B6 rank-one: first staged independent-NUTS prior-SBC and coverage pilot¶

The source code predeclares four new independent prior-generated B6 rank-one sparse univariate datasets, using a separate seed namespace from four-chain reference study R1. Each receives the independent score-marginal PyMC/NUTS model with 4 chains, 700 warmup and 400 retained draws per chain. These are deliberately shorter pilot fits to assess cost and failure modes, not retrospectively selected well-mixed chains.

The two primary invariant targets are the population x mean and x variance at the grid midpoint. For each: preserve the full four-chain ArviZ diagnostic, a discrete truth-versus-posterior SBC rank with reproducible tie handling and one truth-in-90%-interval flag. All six time-indexed functionals remain in the diagnostic evidence, but only one rank per primary quantity per independent dataset enters preliminary rank and coverage summaries. A 10-bin rank histogram with only four ranks is merely bookkeeping, not an interpretable uniformity test.

Dataset-level denominator, fit errors, sampling-screen failures and individual source hash checks are retained. Preliminary binomial intervals are exact Clopper-Pearson intervals among successful fits and explicitly report total attempts, so failures are not silently removed.

Next prespecified calibration stage should set a simulation-precision target, e.g. approximate 95% Monte Carlo half-width ≤.06 for a nominal 90% event needs roughly 100 independent successfully assessed datasets, while failed/nonconverged runs need explicit handling. No fixed-parameter frequentist coverage is studied here: that requires fixing a generating functional truth across repeated observation datasets, distinct from generating truth itself from the prior every replication.

B7 prior calibration, a rank-two posterior reference, posterior predictive checking, implementation model audits and power/cost scaling remain separate workstreams under scientific issue #255. Public release flags remain false.

Completed corrected-source pilot — 11 October 2026¶

The first scientific workflow #38087242217 failed before posterior sampling because direct script execution could not resolve the repository scripts import. This is an entrypoint/harness failure, not posterior nonconvergence or an SBC rank. The correction preserved the statistical model, sampling configuration, seeds and rank definitions.

The corrected source workflow #38087405506 on experimental PR #274 head 3011666b6caeb7e38455a5b439e92bb305ea3be3 finished 8/8 science jobs, including four actual four-chain posterior fits, and passed the checksum-verified failure-inclusive summary. The full corrected PR head passed 25/25 engineering workflows. Each fit uses 700 warmup and 400 retained draws per chain: this budget is intentionally shorter than R1's 1,200 / 800 setting.

The predeclared screen was rank R-hat ≤1.01, bulk/tail ESS ≥400, BFMI ≥0.3 and zero divergences across all identified population functionals. The failure remained in the scientific ledger even though the posterior fit completed successfully.

Prespecified midpoint truth ranks — original case records¶

For each midpoint quantity, observed prior-predictive interval inclusion was 4/4 completed fits, with exact 95% binomial interval approximately 39.8%–100%. These eight outcome checks are dependent within the four independent datasets, not eight independent calibration observations. The four variance ranks happen to be above the midpoint; the sample is far too small to diagnose rank bias or evaluate histogram uniformity.

Source artifacts: four replicate case ledgers 11682921911, 11683660208, 11683911505, 11683087449, and failure-inclusive aggregate 11683762021 (original source run). The SVG plots only the original retained ranks and diagnostic R-hat values; it is not additional Monte Carlo evidence.

Decision: the implementation and rank bookkeeping are operational, but only three of four completed datasets pass the exploratory computational screen, and four datasets cannot quantify SBC rank uniformity or credible-interval coverage. A follow-up should independently refit replicate 1 using the full R1 1,200/800 budget, then expand under a prespecified convergence and simulation-precision protocol, retaining all attempts as denominator observations. Neither fixed-truth coverage nor B7/rank-two SBC was performed; posterior calibration and the 1.2 release remain unqualified. Scientific blocker #255 remains open.