feat(flaky): pass^k multi-trial reliability metric (#13)#21
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pass^k = the unbiased probability that ALL k of k trials pass — reliability under repetition, the complement of pass@k. Uses the Tau-bench estimator C(passed,k)/C(total,k) (sample k of the observed trials without replacement), reusing the existing multi-run aggregation (flaky.py). - flaky.py: pass_hat_k(passed,total,k) (k=1 ⇒ pass rate; <k passes ⇒ 0.0; too few trials ⇒ nan, never fabricated) + reliability_at_k(result,k) + reliability_summary(cases,ks). build_multi_run_report now emits pass^2 and pass^(num_runs) in summary when enough trials exist. Tests: test_pass_hat_k.py (9: k=1=pass-rate, all-pass=1, unbiased C(c,k)/C(n,k), <k passes=0, insufficient=nan, k<1 raises, per-case + summary, report wiring). pytest 9/9, mypy + ruff clean (venv). Closes #13. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_019tXZpN29akdmG8AEjgSZwk
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Closes #13.
What: pass^k = the unbiased probability that all k of k trials pass — reliability under repetition (the complement of pass@k). Uses the Tau-bench estimator
C(passed,k)/C(total,k)(sample k of the observed trials without replacement), reusing the existing multi-run aggregation inflaky.py.How:
pass_hat_k(passed, total, k)—k=1⇒ pass rate; fewer than k passes ⇒0.0; too few trials to draw from ⇒nan(never fabricated).reliability_at_k(result, k)(per case) +reliability_summary(cases, ks)(mean over cases, nan-skipping).build_multi_run_reportnow emitspass^2andpass^(num_runs)insummarywhen enough trials exist.Tests: 9 (k=1=pass-rate, all-pass=1, unbiased C(c,k)/C(n,k), <k passes=0, insufficient=nan, k<1 raises, per-case + summary, report wiring). pytest 9/9, mypy + ruff clean.
Pure-stats, additive (only adds keys to the report summary).