feat(factor): implement TruncFactor with cached evidence

EP truncation factor that operates on a diff variable. Stores its
outgoing message so the cavity computation produces the correct EP
message on each propagation. The first propagation caches the
evidence contribution (cdf-bounded probability) for log_evidence().

Promotes lib::cdf to pub(crate) so the factor can use it.

src/factor/trunc.rs

@@ -1,15 +1,23 @@
 use crate::{
-    N_INF,
+    N_INF, approx, cdf,
     factor::{Factor, VarId, VarStore},
     gaussian::Gaussian,
 };
 
+/// EP truncation factor on a diff variable.
+///
+/// Implements the rectified-Gaussian approximation that turns a diff
+/// distribution into a "this team rank-beats that team" or "tied" likelihood.
+/// Stores its outgoing message to the diff variable so the cavity computation
+/// produces the correct EP message on each propagation.
 #[derive(Debug)]
 pub(crate) struct TruncFactor {
     pub(crate) diff: VarId,
     pub(crate) margin: f64,
     pub(crate) tie: bool,
+    /// Outgoing message to the diff variable (initial: N_INF, the EP identity).
     pub(crate) msg: Gaussian,
+    /// Cached evidence (linear, not log) computed from the cavity on first propagation.
     pub(crate) evidence_cached: Option<f64>,
 }
 
@@ -26,7 +34,97 @@ impl TruncFactor {
 }
 
 impl Factor for TruncFactor {
-    fn propagate(&mut self, _vars: &mut VarStore) -> (f64, f64) {
-        unimplemented!("TruncFactor stub — implemented in Task 6")
+    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+        let marginal = vars.get(self.diff);
+        // Cavity: marginal divided by our outgoing message.
+        let cavity = marginal / self.msg;
+
+        // First-time-only: cache the evidence contribution from the cavity.
+        if self.evidence_cached.is_none() {
+            self.evidence_cached = Some(cavity_evidence(cavity, self.margin, self.tie));
+        }
+
+        // Apply the truncation approximation to the cavity.
+        let trunc = approx(cavity, self.margin, self.tie);
+
+        // New outgoing message such that cavity * new_msg = trunc.
+        let new_msg = trunc / cavity;
+        let old_msg = self.msg;
+        self.msg = new_msg;
+
+        // Update the marginal: marginal_new = cavity * new_msg = trunc.
+        vars.set(self.diff, trunc);
+
+        old_msg.delta(new_msg)
+    }
+
+    fn log_evidence(&self, _vars: &VarStore) -> f64 {
+        self.evidence_cached.unwrap_or(1.0).ln()
+    }
+}
+
+/// P(diff > margin) for non-tie, P(|diff| < margin) for tie.
+fn cavity_evidence(diff: Gaussian, margin: f64, tie: bool) -> f64 {
+    if tie {
+        cdf(margin, diff.mu(), diff.sigma()) - cdf(-margin, diff.mu(), diff.sigma())
+    } else {
+        1.0 - cdf(margin, diff.mu(), diff.sigma())
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::factor::VarStore;
+
+    #[test]
+    fn idempotent_after_convergence() {
+        // After enough iterations, propagate should return ~0 delta.
+        let mut vars = VarStore::new();
+        let diff = vars.alloc(Gaussian::from_ms(2.0, 3.0));
+
+        let mut f = TruncFactor::new(diff, 0.0, false);
+
+        // Propagate many times; delta should drop toward 0.
+        let mut last = (f64::INFINITY, f64::INFINITY);
+        for _ in 0..20 {
+            last = f.propagate(&mut vars);
+        }
+        assert!(last.0 < 1e-10, "expected converged delta, got {}", last.0);
+        assert!(last.1 < 1e-10);
+    }
+
+    #[test]
+    fn evidence_cached_on_first_propagate() {
+        let mut vars = VarStore::new();
+        let diff = vars.alloc(Gaussian::from_ms(2.0, 3.0));
+
+        let mut f = TruncFactor::new(diff, 0.0, false);
+        assert!(f.evidence_cached.is_none());
+
+        f.propagate(&mut vars);
+        assert!(f.evidence_cached.is_some());
+        let first = f.evidence_cached.unwrap();
+
+        // Evidence should be P(diff > 0) for diff ~ N(2, 9) ≈ 0.748
+        assert!(first > 0.7);
+        assert!(first < 0.8);
+
+        // Subsequent propagations don't change it.
+        f.propagate(&mut vars);
+        assert_eq!(f.evidence_cached.unwrap(), first);
+    }
+
+    #[test]
+    fn tie_evidence_uses_two_sided() {
+        let mut vars = VarStore::new();
+        let diff = vars.alloc(Gaussian::from_ms(0.0, 2.0));
+
+        let mut f = TruncFactor::new(diff, 1.0, true);
+        f.propagate(&mut vars);
+
+        // For diff ~ N(0, 4), tie=true with margin=1: P(-1 < diff < 1) ≈ 0.383
+        let ev = f.evidence_cached.unwrap();
+        assert!(ev > 0.35 && ev < 0.42);
     }
 }

src/lib.rs

@@ -163,7 +163,7 @@ fn compute_margin(p_draw: f64, sd: f64) -> f64 {
     ppf(0.5 - p_draw / 2.0, 0.0, sd).abs()
 }
 
-fn cdf(x: f64, mu: f64, sigma: f64) -> f64 {
+pub(crate) fn cdf(x: f64, mu: f64, sigma: f64) -> f64 {
     let z = -(x - mu) / (sigma * SQRT_2);
 
     0.5 * erfc(z)