T0 + T1 + T2: engine redesign through new API surface (#1)

Implements tiers T0, T1, T2 of `docs/superpowers/specs/2026-04-23-trueskill-engine-redesign-design.md`. All three tiers have landed together on this branch because they build on one another; this PR rolls them up for a single review pass.

Per-tier plans:
- T0: `docs/superpowers/plans/2026-04-23-t0-numerical-parity.md`
- T1: `docs/superpowers/plans/2026-04-24-t1-factor-graph.md`
- T2: `docs/superpowers/plans/2026-04-24-t2-new-api-surface.md`

## Summary

### T0 — Numerical parity (internal)

- `Gaussian` switched to natural-parameter storage `(pi, tau)`; mul/div now ~7× faster (218 ps vs 1.57 ns).
- `HashMap<Index, _>` → dense `Vec<_>` keyed by `Index.0` (via `AgentStore<D>`, `SkillStore`).
- `ScratchArena` eliminates per-event allocations in `Game::likelihoods`.
- `InferenceError` seed type added (1 variant).
- 38 → 53 tests passing through T1.
- Benchmark: `Batch::iteration` 29.84 → 21.25 µs.

### T1 — Factor graph machinery (internal)

- `Factor` trait + `BuiltinFactor` enum (TeamSum / RankDiff / Trunc) driving within-game inference.
- `VarStore` flat storage for variable marginals.
- `Schedule` trait + `EpsilonOrMax` impl replacing the hand-rolled EP loop.
- `Game::likelihoods` rebuilt on the factor-graph machinery; iteration counts and goldens preserved to within 1e-6.
- 53 tests passing.
- Benchmark: `Batch::iteration` 23.01 µs (slight regression absorbed in T2).

### T2 — New API surface (breaking)

**Renames:**
- `IndexMap → KeyTable`, `Player → Rating`, `Agent → Competitor`, `Batch → TimeSlice`

**New types:**
- `Time` trait with `Untimed` ZST and `i64` impls; `Drift<T>`, `Rating<T, D>`, `Competitor<T, D>`, `TimeSlice<T>`, `History<T, D, O, K>` all generic.
- `Event<T, K>`, `Team<K>`, `Member<K>`, `Outcome` (`Ranked` variant; `#[non_exhaustive]`).
- `Observer<T>` trait + `NullObserver`.
- `ConvergenceOptions`, `ConvergenceReport`.
- `GameOptions`, `OwnedGame<T, D>`.

**Three-tier ingestion:**
- `history.record_winner(&K, &K, T)` / `record_draw(&K, &K, T)` — 1v1 convenience.
- `history.add_events(iter)` — typed bulk.
- `history.event(T).team([...]).weights([...]).ranking([...]).commit()` — fluent.

**Query API:** `current_skill`, `learning_curve`, `learning_curves` (keyed on `K`), `log_evidence`, `log_evidence_for`, `predict_quality`, `predict_outcome`.

**Game constructors:** `ranked`, `one_v_one`, `free_for_all`, `custom` — all returning `Result<_, InferenceError>`.

**`factors` module:** `Factor`, `Schedule`, `VarStore`, `VarId`, `BuiltinFactor`, `EpsilonOrMax`, `ScheduleReport`, `TeamSumFactor`, `RankDiffFactor`, `TruncFactor` now public.

**Errors:** `InferenceError` gains `MismatchedShape`, `InvalidProbability`, `ConvergenceFailed`; boundary panics converted to `Result`.

**Removed (breaking):** `History::convergence(iters, eps, verbose)`, `HistoryBuilder::gamma(f64)`, `HistoryBuilder::time(bool)`, `History.time: bool`, `learning_curves_by_index`, nested-Vec public `add_events`.

## Behavior change (documented in CHANGELOG)

`Time = Untimed` has `elapsed_to → 0`, so no drift accumulates between slices. The old `time=false` mode implicitly forced `elapsed=1` on reappearance via an `i64::MAX` sentinel — that quirk is not reproducible under a typed time axis. Tests that depended on it now use `History::<i64, _>` with explicit `1..=n` timestamps. One test (`test_env_ttt`) had 3 Gaussian goldens updated to reflect the corrected semantics; documented in commit `33a7d90`.

## Final numbers

| Metric | Before T0 | After T2 | Delta |
|---|---|---|---|
| `Batch::iteration` | 29.84 µs | 21.36 µs | **-28%** |
| `Gaussian::mul` | 1.57 ns | 219 ps | **-86%** |
| `Gaussian::div` | 1.57 ns | 219 ps | **-86%** |
| Tests passing | 38 | 90 | +52 |

All other Gaussian ops unchanged (~219 ps add/sub, ~264 ps pi/tau reads).

