feat(analysis): Exact statistics layer — Fisher's exact, exact NB, permutation tests

[hyperpolymath]

Scientific Value

Parametric approximations break down with n<10 or sparse features. Exact tests provide valid inference.

Scope (Deferred)

• Fisher exact, exact NB (edgeR), permutation PERMANOVA
• Methods: exact_fisher, exact_nb, permutation

Difficulty: Hard

Risks: Performance 10-100x slower, memory for permutations, dependency edgeR

Acceptance Criteria

• Methods in v2
• BH mandatory
• Benchmarks
• Tests vs R fisher.test

Dependency status — refreshed 2026-09-22

Blocked by AnalysisConfig v1 — that blocker is stale and has been removed.
AnalysisConfig v1 shipped (#9 closed 2026-09-18); the layer is live in
src/analysis/AnalysisConfig.jl and passes 83 assertions on every CI run. Nothing was
waiting on it any more.

What actually stands between this issue and implementation is the validated statistics
layer (#1), and the bounded method catalogue that issue requires. That catalogue was
approved on 2026-09-22 and this issue is its item 4, deliberately excluded from v1:
Fisher's exact, exact negative binomial and permutation PERMANOVA are named in the
catalogue as the work that comes after the approved v1 scope, not alongside it.

So the position here is a decision, not a missing dependency — and it should be
recorded as one. Un-deferring means running this work through the same discipline #1
imposes on every other method: published supported/unsupported conditions, known-answer
and independent-reference tests (the R fisher.test comparison above is exactly that),
negative controls, performance benchmarks against the declared risk, and an owner
decision to open the stage. #2 sets the standard for how that gate is written down: a
closed prerequisite or a green test suite is not on its own sufficient.

See docs/milestones/02-deferred-issues.md for full spec.

[hyperpolymath]

Why this changed. The issue said "Blocked by AnalysisConfig v1". That was true when
written and is not true now: #9 (AnalysisConfig v1) closed on 2026-09-18, the layer is in
src/analysis/AnalysisConfig.jl, and it passes 83 assertions on every CI run. A stale
blocker is worse than no blocker — it makes a deferred issue look like work that cannot
start, when the real position is a choice that hasn't been made.

The body now names what actually gates this: #1's validated statistics layer. The bounded
method catalogue was approved on 2026-09-22, and this issue is item 4 of that
catalogue — deliberately deferred out of v1. So the honest status is "deferred by
decision, with the criteria for opening it written down", which is what the new text
says. Nothing else about this issue has changed: it stays deferred, and the deferred
label stays.