jc: D-KIA-C1b — additive statistics battery (κ, ω, R/η², t-tests, φ)

.claude/board/EPIPHANIES.md

@@ -1,3 +1,17 @@
+## 2026-08-04 — E-EXACT-FIT-IS-WHERE-ABSOLUTE-ZERO-GUARDS-BREAK-1 — a misfit guard written as `x < 0.0` rejects the PERFECT case, and the doc example is what caught it
+
+**Status:** FINDING (two measured defects, both fixed in the same commit). **Confidence:** High — reproduced, fixed, and each now carries a regression test. Code: `crates/jc/src/stats.rs` (D-KIA-C1b).
+
+**The defect.** `omega_total` guards against a **Heywood case** — estimated common variance exceeding an item's total variance, `ψ_i = σ_ii − λ_i² < 0`, which means the single-factor model does not fit. Written as `if psi < 0.0 { return None }`, that guard **rejects the best-fitting input there is**: items that are exact multiples of one factor have `ψ = 0` in real arithmetic and land a few ulps *either side* of zero in f64. The perfect model was reported as misfit. Fix: a tolerance **relative to the item's own variance** (`1e-9 · max(|σ_ii|, 1)`), then clamp — only a violation larger than rounding is a real one.
+
+**The generalisation, which is the reusable part.** A guard testing a quantity that is **exactly zero at the ideal** must never use an absolute `< 0` (or `== 0`) comparison. The failure is invisible on ordinary noisy inputs — where `ψ` is comfortably positive — and appears **only on the cleanest possible data**, which is exactly the case a doc example or a smoke test reaches for. Sibling instances to check for: any `variance < 0`, `residual < 0`, `determinant == 0`, or `SS_within <= 0` test in a fitting path.
+
+**The second defect, same commit, different lesson.** The `multiple_r_squared` doc example used predictors `a` and `a + 1` and asserted `R² = 1`. It returned `None` — **correctly**: the design carries an intercept, so `[1, a, a+1]` is rank-deficient. Here the *example* was wrong and the code was right. A duplicated column is the collinearity everyone remembers; **collinearity with the intercept is the one that gets written by accident**, because the two predictor columns are visibly different.
+
+**Why this is filed at all: doc examples are falsifiers, and these two were the only ones that fired.** 31 hand-written unit tests — including hand-computed reference values and five cross-identity checks against independently-computed quantities — passed while both defects were live. The doctests failed. The reason is structural rather than lucky: unit tests here were written around *hand-computable* fixtures (deliberately non-degenerate, so the arithmetic could be checked), while a doc example is written to be *readable*, which selects for the clean, exact, degenerate case — precisely the input class the unit tests avoided. **A test suite optimised for verifiable references systematically under-samples the perfect case.** Consequence for new numeric work: include at least one exact/zero-residual fixture deliberately, and treat a failing doc example as a finding rather than as a doc typo until the code is cleared.
+
+**Paired with the falsifiability rule:** relaxing a guard is the mirror image of adding one, so the same twin applies — `omega_heywood_case_still_returns_none` proves the relaxed guard **still bites** on a real violation (hand-built fixture: `λ₁² = 70/9 ≈ 7.778 > σ₁₁ = 20/3 ≈ 6.667`). Without it, the tolerance fix would have silently disabled the guard, which is the strictly worse defect.
+
 ## 2026-08-04 — E-THE-HYGIENE-RULE-RECURSED-1 — a rule that requires an entry per merged PR generates an infinite chain unless hygiene-only PRs are exempted
 
 **Status:** FINDING + rule amendment (termination clause added to `CLAUDE.md` § Mandatory Board-Hygiene Rule). **Confidence:** High — the chain is three links of observed fact, not a projection. Documentation only.

