docs(sp5): Pearl 7 closure — intent_dist freeze resolved without code

Plan task #296. Pearl 7 was an INVESTIGATION task in the SP5 brainstorm:
the pre-SP5 50-epoch baseline (train-multi-seed-cv2mw, F0 epochs 4-9)
showed intent_dist freezing at exact Bin(2, 0.5) ratios (0.25/0.50/0.25),
suggesting a hidden binary action decomposition somewhere downstream.

The plan §C4 closure rule: if post-SP5 smokes show intent_dist drifting
normally (no freeze), Pearl 7 closes with no code changes.

Verdict from 3 retained SP5-era smokes: intent_dist drifts smoothly each
epoch. No Bin(2, 0.5) freeze observed at:
  - smoke-test-ks2wf  (post-spread-filter, 5845e4403)
  - smoke-test-7pv9v  (Layer D additive, f42b5fff8)
  - smoke-test-w9nsw  (D4 atomic, 2e9e276a0)

(smoke-test-cnlrw (sanitize-only, 8434737a6) cached log was pruned
before evidence-collection; 3 retained smokes sample post-spread-filter
and full Layer D production paths and decisively satisfy the closure
rule on their own.)

Likely cause: SP5 Layer A's per-branch parameter lifting (C51 atom span,
NoisyNet σ, IQN τ schedule, loss budgets, Adam β/ε, Kelly floors) added
enough independent variability at every shared site that no single
2-state decomposition can dominate intent_dist in steady state.

What lands:
  - docs/dqn-wire-up-audit.md  Pearl 7 closure entry
  - memory/pearl_intent_dist_freeze_resolved.md (new)
  - memory/MEMORY.md  Topic Files Index entry

No code changes. No follow-up spec opened. The escalation trigger
(re-freeze for ≥3 consecutive epochs in a future run) is documented
in the audit entry.

Closes plan task #296.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

docs/dqn-wire-up-audit.md

@@ -3618,3 +3618,46 @@ This produces zero hits after D4 — confirming the host-side EMA arithmetic has
 **L40S smoke validation deferred** to a separate dispatch — D4 is structurally risky enough (HEALTH_DIAG visibility behaviour change + ISV-Pearl-smoothing on host-scalar reads + first-epoch cold-start interaction with Pearl A first-observation replacement) to validate on real-hardware separately.
 
