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/mod.rs

@@ -0,0 +1,148 @@
+//! Factor graph machinery for within-game inference.
+
+use crate::gaussian::Gaussian;
+
+/// Identifier for a variable in a `VarStore`.
+///
+/// Variables hold the current Gaussian marginal and are owned by exactly one
+/// `VarStore`. `VarId` is meaningful only within its owning store.
+#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
+pub struct VarId(pub u32);
+
+/// Flat storage of variable marginals.
+///
+/// Variables are allocated by `alloc()` and accessed by `VarId`. The store is
+/// reused across `Game::ranked_with_arena` calls (it lives in the `ScratchArena`); call
+/// `clear()` before reuse.
+#[derive(Debug, Default)]
+pub struct VarStore {
+    pub(crate) marginals: Vec<Gaussian>,
+}
+
+impl VarStore {
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    pub fn clear(&mut self) {
+        self.marginals.clear();
+    }
+
+    pub fn len(&self) -> usize {
+        self.marginals.len()
+    }
+
+    pub fn is_empty(&self) -> bool {
+        self.marginals.is_empty()
+    }
+
+    pub fn alloc(&mut self, init: Gaussian) -> VarId {
+        let id = VarId(self.marginals.len() as u32);
+        self.marginals.push(init);
+        id
+    }
+
+    pub fn get(&self, id: VarId) -> Gaussian {
+        self.marginals[id.0 as usize]
+    }
+
+    pub fn set(&mut self, id: VarId, g: Gaussian) {
+        self.marginals[id.0 as usize] = g;
+    }
+}
+
+/// A factor in the EP graph.
+///
+/// Factors hold their own outgoing messages and propagate them by reading
+/// connected variable marginals from a `VarStore` and writing back updated
+/// marginals.
+pub trait Factor {
+    /// Update outgoing messages and write back to the var store.
+    ///
+    /// Returns the max delta `(|Δmu|, |Δsigma|)` across writes this
+    /// propagation. Used by the `Schedule` to detect convergence.
+    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64);
+
+    /// Optional log-evidence contribution. Default 0.0 (no contribution).
+    fn log_evidence(&self, _vars: &VarStore) -> f64 {
+        0.0
+    }
+}
+
+/// Enum dispatcher for the built-in factor types.
+///
+/// Using an enum instead of `Box<dyn Factor>` keeps factor data inline and
+/// avoids virtual-call overhead in the hot inference loop.
+#[derive(Debug)]
+pub enum BuiltinFactor {
+    TeamSum(team_sum::TeamSumFactor),
+    RankDiff(rank_diff::RankDiffFactor),
+    Trunc(trunc::TruncFactor),
+}
+
+impl Factor for BuiltinFactor {
+    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+        match self {
+            Self::TeamSum(f) => f.propagate(vars),
+            Self::RankDiff(f) => f.propagate(vars),
+            Self::Trunc(f) => f.propagate(vars),
+        }
+    }
+
+    fn log_evidence(&self, vars: &VarStore) -> f64 {
+        match self {
+            Self::Trunc(f) => f.log_evidence(vars),
+            _ => 0.0,
+        }
+    }
+}
+
+pub mod rank_diff;
+pub mod team_sum;
+pub mod trunc;
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::N_INF;
+
+    #[test]
+    fn alloc_assigns_sequential_ids() {
+        let mut store = VarStore::new();
+        let a = store.alloc(N_INF);
+        let b = store.alloc(N_INF);
+        let c = store.alloc(N_INF);
+        assert_eq!(a, VarId(0));
+        assert_eq!(b, VarId(1));
+        assert_eq!(c, VarId(2));
+        assert_eq!(store.len(), 3);
+    }
+
+    #[test]
+    fn get_returns_initial_value() {
+        let mut store = VarStore::new();
+        let g = Gaussian::from_ms(2.5, 1.0);
+        let id = store.alloc(g);
+        assert_eq!(store.get(id), g);
+    }
+
+    #[test]
+    fn set_updates_value() {
+        let mut store = VarStore::new();
+        let id = store.alloc(N_INF);
+        let new = Gaussian::from_ms(3.0, 0.5);
+        store.set(id, new);
+        assert_eq!(store.get(id), new);
+    }
+
+    #[test]
+    fn clear_resets_length_keeping_capacity() {
+        let mut store = VarStore::new();
+        store.alloc(N_INF);
+        store.alloc(N_INF);
+        let cap = store.marginals.capacity();
+        store.clear();
+        assert_eq!(store.len(), 0);
+        assert_eq!(store.marginals.capacity(), cap);
+    }
+}

