[ruslan-splynx]

Closes #566.

Zero observed logical errors currently produce a Wald 0 ± 0, overstating the evidence. Add explicit two-sided, equal-tailed 95% Clopper–Pearson bounds for direct independent Bernoulli tallies: 0/1000 now yields [0, 0.003682], while zero shots yield [0, 1] and no estimate.

The existing Rust result fields and valid-input Wald half-width remain compatible. Add a checked tally constructor and reject invalid/numerically unreliable bound evaluations; the legacy infallible constructor preserves invalid counts with NaN sentinels. Quantiles use bounded bisection over statrs' checked beta function, with stable analytic boundary formulas. statrs with default features disabled is the only new lockfile package.

Threshold CSV appends explicit endpoints/method/evidence metadata. Its plot prefers asymmetric endpoints, omits zero-shot estimates, and shows zero-failure limits separately from the rate curve. Historical CSV widths retain their original meaning with a legacy notice. Comparison reports use named marginal overlap, without equivalence claims; the shared-shot MWPM/PyMatching report retains discordant pairs and uses a conditional exact binomial test instead of assuming independent rates. No weighted/correlated estimator or GPU/hardware API is silently reinterpreted.

Validation:

• 7 Rust interval tests (including randomized counts and exact finite-sum coverage), 5 experiment tests, zero-noise memory integration test, and 2 doctests passed.
• 3 Python CSV migration tests passed; actual 32-row zero-shot threshold CSV checked; zero-event/asymmetric-bound plot rendered and inspected.
• 3633 intervals independently compared with SciPy 1.16.2, including rare-event counts at one billion shots: maximum endpoint difference 6.24e-13. Exact coverage minimum 0.9556901; 10 repeated-sampling points × 20,000 trials reported with simulation standard errors. No numerical rejections in the campaign.
• Workspace all-target clippy, final QEC all-target clippy, rustfmt and diff checks passed.
• The broad local QEC debug suite was intentionally interrupted after >7 minutes to release Mac CPU; it is not claimed as passed. Full CI remains pending.

See docs/qec/binomial-intervals.md for the migration inventory, statistical/numerical limits and reproduction commands, and docs/perf/data/p8-16-binomial-coverage.json for raw coverage/provenance. This is a statistical-correctness fix, with no execution-speed claim or GPU benchmark requirement. Independent branch from main; no draft #569 changes included. Draft pending CI and final review; no merge requested here.