.claude/board/LATEST_STATE.md

@@ -1,3 +1,15 @@
+## 2026-08-04 — branch `claude/x265-x266-plans-review-h9osnl` (PR #887) — D-KIA-C1b SHIPPED: the additive `jc` statistics battery
+
+`crates/jc/src/stats.rs` — **κ** (`cohen_kappa`, the gap that blocked **D3's fusion falsifier**, now closed), **ω** (`omega_total`), **φ** (delegating to `pearson`, `&[bool]` input), **R / R²** (`multiple_r_squared`, OLS with intercept), **η²** (`eta_squared`), and the significance companions (`t_test_one_sample` / `_paired` / `_welch` / `_student`, `anova_one_way`) over one shared regularised-incomplete-beta core. **107 lib + 11 doctests green, clippy-clean.**
+
+**The effect-size family is r** (φ, R, R², η²); **Cohen's d is out by construction** — the t-tests report t/df/p as η²/R²'s significance companion, not as a d-family route.
+
+**Additive constraint held tighter than permitted:** the entire existing-file diff is `fn` → `pub(crate) fn` on `mean` and `all_finite`, plus doc comments and one `pub mod` line. `average_ranks` / `pop_var` were NOT widened (permitted but unused); the new `sample_var` / `sample_cov` use the unbiased `n−1` divisor — a different estimator from `pop_var`'s `n`, not a duplicate.
+
+**Validation is by cross-identity, not self-assertion:** φ vs `pearson`; R² vs `pearson²`; η² vs R² on a dummy; η² vs `t²/(t²+df)` and `F = t²`; ω vs α (equal under tau-equivalence, ω = 0.9473684 > α = 0.8684211 on the hand-computed congeneric fixture).
+
+**Two defects, both surfaced by doc examples** (`E-EXACT-FIT-IS-WHERE-ABSOLUTE-ZERO-GUARDS-BREAK-1`): a Heywood guard written `psi < 0.0` rejected the *perfect* zero-residual model (fixed with a variance-relative tolerance + a can-it-fire test); and a doc example whose two predictors were collinear with the intercept (the example was wrong, the code right).
+
 ## 2026-08-04 — branch `claude/x265-x266-plans-review-h9osnl` (PR #884 MERGED `1e90cef`) — D-KIA-C1b scoped: the r-family, additive-only
 
 Board/plan prose only; **no code, no runtime behaviour**. Carried the post-merge arc entries for #881/#882/#883 (see the entry below) and re-scoped the statistics work removed from #883 as its own deliverable, **D-KIA-C1b** (`Queued` — scope, not code).

.claude/board/PR_ARC_INVENTORY.md

@@ -33,6 +33,20 @@
 > - **Docs** — knowledge files produced (immutable)
 > - **Confidence (YYYY-MM-DD):** — the ONLY mutable field
 
+## 2026-08-04 — lance-graph #887 — D-KIA-C1b: the additive `jc` statistics battery (κ, ω, R/η², t-tests, φ)
+
+**Head:** `<this branch>` (entry written in the same commit as the change, per the hygiene rule's "SAME commit" wording; merge SHA follows on merge). 5 files: 1 new module + 2 visibility lines + 3 board/plan.
+
+- **Added — `crates/jc/src/stats.rs`.** `cohen_kappa`, `omega_total`, `phi`, `multiple_r` / `multiple_r_squared`, `eta_squared`, `t_test_one_sample` / `_paired` / `_welch` / `_student`, `anova_one_way`, plus `TTest` / `Anova` result structs. Every p-value comes from one shared regularised-incomplete-beta core (Lanczos `ln Γ` + modified-Lentz continued fraction), pinned against textbook critical values. **31 new tests: 107 lib + 11 doctests green; `stats.rs` clippy-clean.**
+- **Locked — κ was the real gap and it is now closed.** `cohen_kappa` is a *different estimator* from ICC, not a rename: ICC decomposes variance for interval ratings, κ corrects counts for marginal-expected agreement. **This unblocks D3's fusion falsifier.**
+- **Locked — the effect-size family is r.** φ, R, R², η². **Cohen's d stays out by construction**; the t-tests are the significance companions to η²/R² (they report t/df/p), not a d-family back door.
+- **Locked — φ is not re-implemented.** It delegates to `reliability::pearson` on a 0/1 coding and takes `&[bool]`, so the binary precondition is unforgeable. The marginal-capped ceiling is documented at the function: φ without its marginals is not interpretable.
+- **Locked — the additive constraint held, TIGHTER than permitted.** The whole diff to existing files is `fn` → `pub(crate) fn` on **`mean` and `all_finite` only**, plus doc comments and the `pub mod` line. `average_ranks` and `pop_var` were *not* widened — allowed, but unused here; and `sample_var`/`sample_cov` in the new module use the unbiased `n−1` divisor, a different estimator from `pop_var`'s `n`, not a duplicate. No existing statistic's arithmetic, signature or semantics changed.
+- **Locked — every new estimator is cross-checked against an independently-computed quantity**, not only against itself: φ vs `pearson`; R² vs `pearson²` at one predictor; η² vs R² on a 0/1 dummy; η² vs `t²/(t²+df)` and `F = t²` from the pooled t; ω vs α (equal under tau-equivalence, strictly greater on the hand-computed congeneric fixture: ω = 0.9473684 vs α = 0.8684211). The one-sample p is pinned to a closed-form incomplete-beta evaluation, never to this code's own output.
+- **Corrected — two defects found by the doc examples** (`E-EXACT-FIT-IS-WHERE-ABSOLUTE-ZERO-GUARDS-BREAK-1`): (1) a real bug — the Heywood guard `psi < 0.0` rejected zero-residual models, since ψ = 0 exactly in real arithmetic lands ±ulps in f64; now a variance-relative tolerance, **paired with a can-it-fire test proving the guard still bites**. (2) a wrong example — predictors `a` and `a+1` are collinear *with the intercept*, so `None` was correct.
+- **Deferred.** ω²/ε² (bias-corrected η²); weighted κ; multi-rater Fleiss κ; d-family. None blocks D3.
+- **Confidence (2026-08-04):** working — 107 lib + 11 doctests green on the pinned toolchain.
+
 ## 2026-08-04 — lance-graph #886 — the board-hygiene rule gets a termination clause (it was recursing)
 
