fix(jmle): recognize objective convergence and add recovery evidence

[seonghobae]

Why

PR #760 moved public JMLE Adam, L-BFGS, and adam_lbfgs optimizer loops into Rust, while issue #626 keeps scientific acceptance open until each advertised mode has true-parameter recovery and convergence evidence. The deterministic recovery study exposed a real production defect rather than a test-only gap: L-BFGS could reach a numerically stationary objective yet continue until the next Armijo search reported line_search_failed, misclassifying objective convergence as failure.

Production fix

This Draft changes the Rust L-BFGS loop in crates/mlsirm-core/src/jmle_opt.rs to recognize bounded relative objective reduction as convergence in addition to the existing gradient criterion. The stopping check is evaluated only after an accepted objective-decreasing step and uses the configured optimizer tolerance; it does not convert a failed line search or an increasing objective into success. A focused Rust regression fixes the numerical boundary and the hybrid-mode test no longer accepts line_search_failed as an ordinary successful outcome.

Scientific recovery evidence

tests/test_jmle_optimizer_recovery.py exercises the public fit(..., estimator="jmle", backend="rust", rust_device="cpu") path for adam, lbfgs, and adam_lbfgs on one deterministic, correctly specified unidimensional 2PL-generating sample (gamma=0). For every mode it requires:

• explicit convergence and positive iteration evidence;
• finite objective history ending no worse than it starts;
• an algebraically exact affine identification transform that preserves fitted logits;
• discrimination and easiness bias/MAE/RMSE bounds; and
• standardized theta MAE/RMSE rather than correlation-only recovery.

docs/doctoring/jmle_optimizer_recovery_evidence.md records the identification and interpretation boundary. The finite-sample thresholds are deliberately broad and do not claim penalized JMLE is asymptotically unbiased for item parameters.

Exact-current stack evidence

• base branch: codex/fast-judge-accepted-type-regression at 11291fd5f03cf24e403289b0466a7b633d0d3971;
• exact Draft head: 503564b57ecf7ba504557399a3343f6dd203601e;
• the branch was non-destructively refreshed onto that exact base with no force push;
• exact-head CI run 31548759944: success;
• exact-head ClusterFuzzLite run 31548759922: success.

These stacked-base results prove the current branch itself is green on its exact predecessor. They do not transfer across a later predecessor merge/rebase and are not protected-main release acceptance.

Scope / merge boundary

This PR changes the Rust optimizer convergence contract plus its recovery/test documentation. It does not change the likelihood, public API shape, dependency set, provider credentials, release version, or advertise end-to-end GPU optimizer parity. Keep Draft until #778 is integrated, this unique slice is reconciled onto the resulting protected main, all base-sensitive CI/security/review evidence is recreated on the unchanged final head, zero valid unresolved findings remain, and actual live repository policy is satisfied.

Advances #626.

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