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.

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