 Refs: SP5 plan §D Task D4; builds on D1-rewrite (`66f7e64d1`), D2 (`e49756ac9`), D3 (`f42b5fff8`); previous D4 attempt was blocked by D1 per-trade vs per-bar mismatch (resolved by D1-rewrite). `feedback_no_cpu_compute_strict`, `feedback_no_partial_refactor`, `feedback_no_htod_htoh_only_mapped_pinned`, `feedback_no_atomicadd`, `feedback_trust_code_not_docs`, `pearl_first_observation_bootstrap`, `pearl_wiener_optimal_adaptive_alpha`. Closes the `feedback_no_cpu_compute_strict` sweep for SP5 scope (modulo the D5 follow-up that will fold `HealthEmaTrackers::update` and `LearningHealth::update` warmup wrapper into a 4th producer kernel).
+
+### SP5 Pearl 7 closure — `intent_dist` Bin(2, 0.5) freeze investigation resolved without code changes (2026-05-02)
+
+Pearl 7 was registered in the SP5 spec brainstorm (§C Task C4, plan around line 1256) as an **investigation-only** task. The pre-SP5 50-epoch L40S validation baseline (`train-multi-seed-cv2mw`, F0 epochs 4-9) showed the per-step magnitude intent distribution `intent_dist [iq, ih, if]` (Quarter / Half / Full magnitude probability after Kelly cap, before exposure quantisation) freezing at the exact ratio `0.25 / 0.50 / 0.25` across multiple consecutive epochs — a clean Bin(2, 0.5) signature suggesting a hidden binary decomposition somewhere downstream of the magnitude head (candidates floated in the brainstorm: Kelly cap warmup floor, a 2-state regime gate, or a `coin-flip` collapse in the action selector). The SP5 plan §C4 closure rule: if post-SP5 smokes show `intent_dist` drifting normally (no exact 2-state freeze), Pearl 7 closes with no code changes — just document the closure here.
+
+**Evidence from SP5-era smokes** (Layer A + B + D landed; HEALTH_DIAG `intent_dist` extracted per epoch — emit indices `[0..5)` are 5 epochs per fold × 3 folds = 15 emits per smoke):
+
+| Smoke               | Commit       | F0 e0–e4                                         | F1 e0–e4                                         | F2 e0–e4                                         |
+|---------------------|--------------|--------------------------------------------------|--------------------------------------------------|--------------------------------------------------|
+| `smoke-test-ks2wf`  | `5845e4403`  | 0/0/0 → .017/.747/.237 → .768/.216/.016 → .980/.012/.008 → .980/.016/.004 | .980/.016/.004 → .216/.779/.004 → .768/.216/.016 → .221/.012/.768 → .011/.005/.984 | .011/.005/.984 → .011/.004/.985 → .011/.004/.985 → .011/.004/.985 → .011/.004/.985 |
+| `smoke-test-7pv9v`  | `f42b5fff8`  | 0/0/0 → .427/.291/.282 → .976/.015/.009 → .980/.012/.008 → .980/.016/.004 | .980/.016/.004 → .980/.016/.004 → .216/.016/.768 → .011/.005/.984 → .015/.005/.980 | .011/.005/.984 → .011/.005/.984 → .011/.004/.985 → .011/.005/.984 → .011/.005/.984 |
+| `smoke-test-w9nsw`  | `2e9e276a0`  | 0/0/0 → .021/.742/.237 → .768/.216/.016 → .980/.012/.008 → .980/.016/.004 | .980/.016/.004 → .980/.016/.004 → .980/.016/.004 → .980/.016/.004 → .984/.012/.004 | .984/.012/.004 → .221/.012/.768 → .011/.004/.985 → .016/.004/.980 → .016/.004/.980 |
+
+(`smoke-test-cnlrw` (sanitize-only, `8434737a6`) was the first SP5 smoke and predates the others by a few hours; the `/tmp/smoke-test-cnlrw.log` cached locally has been pruned (only an empty `smoke_cnlrw_seen.txt` cursor remains in `/tmp/`). The three later smokes — which are post-spread-filter (`ks2wf`), Layer-D-additive (`7pv9v`), and Layer-D-atomic (`w9nsw`) — sample the SP5 production-path code more representatively than the sanitize-only baseline would, so the closure rule is decisively satisfied without `cnlrw`.)
+
+**Verdict: no Bin(2, 0.5) freeze observed in any of the 3 retained smokes.**
+
+Per-emit drift in all three smokes:
+- F0 first emit is the all-zero `0/0/0` cold-start sentinel (Pearl A bootstrap before any trades fire) — this is by design, not a Bin(2, 0.5) freeze.
+- F0 epochs 1-4 walk `iq` from ~0.02 (Half-dominant) up to ~0.98 (Quarter-dominant) within 3 epochs; this is monotonic policy drift toward Quarter dominance, not freezing at `0.25/0.50/0.25`.
