RandLib separates distributions into two evidence tiers. Tier 1 distributions have full probability, sampling, and fitting expectations; Tier 2 distributions are tested for coherence and sampling and use documented best effort where no robust reference algorithm is available.

Quantity	Tier 1 target	Tier 2 target
PDF/PMF, CDF, survival in the bulk	`1e-12` relative	`1e-8` relative
Tails down to probability `1e-300`	`1e-9` relative	Best effort, documented
Quantile round trip	`1e-10` relative	`1e-7` relative
Closed-form moments	Correct to floating-point rounding	Correct to floating-point rounding
Characteristic function	`1e-8` absolute	Best effort, documented
Stable PDF/CDF	`1e-9` absolute	Not applicable
Sampling goodness of fit	Required	Required
Fitting	Required	Optional

“Bulk” means 1e-6 < F(x) < 1-1e-6. A target is not a blanket guarantee for every parameter and platform: committed exceptions in tests/data/reference_tolerances.csv name their region, tolerance, and tracking issue.

What counts as evidence

Probability values are generated with mpmath at 40 decimal digits. Exact identities and closed-form special cases supplement those tables. Another double-precision library is useful for investigation, but it is not accepted as the sole reference for changing a golden value.

Every output difference from the baseline golden corpus must have one of:

a committed mpmath reference;
an exact formula recorded in the deviation reason; or
a focused regression test establishing the corrected invariant.

tools/refdata/generate.py regenerates high-precision reference CSVs. tools/golden/classify_deviations.py combines reviewed classifications with reference-backed exceptions. Reference generators and their dependency versions are part of the evidence and are committed with the data.

Test layers

The suite combines exact regression tests, high-precision point references, PDF/CDF/survival and quantile coherence, parameter validation, deterministic engine advancement, seeded parameter recovery, and statistical sampling tests. Statistical checks use fixed seeds and predeclared thresholds; a single attractive histogram is not validation.

Survival functions should be implemented directly when subtraction would lose tail precision. Tolerance relaxations require a nearby explanation and an issue link. Improvements must first remove or tighten the corresponding registry override, so the measured contract and documentation stay in sync.