VIOLET V3d: base-sizer parity harness + gate vs recorded BLUE

parity_harness.py: median-curve parity of V3a VioletBetSizer vs recorded
dolphin.trade_events (vel_div->leverage), restricted to short-signal domain.
GATE PASSES on prod host: pearson 0.9998, max_abs_err 0.238 (budget 1.0) over
23 bins -> base conviction sizer reproduces BLUE's central tendency. Per-trade
scatter is the deferred SC/ACB/OB/gold modulation layer (separate finding doc).
3 unit + 1 gate green.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

prod/docs/VIOLET_FINDING__MODULATION_LAYER_VS_UNDERUTILIZATION.md

@@ -0,0 +1,77 @@
+# VIOLET Finding — The Sizing-Modulation Layer vs. the Capital-Under-Utilization Result
+
+**Status:** Finding / caveat, 2026-06-13. Separate doc by operator request. Qualifies
+(does NOT overturn) the [[blue_margin_envelope_study]] and constrains the
+`VIOLET_STUDY_SPEC__BASE_FRACTION_SIZING.md` (#3) and any pre-V4 sizing work.
+
+## TL;DR
+
+The newly-isolated downstream **sizing-modulation layer** (SC-haircut / ACB / OB-cascade
+/ "gold" — the organs that ride along ACBv6) does **not** counter the margin study: that
+study used **actual recorded notionals**, which are already post-modulation. But it
+**sharpens** what "under-utilized capital" means, and makes the modulation layer a
+**required** pre-execution component for VIOLET — not optional.
+
+## 1. Why the margin study is NOT contradicted
+
+The margin/viability study computed `our_leverage = entry_price·quantity / capital_before`
+from `dolphin.trade_events` — i.e. from the **notionals BLUE actually traded**, haircuts
+and boosts already baked in. The modulation is therefore *inside* the measured numbers,
+not a missed factor. Conclusions stand on the as-traded data:
+
+- max realized `our_leverage` ≈ **1.81**
+- **100%** of trades margin-feasible at **2×** exchange leverage
+- **+$47k** clean deduped edge
+
+## 2. How recorded leverage decomposes (the discovery)
+
+Recorded conviction `leverage` is **NOT** the base bet-sizer output alone:
+
+```
+recorded_leverage(trade)  =  base_sizer(vel_div)  ±  modulation(SC, ACB, OB, gold)
+```
+
+- **base_sizer(vel_div)** — cubic-convex strength³ curve; VIOLET's V3a `VioletBetSizer`
+  reproduces it (validated on binned MEDIANS: vd −0.03→0.83, −0.04→2.78, −0.05→9.0 with
+  max_leverage=9 / thr −0.02 / extreme −0.05 / convexity 3).
+- **modulation** — mostly **downward haircuts** (mins far below the median per vel_div
+  bin), with some upward boosts to the 9 cap. This is the per-trade scatter that drops
+  exact per-trade parity to ~34% while the median curve matches.
+
+## 3. The sharpening (this is the load-bearing part)
+
+The study's **median wallet utilization was ~6.8%** (`our_leverage` p50 ≈ 0.068). That
+low median is **largely the haircut layer at work** — BLUE deliberately sized most trades
+far below the base curve. The **max 1.81** is the *un-haircut, base-saturated* tail.
+
+Consequences:
+
+1. **Margin feasibility is robust** even if the haircuts are later dropped: the study's
+   worst case (1.81) already equals the base-saturated value, and 2× covers it. Sizing at
+   full base does not break margin.
+2. **"Under-utilized ⇒ free ROI" is now GUARDED.** Much of the idle ~93% is **not waste**
+   — it is the modulation layer **deliberately de-risking** (cutting size on
+   lower-conviction / higher-risk setups). It is risk knowledge encoded as size.
+
+## 4. Binding implications
+
+- **#3 base-fraction study MUST NOT read the 6.8% median as free headroom.** A large part
+  of it is risk-management. Any base-fraction increase must be evaluated *with* the
+  modulation layer modeled, conditioned on the regime-robustness work — never by naively
+  reclaiming the idle capital.
+- **The modulation layer is REQUIRED before live execution (V4).** VIOLET running the
+  **base sizer alone** would size *bigger than BLUE did* on exactly the trades BLUE chose
+  to haircut → utilization jumps from ~7% median toward the base, and **realized
+  risk/return diverges from the recorded +$47k** (more variance, possibly worse
+  risk-adjusted). Median-curve base parity (V3d) is necessary but **not sufficient** for
+  faithful BLUE replication.
+- **New deferred task (pre-V4):** wrap the SC-haircut / ACB / OB-cascade / "gold"
+  modulation organs as a VIOLET sizing-modulation layer on top of the base
+  `VioletBetSizer`, with its own per-trade parity gate vs recorded `leverage`.
+
+## 5. Related
+
+[[blue_margin_envelope_study]] · [[violet_v3_alpha_doctrine]] (#9 keystone, #11 parity
+finding) · `VIOLET_STUDY_SPEC__BASE_FRACTION_SIZING.md` · `prod/clean_arch/violet/alpha_wrappers.py`
+(base sizer) · live organs in `prod/nautilus_event_trader.py`
+(`_apply_sc_entry_size_multiplier`, `_record_sc_haircut`, `AdaptiveCircuitBreaker`).