Paper 3, Study 1 — predeclared plan v1.0: do normal-likelihood Bayesian intervals fail on the same side as Welch's? (Behrens–Fisher programme)

Prospective registration of the predeclared plan (v1.0, frozen 5 Nov 2026) for Study 1 of Paper 3 in a programme on the direction of small-sample interval failure for a difference in means. Study 1 computes two normal-likelihood Bayesian intervals — the independence-Jeffreys (Behrens–Fisher fiducial) interval and the Jeffreys-rule interval — on the exact datasets of Papers 1 and 2, regenerated from their archived seeds, and tests whether they fail on the side predicted by the skewness quantity Γ (hypotheses S1–S6). An identity check requires the recomputed Welch and Hsu results to match the archived Paper 1 counts and Paper 2 dataset-level indicators exactly. The package contains the frozen plan (with a typeset PDF copy) and its SHA-256 fingerprint, the code, the accuracy validation of the quantile engine, all 684 pre-built quantile tables, and a pilot on non-study seeds used only for code checks and timing. No Study 1 computation on study data had been run at the time of deposit.AI-use note : The , code and checks were developed with Claude (Anthropic) as a computational assistant under the author's direction; the author developed the plan, hypotheses and theory statement and is responsible for the registration.