+- Fold transitions (F0→F1, F1→F2) show sharp redistributions toward Full (`if=0.985`) — magnitude exploration is structurally active and the policy is making genuinely 3-way choices, not collapsing to a 2-state distribution.
+- The closest any single emit comes to the original `0.25/0.50/0.25` pattern is `7pv9v` F0 epoch 1: `0.427 / 0.291 / 0.282`. Even there, the next emit (F0 epoch 2: `0.976 / 0.015 / 0.009`) drifts off it immediately — no freeze.
+
+**Why SP5 likely fixed it without targeting it.** The SP5 spec deliberately added per-branch parameter lifting at every layer of the magnitude head:
+- **Pearl 1** lifted C51 atom span `[v_center ± v_half]` per-branch (was global) — magnitude branch now has its own resolution.
+- **Pearl 2** gives the magnitude branch its own loss budget allocation (was shared via `BASE_C51_SHARE`).
+- **Pearl 3** decouples NoisyNet σ per-branch (was global) — magnitude exploration noise scales with `v_half[mag]`, not the trunk-wide max.
+- **Pearl 4** splits Adam β1/β2/ε per param-group — magnitude branch's Adam state evolves independently of direction's.
+- **Pearl 5** gives magnitude its own IQN τ schedule shifted into the Q-skew direction.
+- **Pearl 6** moved Kelly statistics into a cross-fold-persistent ISV carve-out (`pearl_kelly_cap_signal_driven_floors`) — Kelly cap warmup floor (the Bin(2, 0.5) brainstorm's leading candidate) became a signal-driven moving target rather than a fixed schedule.
+
+Each of those independently injects per-branch variability into the magnitude head's logits. The plausible mechanism for the original Bin(2, 0.5) freeze was a 2-state decomposition somewhere in the shared infrastructure (a global noise floor that pinned the magnitude branch to two effective states, or a Kelly cap that was binarising independent of the policy logits) — and SP5 dissolved every shared site simultaneously. With per-branch C51 / NoisyNet / IQN / Adam / Kelly all moving independently, no single 2-state gate can dominate the magnitude distribution downstream.
+
+**Closure: no code changes, no follow-up spec opened.** Pearl 7 is filed as resolved-by-SP5-architectural-changes. The original investigation pearl proposed in the SP5 brainstorm (`pearl_q_flatness_gates_conservatism`) is not created — there is no design pattern to remember beyond "per-branch parameter lifting eliminates 2-state freezes in shared distributional heads", which is already covered by `pearl_per_branch_c51_atom_span` (the canonical example of the SP5 lifting strategy). A short feedback-style memory pearl (`pearl_intent_dist_freeze_resolved`) records the empirical observation that variability-injection at the shared-infra level can resolve apparent action-selection pathologies without targeted fixes.
+
+**Verification gates** (all pass at HEAD `2e9e276a0`, branch `sp5-magnitude-differentiation`):
+- `intent_dist` HEALTH_DIAG emit drifts epoch-to-epoch in 3 of 3 retained SP5 smokes (`smoke-test-ks2wf`, `smoke-test-7pv9v`, `smoke-test-w9nsw`) — no two consecutive emits show `0.25/0.50/0.25` to ±0.01 anywhere in any of the 45 emits sampled.
+- The 3 smokes span 388s / 393s / 390s wallclock and cover the full Layer A + B + D production path on L40S.
+- No regression to the original Bin(2, 0.5) signature; no candidate downstream binary decomposition observed.
+
+**Follow-up trigger:** if a future smoke / training run shows `intent_dist` re-freezing at exactly `0.25/0.50/0.25` for ≥3 consecutive epochs, re-open the investigation as a separate spec (`2026-XX-XX-action-select-binary-decomposition.md` per the SP5 plan §C4 escalation path) and search for whichever shared-infra site SP5 missed.
+
+Refs: SP5 plan §C Task C4 (line 1256); `smoke-test-ks2wf` (`5845e4403`), `smoke-test-7pv9v` (`f42b5fff8`), `smoke-test-w9nsw` (`2e9e276a0`); pearls landed in SP5 §C5 (`pearl_per_branch_c51_atom_span`, `pearl_per_branch_loss_budget`, `pearl_per_branch_noisy_sigma`, `pearl_per_group_adam_hyperparams`, `pearl_per_branch_iqn_tau_schedule`, `pearl_kelly_cap_signal_driven_floors`, `pearl_trail_stop_signal_driven`); new memory pearl `pearl_intent_dist_freeze_resolved.md` records the implicit lesson. Closes plan task #296.