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);
+    }
+}

src/factor/team_sum.rs

@@ -0,0 +1,98 @@
+use crate::{
+    N00,
+    factor::{Factor, VarId, VarStore},
+    gaussian::Gaussian,
+};
+
+/// Computes the weighted sum of player performances into a team-perf var.
+///
+/// Inputs are pre-computed player performance Gaussians (i.e., rating priors
+/// already with beta² noise added via `Rating::performance()`). The factor
+/// runs once per game and writes the weighted sum to the output var.
+#[derive(Debug)]
+pub struct TeamSumFactor {
+    pub inputs: Vec<(Gaussian, f64)>,
+    pub out: VarId,
+}
+
+impl Factor for TeamSumFactor {
+    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
+        let perf = self.inputs.iter().fold(N00, |acc, (g, w)| acc + (*g * *w));
+        let old = vars.get(self.out);
+        vars.set(self.out, perf);
+        old.delta(perf)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::N_INF;
+
+    #[test]
+    fn single_player_unit_weight() {
+        let mut vars = VarStore::new();
+        let out = vars.alloc(N_INF);
+        let g = Gaussian::from_ms(25.0, 5.0);
+        let mut f = TeamSumFactor {
+            inputs: vec![(g, 1.0)],
+            out,
+        };
+
+        f.propagate(&mut vars);
+        let result = vars.get(out);
+        assert!((result.mu() - 25.0).abs() < 1e-12);
+        assert!((result.sigma() - 5.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn two_players_summed() {
+        let mut vars = VarStore::new();
+        let out = vars.alloc(N_INF);
+        let g1 = Gaussian::from_ms(20.0, 3.0);
+        let g2 = Gaussian::from_ms(30.0, 4.0);
+        let mut f = TeamSumFactor {
+            inputs: vec![(g1, 1.0), (g2, 1.0)],
+            out,
+        };
+
+        f.propagate(&mut vars);
+        let result = vars.get(out);
+        // sum: mu = 20 + 30 = 50, var = 9 + 16 = 25, sigma = 5
+        assert!((result.mu() - 50.0).abs() < 1e-12);
+        assert!((result.sigma() - 5.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn weighted_inputs() {
+        let mut vars = VarStore::new();
+        let out = vars.alloc(N_INF);
+        let g = Gaussian::from_ms(10.0, 2.0);
+        let mut f = TeamSumFactor {
+            inputs: vec![(g, 2.0)],
+            out,
+        };
+
+        f.propagate(&mut vars);
+        let result = vars.get(out);
+        // g * 2.0: mu = 10*2 = 20, sigma = 2*2 = 4
+        assert!((result.mu() - 20.0).abs() < 1e-12);
+        assert!((result.sigma() - 4.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn delta_is_zero_on_repeat_propagate() {
+        let mut vars = VarStore::new();
+        let out = vars.alloc(N_INF);
+        let g = Gaussian::from_ms(5.0, 1.0);
+        let mut f = TeamSumFactor {
+            inputs: vec![(g, 1.0)],
+            out,
+        };
+
+        f.propagate(&mut vars);
+        let (dmu, dsig) = f.propagate(&mut vars);
+        assert!(dmu < 1e-12, "expected ~0 delta on repeat, got {}", dmu);
+        assert!(dsig < 1e-12);
+    }
+}

src/factor/trunc.rs

@@ -0,0 +1,130 @@
+use crate::{
+    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 struct TruncFactor {
+    pub diff: VarId,
+    pub margin: f64,
+    pub 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>,
+}
+
+impl TruncFactor {
+    pub fn new(diff: VarId, margin: f64, tie: bool) -> Self {
+        Self {
+            diff,
+            margin,
+            tie,
+            msg: N_INF,
+            evidence_cached: None,
+        }
+    }
+}
+
+impl Factor for TruncFactor {
+    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);
+    }
+}