How much coverage does a small benchmark have?

What will you examine?

Binomial model: n = 20, exact p = 1/20, nominal coverage 19/20.

The platform predicate uses rational z = 1959963984540054/10^15; the author enumeration records Python NormalDist().inv_cdf(0.975). These are distinct stated conventions.

Enumerate counts 0 through 20. Clip Wald to [0,1], do not additionally clip Wilson, and include endpoints without membership tolerance.

A separate descriptive simulation uses 4,000 repetitions and seed 12001 with paired method comparisons.

What does the question assume?

Independent Bernoulli trials share the same fixed success probability.

The displayed fixed interval convention and rational quantile approximation define the checked model; source-output alignment remains a separate question.

What should you compare?

Sum binomial probability over each of the 21 counts whose interval contains p. Full enumeration does not imply exact floating-point arithmetic.

At ideal p = 1/20 the reference membership sets are Wald counts 1–4 and Wilson counts 0–2; compare the recorded interval endpoints and membership before summing.

Retain every count's probability, endpoints and membership, model coverage, simulated coverage, repetition count and seed. Do not fit a pass threshold to the simulation.

Freeze absolute tolerance 1e-12 for numerical endpoint, mass and coverage comparisons; membership booleans must match exactly.

What could the evidence establish?

Nominal 95% is a design label; actual model coverage may differ substantially.

The model does not describe correlated benchmark tasks, heterogeneous probabilities or every sample size.

The fixed-model binomial predicate requires its separately qualified runtime and quote. It does not verify author code, output or simulation; no check has run during preparation.

Prepare, then authorize the work.

1. Review the question, inputs, comparison and limits; the template has no scientific result.

2. Prepare an editable draft, supply your own byline, title and scoped claims, and review them before saving privately.

3. Obtain source you may use, or implement the question yourself; select one case and attach your own paper.md in the source ZIP. Do not run submitted code on your host.

4. Upload opaque source bytes through your project. Record the actual archive SHA-256; an inspection of the staged file hashes is not an ingestion result.

5. Review and accept the current bounded ingestion quote. Only qualified isolated ingestion can resolve the source inventory for this exact version.

6. Then review and accept a separate quote for the one author job. Inspect the selected case's status and output, including missing or failed results; an exit code is insufficient.

7. Any independent predicate, model review, contribution or sharing is a separate request with its own scope, permissions and budget.

Bring source you may use.

The inspected original source remains local staging material. Its MIT/CC BY/CC0 terms are proposed, not a released license grant. Obtain permitted source or supply your own implementation. The source-version digest is not an archive digest.

The staged task-template archive is unavailable. That source remains local staging material with proposed, unreleased license terms.