bench: capture T0 final numbers and post-mortem

Batch::iteration: 29.840 µs → 21.253 µs (1.40×)
Gaussian::mul:     1.568 ns →  218.69 ps (7.17×)
Gaussian::div:     1.572 ns →  218.64 ps (7.19×)

Gaussian arithmetic hit target (7×+ vs 1.5–2× expected). Batch::iteration
reached 1.40× vs the 3× target. Post-mortem: the bench exercises 100 tiny
2-team events and the dominant cost is still Vec allocation in within_priors,
sort_perm, and Game::likelihoods. The HashMap→Vec win shows at the History
level (forward/backward sweep) which this bench doesn't exercise.

Remediation plan documented in benches/baseline.txt: arena-ify sort_perm,
within_priors, and Game::likelihoods in T1 when Game's internals are
redesigned around the new factor graph.

38/38 tests passing. Closes T0 tier.

benches/baseline.txt

@@ -5,8 +5,39 @@
 Batch::iteration          29.840 µs
 Gaussian::add            219.58 ps
 Gaussian::sub            219.41 ps
-Gaussian::mul              1.568 ns
-Gaussian::div              1.572 ns
+Gaussian::mul              1.568 ns   ← hot path; target ≥1.5× improvement
+Gaussian::div              1.572 ns   ← hot path; target ≥1.5× improvement
 Gaussian::pi             262.89 ps
 Gaussian::tau            262.47 ps
 Gaussian::pi_tau_combined 219.40 ps
+
+# After T0 (2026-04-24, same hardware)
+
+Batch::iteration           21.253 µs   (1.40× — below 3× target; see post-mortem)
+Gaussian::add             218.62 ps    (1.00× — unchanged, Add/Sub use moment form)
+Gaussian::sub             220.15 ps    (1.00×)
+Gaussian::mul             218.69 ps    (7.17× — nat-param: now two f64 adds, no sqrt)
+Gaussian::div             218.64 ps    (7.19× — nat-param: now two f64 subs, no sqrt)
+Gaussian::pi              263.19 ps    (1.00× — now a field read, same cost)
+Gaussian::tau             263.51 ps    (1.00× — now a field read, same cost)
+Gaussian::pi_tau_combined 219.13 ps    (1.00×)
+
+# Post-mortem: Batch::iteration 1.40× vs. 3× target
+#
+# Root cause: the bench has 100 tiny 2-team events. Each event still allocates
+# ~10 Vecs per iteration (down from ~18). The arena covers teams/diffs/ties/margins
+# (was 4 Vecs, now 0 new allocs) but the following remain:
+#   - within_priors() returns Vec<Vec<Player<D>>>: 3 Vecs per event (300 total)
+#   - event.outputs() returns Vec<f64>: 1 Vec per event (100 total)
+#   - sort_perm() allocates 2 scratch Vecs: 200 total
+#   - Game::likelihoods = collect() allocates Vec<Vec<Gaussian>>: 4 Vecs (400 total)
+# Total remaining: ~1000 allocs per iteration call vs. ~1800 before (44% reduction).
+#
+# The HashMap → dense Vec win (target 2–4×) benefits the History-level forward/backward
+# sweep, NOT Batch::iteration in isolation — so this bench doesn't show it.
+#
+# To hit ≥3× on Batch::iteration:
+#   - Arena-ify sort_perm (use a stack-fixed array for small n_teams)
+#   - Pass a within_priors output buffer through the arena
+#   - Make Game::likelihoods write into an arena slice rather than allocating
+# These land in T1 (factor graph) when we redesign Game's internals.