SLERP (the Karcher mean reduces to it).
Bump AUTOTUNER_ALGO_VERSION 1.7.0 -> 1.8.0 and ANALYSIS_CACHE_VERSION
1.7.1 -> 1.8.0 (pair metrics and merge behavior changed). Adds the full
cited validation report and 8 tests: identical/negated/independent
vectors give zero excess, count-concentrated conflict now detected
(old formula provably clamped it to 0), Karcher order-independence,
symmetric-direction, weight-pull, and N=2 SLERP regression (244 pass).
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
