test(math-foundry): typed tanh/atanh rewrites for NARS, Bayes and Fisher

.claude/board/entries/2026-10-22-pal256-egraph-evidence-law-admission.md

@@ -0,0 +1,20 @@
+# Cold mathematical candidate laws for typed evidence families
+
+Scope **test-only / not egglog rule admission yet**. The Math Foundry E1 probe (#1690/#1693/#1696/#1698), R2IL and mask-risc remain sole owners. MeTTa/MORK/OpenNARS are source languages or independent differential oracles, never replacement hot execution engines.
+
+Candidate laws:
+1. `tanh(atanh(x)) = x` on the open real unit interval; finite-precision LUT cancellation needs a separate quantization/error proof.
+2. `tanh(a+b)=(tanh(a)+tanh(b))/(1+tanh(a)tanh(b))` on finite real operands.
+3. NARS positive/negative independent evidence counts merge by additive counts.
+4. Bayesian log-likelihood contributions add only with correctly identified prior, likelihood and conditional independence.
+
+Refuse:
+- mapping arbitrary embedding cosine to Pearson sample r or sample-size evidence;
+- treating `sum(atanh(cos))` as NARS revision;
+- `c=tanh(|z|)` as sample-aware confidence;
+- global e-graph `3σ -> 0` equivalence;
+- float re-association, saturation, LUT roundtrips, or non-idempotent memory effects without typed guards.
+
+Next cold stage: attach admitted typed predicates to existing `egglog-r2il-probe` *without* adding a second e-graph, emit R2IL via `FoldDialect`, independent oracle/replay capsule, compare to baseline under altered binding and ABI witness. Keep proof/law, compiled recipe, dataset/source evidence and execution receipts separate.
+
+Run: `cargo test --manifest-path crates/egglog-r2il-probe/Cargo.toml --test palette256_typed_evidence_laws`.

.claude/board/entries/README.md

@@ -25,14 +25,15 @@ 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.
 
-438 entries, 2026-08-06 .. 2026-10-22.
+440 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-hebbian-overlay-plasticity` |  | [2026-10-22-pal256-hebbian-overlay-plasticity.md](2026-10-22-pal256-hebbian-overlay-plasticity.md) |
+| 2026-10-22 | `pal256-egraph-evidence-law-admission` |  | [2026-10-22-pal256-egraph-evidence-law-admission.md](2026-10-22-pal256-egraph-evidence-law-admission.md) |
 | 2026-10-22 | `pal256-bnn-disambiguation` |  | [2026-10-22-pal256-bnn-disambiguation.md](2026-10-22-pal256-bnn-disambiguation.md) |
 | 2026-10-22 | `pal256-argextrema-margins` |  | [2026-10-22-pal256-argextrema-margins.md](2026-10-22-pal256-argextrema-margins.md) |
 | 2026-10-22 | `pal256-64hop-error-containment` |  | [2026-10-22-pal256-64hop-error-containment.md](2026-10-22-pal256-64hop-error-containment.md) |

crates/egglog-r2il-probe/tests/palette256_typed_evidence_laws.rs

@@ -0,0 +1,77 @@
+//! Cold admission probes for mathematical candidate laws, *not* a new runtime
+//! e-graph. Keep existing egglog -> R2IL -> mask-risc ownership boundaries.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+enum Domain {
+    OpenUnitReal,
+    IndependentCounts,
+    BayesLogLikelihood,
+    FisherCorrelation,
+    QuantizedPalette,
+}
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+enum Law {
+    TanhAtanhCancel,
+    MergeIndependentCounts,
+    AddLogLikelihoodRatios,
+    UnconditionalThreeSigmaPrune,
+}
+fn admit(law: Law, domain: Domain) -> bool {
+    matches!(
+        (law, domain),
+        (Law::TanhAtanhCancel, Domain::OpenUnitReal)
+            | (Law::MergeIndependentCounts, Domain::IndependentCounts)
+            | (Law::AddLogLikelihoodRatios, Domain::BayesLogLikelihood)
+    )
+}
+#[test]
+fn exact_identity_is_admitted_only_in_its_declared_numeric_domain() {
+    for x in [-0.99_f64, -0.5, 0.0, 0.25, 0.99] {
+        assert!((x.atanh().tanh() - x).abs() < 1e-12);
+    }
+    assert!(admit(Law::TanhAtanhCancel, Domain::OpenUnitReal));
+    assert!(!admit(Law::TanhAtanhCancel, Domain::QuantizedPalette));
+    assert!(!admit(Law::TanhAtanhCancel, Domain::FisherCorrelation));
+    assert!(!admit(
+        Law::UnconditionalThreeSigmaPrune,
+        Domain::OpenUnitReal
+    ));
+    assert!(1.0_f64.atanh().is_infinite());
+}
+#[test]
+fn bayesian_log_likelihood_addition_is_not_nars_frequency_revision() {
+    let f1 = 0.7_f64;
+    let f2 = 0.7_f64;
+    let nars_revision: f64 = (7.0 + 7.0) / (10.0 + 10.0);
+    let signed1 = 2.0 * f1 - 1.0;
+    let signed2 = 2.0 * f2 - 1.0;
+    let hyperbolic = ((signed1.atanh() + signed2.atanh()).tanh() + 1.0) * 0.5;
+    assert!((nars_revision - 0.7).abs() < 1e-12);
+    assert!(
+        hyperbolic > 0.8,
+        "different evidence algebra, not a compiler optimization"
+    );
+    assert!(admit(
+        Law::MergeIndependentCounts,
+        Domain::IndependentCounts
+    ));
+    assert!(!admit(
+        Law::MergeIndependentCounts,
+        Domain::BayesLogLikelihood
+    ));
+    assert!(admit(
+        Law::AddLogLikelihoodRatios,
+        Domain::BayesLogLikelihood
+    ));
+    assert!(!admit(
+        Law::AddLogLikelihoodRatios,
+        Domain::IndependentCounts
+    ));
+}
+#[test]
+fn tanh_addition_identity_is_a_distinct_true_mathematical_law() {
+    let a: f64 = 0.4;
+    let b: f64 = -0.2;
+    let left = (a + b).tanh();
+    let right = (a.tanh() + b.tanh()) / (1.0 + a.tanh() * b.tanh());
+    assert!((left - right).abs() < 1e-12);
+}