0010 — Each algorithm follows its defining document

Status: accepted · Date: 2026-10-17

Context

0005 proves each family against values frozen from its canonical Python library, and 0007 accepts a divergence from that library only where reproducing it would reproduce a defect. Read together, they made the library the authority on behaviour as well as on numbers, its degenerate answers included.

The Review B after #1702 showed what that costs. Aligning Lodestar.Stats with scipy one test at a time answered NaN for an empty sample in some tests and refused it in others, and reached a Shapiro-Wilk constant sample that scipy answers NaN for and that Royston's own algorithm, AS R94, refuses as its sixth fault. scipy's answers on degenerate input are scipy's choices, made test by test; the method is defined elsewhere.

Decision

Each algorithm follows the document that defines it — the paper or the published algorithm — and the Python library is the numeric oracle wherever it implements that document. Where the document states a fault, a range or a limit, the code follows it: Shapiro-Wilk refuses fewer than three values and a range below 1e-19, and computes past 5000 values, as AS R94 does. Where the document is silent and the input leaves the statistic undefined — an empty sample, every value tied, an empty group — the answer is NaN, the same whether the input arrived so or was left so by omission, which keeps 0007's reason for treating both paths alike.

This amends 0005: a corpus frozen from the library still proves the numbers, and no longer decides a behaviour the defining document decides otherwise. It amends 0007's row for Shapiro-Wilk and Kruskal-Wallis under omission: a sample left degenerate answers NaN where the document is silent, and is refused where the document refuses it. A divergence from the library is now recorded against the document, in ../equivalence.md, rather than justified against the library.

Consequences

• Lodestar.Stats applies it first. Kruskal-Wallis on a fully tied pool, the t-tests, Mann-Whitney, Kolmogorov-Smirnov and Wilcoxon on an empty sample, and the five k-sample tests on an empty group answer NaN; Shapiro-Wilk follows AS R94's faults. equivalence.md states, row by row, each answer that follows the document rather than the library.
• The other packages follow as their reviews reach them. A family whose library departs from its document keeps the library's corpus for the inputs where the two agree, and states the rest in equivalence.md.
• A degenerate behaviour now needs its document read first. The library's answer is evidence of what the document allows, not the rule.