test: add property-based tests, a shared finiteness helper, and boundary inputs

Most of what remained on #26.

**Property tests (`tests/properties.rs`, proptest as a dev-dependency).** Four
invariants over generated 1v1 schedules rather than hand-written fixtures,
which is where this crate's shipped defects actually hid — a linear evidence
product that underflowed only past ~1000 teams, and a batching path no golden
exercised because every golden ingests in one call:

- converged posteriors are always finite with positive sigma
- log-evidence, batch and filtered, is finite and never above zero
- filtered evidence is invariant to whether `converge` has run
- one-at-a-time ingestion reaches the same fixed point as batched

The invariance property was mutation-proved: making `filtered_step` read
`skill.forward` instead of the carried message fails it with
`-1.1038430064192069 -> -1.1135747072822761`.

**Shared finiteness helper (`tests/common/mod.rs`).** `assert_finite` was local
to `degenerate_inputs.rs`. It now also rejects a non-positive sigma, which the
old version let through — `Gaussian::sigma` reports a non-positive precision as
improper rather than trapping, so a collapsed posterior would have passed a
finite-only check.

**Boundary inputs.** Zero and negative weights, out-of-order timestamps, and
extreme beta/sigma combinations. Worth recording that zero weight reaches
`(m - performance.exclude(..)) * (1.0 / w)` — a division by zero — and the
posterior comes out finite anyway; the test pins that rather than asserting
what ought to happen. The weight tests `expect()` the commit rather than
returning early on error, because an early return would have made them vacuous
the moment validation changed. I checked that specifically by turning the
return into a failure and confirming it did not fire.

Not done, and left on #26: benchmark regression gating. Nothing fails on a
regression today; making it fail needs a threshold chosen against how noisy the
shared runner is, which is a policy call rather than a mechanical one.

60 test binaries, up from 56. MSRV 1.85 verified with proptest in the graph.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01T5SYDExxL4vZgvunrcNSMc

tests/degenerate_inputs.rs

@@ -3,6 +3,9 @@
 //! These run in both debug and release: the defects they pin were all
 //! guarded only by `debug_assert!`, so a debug-only suite never saw them.
 
+mod common;
+
+use common::assert_finite;
 use trueskill_tt::{
     ConstantDrift, ConvergenceOptions, Game, GameOptions, Gaussian, History, InferenceError,
     NullObserver, Outcome, Rating,
@@ -18,15 +21,6 @@ fn rating() -> R {
     )
 }
 
-fn assert_finite(g: Gaussian, what: &str) {
-    assert!(
-        g.mu().is_finite() && g.sigma().is_finite(),
-        "{what} must be finite, got mu={} sigma={}",
-        g.mu(),
-        g.sigma()
-    );
-}
-
 #[test]
 fn record_draw_without_draw_probability_is_rejected() {
     let mut h = History::default();
@@ -318,3 +312,112 @@ fn empty_history_has_no_filtered_estimates() {
 
     assert!(history.filtered_learning_curve("nobody").is_empty());
 }
+
+// --- Boundary inputs (#26) ----------------------------------------------
+
+fn tight() -> ConvergenceOptions {
+    ConvergenceOptions {
+        max_iter: 2_000,
+        epsilon: 1e-12,
+        ..ConvergenceOptions::default()
+    }
+}
+
+fn assert_curve_finite(h: &History, keys: &[&str], what: &str) {
+    for key in keys {
+        for (time, g) in h.learning_curve(*key) {
+            assert!(
+                g.mu().is_finite() && g.sigma().is_finite(),
+                "{what}: non-finite posterior for {key} at t={time} (mu={} sigma={})",
+                g.mu(),
+                g.sigma()
+            );
+        }
+    }
+}
+
+/// A zero weight reaches `(m - performance.exclude(..)) * (1.0 / w)`, i.e. a
+/// division by zero. The commit is accepted today, so this pins that the
+/// resulting posterior is still finite rather than quietly NaN.
+#[test]
+fn zero_weight_does_not_produce_a_non_finite_posterior() {
+    let mut h = History::builder().build();
+
+    h.event(1)
+        .team(["a"])
+        .weights([0.0])
+        .team(["b"])
+        .winner(0)
+        .commit()
+        .expect("a zero weight is accepted today; update this test if that changes");
+
+    h.converge().unwrap();
+
+    assert_curve_finite(&h, &["a", "b"], "zero weight");
+}
+
+#[test]
+fn negative_weight_does_not_produce_a_non_finite_posterior() {
+    let mut h = History::builder().build();
+
+    h.event(1)
+        .team(["a"])
+        .weights([-1.0])
+        .team(["b"])
+        .winner(0)
+        .commit()
+        .expect("a negative weight is accepted today; update this test if that changes");
+
+    h.converge().unwrap();
+
+    assert_curve_finite(&h, &["a", "b"], "negative weight");
+}
+
+/// Events supplied newest-first must land in the same slices as oldest-first:
+/// ingestion sorts by time rather than trusting arrival order.
+#[test]
+fn out_of_order_timestamps_converge_to_the_same_answer() {
+    fn build(descending: bool) -> History {
+        let mut h = History::builder().convergence(tight()).build();
+
+        let mut times: Vec<i64> = (1..=6).collect();
+        if descending {
+            times.reverse();
+        }
+
+        for time in times {
+            h.record_winner(&"a", &"b", time).unwrap();
+        }
+
+        h.converge().unwrap();
+        h
+    }
+
+    let ascending = build(false);
+    let descending = build(true);
+
+    let one = ascending.current_skill("a").unwrap();
+    let other = descending.current_skill("a").unwrap();
+
+    assert!(
+        (one.mu() - other.mu()).abs() < 1e-8 && (one.sigma() - other.sigma()).abs() < 1e-8,
+        "arrival order changed the answer: ascending mu={} sigma={}, descending mu={} sigma={}",
+        one.mu(),
+        one.sigma(),
+        other.mu(),
+        other.sigma()
+    );
+}
+
+#[test]
+fn extreme_beta_and_sigma_stay_finite() {
+    for (beta, sigma) in [(1e-6, 1e-6), (1e6, 1e6), (1e-6, 1e6), (1e6, 1e-6)] {
+        let mut h = History::builder().beta(beta).sigma(sigma).build();
+
+        h.record_winner(&"a", &"b", 1).unwrap();
+        h.record_winner(&"a", &"b", 2).unwrap();
+        h.converge().unwrap();
+
+        assert_curve_finite(&h, &["a", "b"], &format!("beta={beta} sigma={sigma}"));
+    }
+}