Validation Record

• R: (i-0.5)/n plotting positions, qnorm / -log(1-p) / p / log(-log(1-p)) for the theoretical axes
• R ppoints() recorded alongside — it uses a = 3/8 at n <= 10, so it agrees with Stratum only above that
• normalQuantile pinned to Acklam's published 1.15e-9 RELATIVE bound against R qnorm

Not yet covered: The CONFIDENCE BAND (QQConfidenceBand) has no fixture — only the points and the theoretical axes are covered.

• R stats::lm for all six parametric forms — raw-power polynomials, lm(y ~ log(x)), lm(log(y) ~ log(x)), lm(log(y) ~ x)
• r-squared recomputed on the ORIGINAL y scale against the back-transformed prediction, which is what Stratum reports; R's model-scale summary()$r.squared is recorded beside it and asserted to differ for exactly the power and exponential forms

Not yet covered: The non-parametric smoothers — LOWESS, kernel smoother and moving average — have no fixture. Their implementations differ in detail between packages, so pinning one spelling of LOWESS would pin R's choices rather than a shared definition; closing this means deciding which definition Stratum claims first.

• grid geometry from the engine's own 2-D rule, h = 1.06*max(sd, range*1e-3)*n^(-1/6)*scale, pad = clamp(2.5h, 3%, 15%) — the bandwidth is not exposed, but x0 and dx are functions of it, so the geometry pins the rule exactly
• a DIRECT 2-D Gaussian kernel sum in numpy, compared in shape against the engine's binned separable blur within a measured bound (6%, 12% on the coarse grid)

Not yet covered: The blur is an APPROXIMATION to a 2-D KDE, so the surface is checked for shape against the exact estimator rather than value-for-value — the bound is a recorded measurement, not an equality. The value and aggregate modes (with a Z column) and their 2% masking threshold have no fixture. Note this chart does NOT share KernelDensityEngine: it uses the 2-D n^(-1/6) exponent where Density uses n^(-1/5), so it inherits nothing from that fixture.

• sklearn.metrics.roc_curve(drop_intermediate=False) / roc_auc_score
• sklearn.inspection.partial_dependence(kind='average')

Not yet covered: The DIAGNOSTICS (ROC, AUC, calibration binning, partial dependence) are pinned; the fitted TREE is not. A single tree can be matched to sklearn exactly given the same split rule and deterministic tie-breaking, so this is a gap to close, not an impossibility.

• sklearn.metrics.roc_curve / roc_auc_score

Not yet covered: Diagnostics only. An ensemble cannot be matched tree-for-tree against sklearn — the RNG streams and split tie-breaking differ by construction — so the model itself needs invariants (OOB convergence, importance monotonicity) rather than a value comparison.

• sklearn.metrics.roc_curve / roc_auc_score

Not yet covered: Diagnostics only — same reasoning as Random Forest.

• R ca::ca()
• an independent numpy implementation from the definition (Greenacre), not a transcription of the engine
• scipy.stats.chi2_contingency — pins the identity n * total inertia == chi-square

Not yet covered: The DISPLAY CAP is not covered. Above StratumLimits.maxReportGroups the engine pools the tail into 'Other' and decomposes the POOLED grid, which moves both the inertia and the degrees of freedom; every fixture table is well under the cap. Row/column contributions and quality (cos²) have no fixture yet either.

• R stats::hclust(dist(X), method=single/complete/average/ward.D2)
• scipy.cluster.hierarchy.linkage
• sklearn.cluster.KMeans (well-separated data only)
• local optimality: nearest-centroid assignment, and centroid is the cost-minimising centre — mean under Euclidean, median under Manhattan

Not yet covered: The k-means PARTITION is compared to scikit-learn only where the optimum is unambiguous. On ambiguous data, and under the Manhattan cost (which sklearn's KMeans does not implement), the evidence is invariants rather than an outside implementation — because no outside implementation of that estimator exists to compare against, not because the check was skipped. Elbow and silhouette have no fixture yet.

• d2 by Gauss-Legendre quadrature
• c4 via scipy.special.gammaln

Not yet covered: The unbiasing CONSTANTS are pinned to first principles; the Nelson / Western Electric run rules are not, and they are a documented convention rather than a computed quantity.

• d2 / c4 as for I-MR

Not yet covered: Constants pinned; run rules are convention. Same as I-MR.

• binomial limits

Not yet covered: Attribute-chart limits are not yet cross-checked against an outside tool.

• Poisson limits

Not yet covered: Attribute-chart limits are not yet cross-checked against an outside tool.