# Tasks: Personalization Correctness Verification

## T1: Decay correctness tests

Create `tidal/tests/pg1_personalization_correctness.rs` with the test schema helper and analytical reference implementation. Implement decay verification tests:

- `single_event_decay_matches_analytical`: One signal event, query at multiple future times, compare against `w * exp(-lambda * dt)`.
- `multi_event_decay_matches_analytical`: 10 signal events at known timestamps, compare final score against sum of `w_i * exp(-lambda * (t_q - t_i))`.
- `out_of_order_converges_to_in_order`: Same events submitted in random order vs chronological order produce scores within 1e-10 relative error.
- `decay_score_zero_after_many_half_lives`: After 100 half-lives, score is effectively zero (< 1e-20).

**Acceptance:** All 4 tests pass with assertions on relative error < 1e-10.

## T2: Windowed count and velocity tests

Add windowed count and velocity verification tests:

- `one_hour_window_exact_count`: Record N events within the last hour, verify `read_windowed_count(OneHour)` returns exactly N.
- `velocity_equals_count_over_duration`: Verify `read_velocity(OneHour)` equals `count / 3600.0`.
- `all_time_count_monotonic`: Record signals, verify AllTime count increases monotonically and never decreases.

**Acceptance:** All 3 tests pass with exact count assertions.

## T3: Preference vector EMA tests

Add preference vector verification tests:

- `ema_matches_manual_computation`: Create PreferenceVectors, update with known embeddings, verify result matches manual EMA `v_new = (1-alpha)*v_old + alpha*embedding` with L2 normalization.
- `adaptive_learning_rate_decays`: Verify that after N updates, effective alpha = `base / (1 + ln(N + 1))` decreases.
- `dimension_mismatch_is_noop`: Verify that updating with wrong-dimension embedding returns false and does not modify the stored vector.

**Acceptance:** All 3 tests pass.

## T4: Ranking reactivity tests

Add reactivity verification tests:

- `signal_immediately_visible_in_retrieve`: Write signal, immediately retrieve, verify the signal's effect is reflected, total elapsed < 100ms.

**Acceptance:** Test passes with timing assertion < 100ms.

## T5: Score ordering and invariant tests

Add score ordering and formula invariant tests:

- `more_engagement_ranks_higher`: Items with more views rank above items with fewer views under `for_you` profile.
- `interaction_boost_is_additive`: Items from interacted creators rank above equivalent items from non-interacted creators.
- `no_nan_or_infinity_in_scores`: All scores in results are finite.
- `gate_below_threshold_excluded`: Items below gate threshold do not appear in results.
- `max_per_creator_enforced`: After diversity enforcement, no creator exceeds the max_per_creator limit.

**Acceptance:** All 5 tests pass.