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Oct 15, 2026
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docs: an Applications-in-practice section #63

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docs: an Applications-in-practice section -- the discipline earned on…
hyperpolymath Oct 15, 2026
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docs: link the PERMANOVA worked case directly (CodeRabbit, PR #63)
hyperpolymath Oct 15, 2026
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20 changes: 20 additions & 0 deletions README.adoc
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Expand Up @@ -305,3 +305,23 @@ If you use ZeroProb.jl in research, please cite:
* **Author:** Jonathan D.A. Jewell <j.d.a.jewell@open.ac.uk>
* **GitHub:** https://github.com/hyperpolymath/ZeroProb.jl
* **Issues:** https://github.com/hyperpolymath/ZeroProb.jl/issues

== Applications in practice

The worked case is permutation testing, as in MetaManifold's PERMANOVA
integration (the theorems:
link:https://github.com/hyperpolymath/MetaManifold-WebUI/blob/7d5e9a4/proofs/agda/MetaManifold/Permanova.agda[proofs/agda/MetaManifold/Permanova.agda],
pinned on the fork's `main` at 7d5e9a4 and proposed upstream as
link:https://github.com/JoshuaJewell/MetaManifold-WebUI/pull/55[PR #55],
with the Julia oracle at
link:https://github.com/hyperpolymath/MetaManifold-WebUI/blob/7d5e9a4/test/unit/test_permanova.jl[test/unit/test_permanova.jl]):
for `B` permutations the smallest attainable p-value is the
*floor* `1/(B+1)` -- attained exactly when no permutation reaches the
observed statistic -- and the proved theorems pin that floor. What ZeroProb
adds in practice is the honest language around it: a p-value at the floor is
near-zero but *not* measure-zero, and any claim of the form "essentially
impossible" must survive the same scrutiny as a density-ratio or
epsilon-neighbourhood argument. Pipelines that report "p = 0" for
insufficient permutations are publishing a measure-zero claim about a
discrete test -- this library is where that claim goes to be checked
before it reaches a figure.
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