Add predict_rating game-outcome prediction (PlayerRatings predict.rating)

[seonghobae]

Summary

Implements predict_rating / predict_rating_multi — game-outcome prediction from fitted rating states, a Rust reimplementation of CRAN PlayerRatings 1.1-0 predict.rating (R/ratings.R lines 1056–1133, READ and normative; no journal paper exists for this dispatch — CRAN package provenance only). Stacked on #305 (fide). This completes coverage of the PlayerRatings package (elo, glicko, glicko2, steph, elom, fide, metrics, predict).

Model contract

Three branches, matching the R dispatch:

• Elo logistic (no deviations): pred = 1 / (1 + 10^((brat − wrat − gamma)/400)), per-game or scalar gamma.
• Glicko-family deviation shrink: exponent multiplied by vec = 1/sqrt(1 + qip3·(wdev² + bdev²)) with qip3 = 3(ln10/400/π)² — the joint two-player shrink from the R source (both players' squared deviations inside ONE sqrt).
• EloM multi-player: pred = (rating − rowmean_{na.rm})/40 per row of a nr×np player matrix; optional placing returns min-tie ranks of −pred with NaN kept.

R semantics preserved: strict games < tng unrated cutoff (stored value → NA), trat replaces ALL missing extracted values (unmatched −1, low-games, stored-NA alike), pred >= thresh → 1/0 with NaN propagation.

REDUCED-SCOPE vs R: index-based players (−1 = unmatched; caller does name matching), no data-frame plumbing.

Verification evidence

• Spec-verify (adversarial, before implementation): APPROVED-WITH-CHANGES; all 4 mandatory changes adopted (trat-replaces-stored-NA semantics, oracle header wording, NaN-allowed/Inf-rejected error contract, P9 stored-NA fixtures + scalar-gamma broadcast test).
• Exact oracle EXECUTED (predict_oracle.py, fixtures P1–P9): pins include P2 = 0.7898441797581306, P3 = 0.776912664201114, P9 = 0.7844611342833985, qip3 = 1.007239860196398e-05.
• Mutation testing — 7/7 EXECUTED kills (source restored byte-identical):

  Mutant	Mutation	Killed by
  MU1	gamma sign flip	pr_anchor_elo_gamma_sign
  MU2	qip3 factor 3→2	pr_deviation_shrink
  MU3	two-player < tng → <=	pr_tng_boundary
  MU3b	multi < tng → <=	pr_elom_rowmean
  MU4	divisor 400→200	pr_anchor_elo_gamma_sign
  MU5	placing rank > → >=	pr_placing_min_ties
  MU6	thresh >= → >	pr_thresh_ge_and_nan

• Every assert reads crate/wrapper outputs (no test-local identities).
• Suites: cargo test -p mlsirm-core --lib → 833 passed, 0 failed; pytest tests/test_paper_features.py → 328 passed (incl. new TestPredict ×6). pr_mc_500_invariants MC-500 #[ignore] test passes.

Adversarial impl-review outcome

• Round 1: FINDINGS (2 MAJOR) — (1) Python wrappers lost games/tng integer fidelity above 2^53 via a float round-trip, shifting the strict games < tng cutoff; (2) predict_rating_multi computed nr * np unchecked, so a wrapping product could pass the length check and panic across the PyO3 boundary. Both fixed in 4cbba18: lossless _predict_games_u64/_predict_tng_u64 validators (int inputs exact to u64; float inputs bounded by the source dtype's exact-integer limit) and checked_mul with a checked error, plus Rust + pytest regressions for both.
• Round 2: CLEAN — round-1 repros re-run (NaN / ValueError, no panic), new edge probes (u64-max games, float32 fidelity bound, np scalar/0-d tng, Fraction/Decimal, bool/masked rejection) passed, pr_ suite 8 pass, TestPredict 7 pass, oracle pins unchanged.

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[seonghobae]

Note: this PR was squash-merged into a non-main stacked base, so its commits did not land on main via this PR. The feature set reached main via #374 (stack tip integration) after #290.