 **Head:** `<this branch>` (entry written in the same commit as the change, per the rule's own "SAME commit" wording; merge SHA follows on merge). 3 files, doc/board prose only — **no code, no runtime behaviour.**

.claude/board/STATUS_BOARD.md

@@ -6,7 +6,7 @@ Plan: `.claude/plans/kanban-64k-inverted-awareness-v1.md` (operator anchors a/b;
 |---|---|---|---|---|
 | D-KIA-0 | jc capability map + dichotomous-statistics decision note (phi/KR-20/kappa naming; Spearman dropped at view 2) | lance-graph | Queued | plan W0 |
 | D-KIA-A1 | ⊘ RESCOPED 2026-08-04 (E-ACTOR-IS-NOT-THE-PHASE-PATH-1): #879 is the complete phase-progression path; KanbanActor has no assigned architectural responsibility (legacy compatibility code). SHIPPED: held-owner reschedule/wake. OPEN: run_cycle drained-writer retry guard; missing-owner counter in cognitive_pass | lance-graph | Queued | plan W1 |
-| D-KIA-C1b | jc additive-only extension: kappa + McDonald's omega + r-family effect size (R/R-squared, eta-squared = explained variance) + t-test (t/df/p) + a named phi wrapper. Cohen's d explicitly OUT — calculated separately if ever wanted. HARD CONSTRAINT: additive only — pearson/spearman/cronbach_alpha/icc keep their arithmetic, signature and semantics; any diff changing an existing jc statistic is an automatic reject. ONE sanctioned edit: widening reliability.rs private helpers (mean/all_finite/average_ranks/pop_var) to pub(crate) for reuse, visibility only, no body change. C1 audit found phi = pearson-on-binaries (already present in substance) and KR-20 = alpha-on-dichotomous (naming only); kappa absent = the real gap. Blocks D3's fusion falsifier | lance-graph | Queued | plan W0/C1b |
+| D-KIA-C1b | jc additive-only extension: kappa + McDonald's omega + r-family effect size (R/R-squared, eta-squared = explained variance) + t-test (t/df/p) + a named phi wrapper. Cohen's d explicitly OUT — calculated separately if ever wanted. HARD CONSTRAINT: additive only — pearson/spearman/cronbach_alpha/icc keep their arithmetic, signature and semantics; any diff changing an existing jc statistic is an automatic reject. ONE sanctioned edit: widening reliability.rs private helpers (mean/all_finite/average_ranks/pop_var) to pub(crate) for reuse, visibility only, no body change. C1 audit found phi = pearson-on-binaries (already present in substance) and KR-20 = alpha-on-dichotomous (naming only); kappa absent = the real gap. SHIPPED as crates/jc/src/stats.rs: cohen_kappa, omega_total, phi, multiple_r/multiple_r_squared, eta_squared, t_test_one_sample/paired/welch/student, anova_one_way; 31 new tests (107 lib + 11 doctests green), clippy-clean. Existing-file diff is visibility-only (mean/all_finite -> pub(crate); average_ranks/pop_var NOT widened, unused). Unblocks D3's fusion falsifier | lance-graph | In PR | plan W0/C1b |
 | D-KIA-A2 | parallelism falsifier (protocol pre-registered: median-of-5, >=2x at >=4k owners, +/-10% stay-silent; kill = regrade claim (a)) | lance-graph | Queued | plan W2 |
 | D-KIA-B1 | catalog binary-range criterion contract type + generalized catalog-mirror drift guard | lance-graph | Queued | plan W3 |
 | D-KIA-C5 | cohort-statistic witness type under the ELEVATED carve-out + held-out anti-circularity gate | lance-graph | Queued | plan W4 |

.claude/plans/kanban-64k-inverted-awareness-v1.md

@@ -246,6 +246,32 @@ signature, or semantics is an automatic reject, independent of merit.**
 
 Blocks D3.
 