## Test plan

- [x] `cargo test --features approx` — 90/90 pass (68 lib + 10 api_shape + 6 game + 4 record_winner + 2 equivalence)
- [x] `cargo clippy --all-targets --features approx -- -D warnings` — clean
- [x] `cargo +nightly fmt --check` — clean
- [x] `cargo bench --bench batch` — 21.36 µs
- [x] `cargo bench --bench gaussian` — unchanged from T1
- [x] `cargo run --example atp --features approx` — rewritten in new API, runs clean
- [x] Historical Game-level goldens preserved in `tests/equivalence.rs`
- [x] Public API matches spec Section 4 (verified by integration tests in `tests/api_shape.rs`)

## Commit history

~45 commits total across T0 + T1 + T2. Each task is self-contained and individually tested; the branch is bisectable. See `git log main..t2-new-api-surface` for the full list.

## Deferred to later tiers

- `Outcome::Scored` + `MarginFactor` — T4
- `Damped` / `Residual` schedules — T4
- `Send + Sync` bounds + Rayon parallelism — T3
- N-team `predict_outcome` — T4
- `Game::custom` full ergonomics — T4

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Reviewed-on: #1
Co-authored-by: Anders Olsson <anders.e.olsson@gmail.com>
Co-committed-by: Anders Olsson <anders.e.olsson@gmail.com>

src/factor/rank_diff.rs

@@ -0,0 +1,95 @@
+use crate::factor::{Factor, VarId, VarStore};
+
+/// Maintains the constraint `diff = team_a - team_b` between three vars.
+///
+/// On each propagation:
+/// - Reads marginals at `team_a` and `team_b` (which already incorporate any
+///   incoming messages from neighboring factors).
+/// - Computes `new_diff = team_a - team_b` (variance addition; see Gaussian::Sub).
+/// - Writes the new marginal to `diff`.
+/// - Returns the delta against the previous diff value.
+///
+/// This factor does NOT store an outgoing message; the diff variable is
+/// effectively replaced on each propagation. The TruncFactor on the same diff
+/// var holds the EP-divide message that produces the cavity.
+#[derive(Debug)]
+pub struct RankDiffFactor {
+    pub team_a: VarId,
+    pub team_b: VarId,
+    pub diff: VarId,
+}
+
+impl Factor for RankDiffFactor {
+    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+        let a = vars.get(self.team_a);
+        let b = vars.get(self.team_b);
+        let new_diff = a - b;
+        let old = vars.get(self.diff);
+        vars.set(self.diff, new_diff);
+        old.delta(new_diff)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{N_INF, gaussian::Gaussian};
+
+    #[test]
+    fn diff_of_two_known_gaussians() {
+        let mut vars = VarStore::new();
+        let team_a = vars.alloc(Gaussian::from_ms(25.0, 3.0));
+        let team_b = vars.alloc(Gaussian::from_ms(20.0, 4.0));
+        let diff = vars.alloc(N_INF);
+
+        let mut f = RankDiffFactor {
+            team_a,
+            team_b,
+            diff,
+        };
+        f.propagate(&mut vars);
+
+        let result = vars.get(diff);
+        // mu = 25 - 20 = 5; var = 9 + 16 = 25; sigma = 5
+        assert!((result.mu() - 5.0).abs() < 1e-12);
+        assert!((result.sigma() - 5.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn delta_zero_on_repeat() {
+        let mut vars = VarStore::new();
+        let team_a = vars.alloc(Gaussian::from_ms(10.0, 2.0));
+        let team_b = vars.alloc(Gaussian::from_ms(8.0, 1.0));
+        let diff = vars.alloc(N_INF);
+
+        let mut f = RankDiffFactor {
+            team_a,
+            team_b,
+            diff,
+        };
+        f.propagate(&mut vars);
+        let (dmu, dsig) = f.propagate(&mut vars);
+        assert!(dmu < 1e-12);
+        assert!(dsig < 1e-12);
+    }
+
+    #[test]
+    fn delta_reflects_team_change() {
+        let mut vars = VarStore::new();
+        let team_a = vars.alloc(Gaussian::from_ms(10.0, 1.0));
+        let team_b = vars.alloc(Gaussian::from_ms(0.0, 1.0));
+        let diff = vars.alloc(N_INF);
+
+        let mut f = RankDiffFactor {
+            team_a,
+            team_b,
+            diff,
+        };
+        f.propagate(&mut vars);
+
+        // change team_a, repropagate; delta should be positive
+        vars.set(team_a, Gaussian::from_ms(15.0, 1.0));
+        let (dmu, _dsig) = f.propagate(&mut vars);
+        assert!(dmu > 4.0, "expected ~5 delta, got {}", dmu);
+    }
+}