test(nars): independent evidence counts and Jeffreys Bayesian correspondence

.claude/board/entries/2026-10-22-pal256-nars-bayes-evidence-contract.md

@@ -0,0 +1,11 @@
+# NARS revision and Bayesian updates: one measurable evidence basis
+
+Status: **lab-only executable mathematics**, not a replacement for `causal-edge` truth semantics.
+
+Existing measured result: `.claude/board/entries/2026-10-10-d-rpf-p5-nars-beta-correspondence.md`. NARS expectation with horizon k=1 equals the Jeffreys Beta(1/2,1/2) posterior mean for Bernoulli counts **before u8 information loss**; that is a special correspondence, not universal Bayesian equivalence.
+
+Proposed cold typed algebra: `EvidenceCounts {positive, negative, independent_sources}`. Allow exact count sum only when source roots are disjoint; preserve n with a provenance witness outside the u8 F/C lanes. A future `BayesianLogLikelihood` type is distinct and may be summed only under its own independence/model assumptions. Absolutely no `sum(atanh(cosine)) == NARS revision` rule.
+
+Falsifiers: same f at very different n has different c; duplicate roots refuse; two groups with 7/10 produce 14/20, *not* tanh(2*atanh(0.4)).
+
+Run: `cargo test --manifest-path crates/causal-edge/Cargo.toml --test palette256_nars_bayes_evidence_probe`.

.claude/board/entries/README.md

@@ -25,11 +25,12 @@ index row, (3) no duplicate entry id. Checks 1 and 2 are deliberately
 opposite directions; the stranding this convention prevents shows up in
 exactly one of them, never both.
 
-434 entries, 2026-08-06 .. 2026-10-22.
+436 entries, 2026-08-06 .. 2026-10-22.
 
 | date | entry id | finding | file |
 |---|---|---|---|
 | 2026-10-22 | `pal256-salience-mp3-probe` |  | [2026-10-22-pal256-salience-mp3-probe.md](2026-10-22-pal256-salience-mp3-probe.md) |
+| 2026-10-22 | `pal256-nars-bayes-evidence-contract` |  | [2026-10-22-pal256-nars-bayes-evidence-contract.md](2026-10-22-pal256-nars-bayes-evidence-contract.md) |
 | 2026-10-22 | `pal256-immutable-needle-distribution-probe` |  | [2026-10-22-pal256-immutable-needle-distribution-probe.md](2026-10-22-pal256-immutable-needle-distribution-probe.md) |
 | 2026-10-22 | `pal256-argextrema-margins` |  | [2026-10-22-pal256-argextrema-margins.md](2026-10-22-pal256-argextrema-margins.md) |
 | 2026-10-22 | `pal256-3sigma-statistical-gate` |  | [2026-10-22-pal256-3sigma-statistical-gate.md](2026-10-22-pal256-3sigma-statistical-gate.md) |

crates/causal-edge/tests/palette256_nars_bayes_evidence_probe.rs

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+//! Distinguish NARS independent evidence count, Bayesian posterior, and
+//! quantized palette projection. A similarity score is not a sample size.
+#[derive(Clone, Copy)]
+struct Evidence {
+    positive: u64,
+    negative: u64,
+    sources: u64,
+}
+impl Evidence {
+    fn merge(self, other: Self) -> Option<Self> {
+        (self.sources & other.sources == 0).then_some(Self {
+            positive: self.positive.checked_add(other.positive)?,
+            negative: self.negative.checked_add(other.negative)?,
+            sources: self.sources | other.sources,
+        })
+    }
+    fn frequency(self) -> f64 {
+        self.positive as f64 / (self.positive + self.negative) as f64
+    }
+    fn nars_confidence(self) -> f64 {
+        let n = self.positive + self.negative;
+        n as f64 / (n as f64 + 1.0)
+    }
+    fn jeffreys_posterior_mean(self) -> f64 {
+        (self.positive as f64 + 0.5) / ((self.positive + self.negative) as f64 + 1.0)
+    }
+}
+#[test]
+fn independent_equal_frequency_groups_do_not_increase_frequency() {
+    let a = Evidence {
+        positive: 7,
+        negative: 3,
+        sources: 1,
+    };
+    let b = Evidence {
+        positive: 7,
+        negative: 3,
+        sources: 2,
+    };
+    let both = a.merge(b).unwrap();
+    assert!((both.frequency() - 0.7).abs() < 1e-12);
+    assert!((both.nars_confidence() - (20.0 / 21.0)).abs() < 1e-12);
+    assert!((both.jeffreys_posterior_mean() - 14.5 / 21.0).abs() < 1e-12);
+}
+#[test]
+fn frequency_is_not_evidence_mass_and_duplicate_sources_do_not_count() {
+    let low = Evidence {
+        positive: 1,
+        negative: 1,
+        sources: 1,
+    };
+    let high = Evidence {
+        positive: 50,
+        negative: 50,
+        sources: 2,
+    };
+    assert_eq!(low.frequency(), high.frequency());
+    assert!(high.nars_confidence() > low.nars_confidence());
+    assert!(
+        low.merge(low).is_none(),
+        "do not double-count the same source"
+    );
+}