+> **✅ C1b SHIPPED (2026-08-04) — `crates/jc/src/stats.rs`.** All six rows
+> delivered: `cohen_kappa`, `omega_total`, `phi`, `multiple_r` /
+> `multiple_r_squared`, `eta_squared`, and `t_test_one_sample` / `_paired` /
+> `_welch` / `_student` + `anova_one_way` (each returning `t`/`F`, df and p via
+> a shared regularised-incomplete-beta core). 31 new tests — **107 lib + 11
+> doctests green**, `stats.rs` clippy-clean.
+>
+> **The additive constraint held, tighter than permitted:** the entire diff to
+> existing files is `fn` → `pub(crate) fn` on **`mean` and `all_finite` only**
+> (plus doc comments and the `pub mod` line). `average_ranks` and `pop_var`
+> were NOT widened — the carve-out allowed it, but this module does not consume
+> them, and `sample_var`/`sample_cov` here use the unbiased `n−1` divisor,
+> which is a different estimator from `pop_var`'s `n`, not a duplicate of it.
+>
+> **Every new estimator is cross-checked against independently-computed
+> quantities** rather than only against itself: φ vs `pearson` on the 0/1
+> coding; R² vs `pearson²` at one predictor; η² vs `R²` on a 0/1 dummy; η² vs
+> `t²/(t²+df)` and `F = t²` from the pooled t; ω vs α (equal under
+> tau-equivalence, strictly greater under the hand-computed congeneric fixture,
+> ω = 0.9473684 vs α = 0.8684211). The t/F tails are pinned against textbook
+> critical values, and the one-sample p against a closed-form incomplete-beta
+> evaluation — not against this code's own output.
+>
+> **Two defects found by the doc examples, both fixed** — see
+> `E-EXACT-FIT-IS-WHERE-ABSOLUTE-ZERO-GUARDS-BREAK-1`.
+
 **C2 — name the dichotomous statistics correctly.** Over binary catalog
 criteria: Pearson→**φ** (report the marginal-capped ceiling), Cronbach's
 α→**KR-20**; **κ is a SEPARATE estimator, not a renamed ICC** — where a

crates/jc/src/lib.rs

@@ -49,6 +49,16 @@ pub mod weyl;
 // (I-NOISE-FLOOR-JIRAK). See `src/reliability.rs`.
 pub mod reliability;
 
+// Second statistics battery (D-KIA-C1b) — chance-corrected agreement (Cohen's
+// κ, the estimator `reliability` lacked and D3's fusion falsifier needs),
+// congeneric reliability (McDonald's ω), the r-family effect sizes (φ, R, R²,
+// η²) and their significance companions (t-tests, one-way ANOVA). Like
+// `reliability` it is NOT a pillar. Strictly ADDITIVE: it borrows two private
+// helpers from `reliability` (`mean`, `all_finite`) and re-uses `pearson` for
+// φ, but changes no existing estimator's arithmetic, signature or semantics.
+// Cohen's d is deliberately out of scope — the effect-size family here is r.
+pub mod stats;
+
 // PROBE-SIG-CHECKSUM — depth-2 truncated signature as a replayable
 // trajectory digest (H.268 probe wave, grades E-WH-TWO-SIDES-SIG-CHECKSUM-1
 // leg 2). A probe, not a 12th pillar: intentionally NOT added to the

crates/jc/src/reliability.rs

@@ -54,8 +54,12 @@
 //! or returning `NaN` — the caller decides how to treat an undefined estimate.
 
 /// Arithmetic mean of a slice, or `None` if empty.
+///
+/// `pub(crate)` for reuse by [`crate::stats`] (visibility only — the behaviour
+/// is unchanged); a second `mean` in that module would be a second source of
+/// truth.
 #[inline]
-fn mean(xs: &[f64]) -> Option<f64> {
+pub(crate) fn mean(xs: &[f64]) -> Option<f64> {
     if xs.is_empty() {
         return None;
     }
@@ -67,8 +71,12 @@ fn mean(xs: &[f64]) -> Option<f64> {
 /// as "equal" in the rank step and would otherwise receive an ordinary rank,
 /// silently producing a finite-but-garbage Spearman ρ (and `Some(NaN)` for the
 /// other three). Every public metric guards on this before computing.
+///
+/// `pub(crate)` for reuse by [`crate::stats`] (visibility only — the behaviour
+/// is unchanged); the no-NaN contract must be enforced identically in both
+/// modules, which a copy would not guarantee.
 #[inline]
-fn all_finite(xs: &[f64]) -> bool {
+pub(crate) fn all_finite(xs: &[f64]) -> bool {
     xs.iter().all(|v| v.is_finite())
 }