Davis-Norman (1990) is a theorem about MANAGING existing hedge
positions; it tells the agent NOT to micro-adjust within the band. It
says nothing about whether to open from flat.
The `±|tanh|` activation in rl_band_head_forward.cu guarantees
`b_l ≤ 0 ≤ b_u` (the Davis-Norman invariant). Combined with the foxhunt
invariant that agents start FLAT (position=0), every flat-batch was
being masked to Hold — agents never opened, positions never moved, the
sigmoid surrogate on (b_l, b_u) sat deep-in-band where its derivative
≈ 0, and the band loss had no gradient signal.
Verified empirically at 1c23ff368 (Phase 4-A2 smoke): action_hist
collapsed to bimodal [0,0,109,0,0,0,0,0,19,0,0] from step 100 onward,
total_trades = 8 over 2000 steps.
Fix (rl_band_mask.cu): immediately after the master-gate and
exploration-bypass checks, return when `position_lots == 0`. Flat
positions get free choice — opens from flat are NOT band-constrained.
Reads the same canonical offset as the existing band-position check.
Tests (band_invariants.rs):
* New: `band_mask_allows_opens_from_flat` — master gate ON, exploration
bypass DISABLED, all positions=0, band [-0.5, +0.5]; pre-A3 this
would mask every batch to Hold. Asserts the position-zero exception
preserves every batch's original (non-Hold) action.
* Updated: `band_mask_forces_hold_when_in_band` now uses position=1 in
band [-4, +4] (position=0 would unconditionally bypass post-A3).
* Updated: `band_mask_respects_exploration_bypass` now uses position=1
in band [-2, +2] so the exploration-bypass path can be exercised
without the position-zero exception pre-empting it.
11/11 band_invariants PASS. Determinism preserved across band-OFF,
band-ON, and multi-head+band-ON (`./scripts/determinism-check.sh
--quick` exit 0 in all three modes — the new check is integer-equality
and the master gate at slot 799 still defaults OFF, so bit-equality
with the Phase 3D baseline is intact when the band is disabled.
Single-seed smoke (FOXHUNT_BAND_ENABLED=1, seed 42, b=128):
* total_trades 8 → 1911 (trades restored)
* positions: 88/128 non-zero at step 1999 (was 0/128)
* band.width_mean trajectory 4.32 (step 100) → 7.37 (step 1999) —
band NOT collapsing now (was → 0.085 in 4-A2)
* band.frac_masked = 0.797 ∈ (0, 0.85) — band doing meaningful work
* eval pnl = -$793k vs -$8M kill threshold
* NaN count = 0
Falsification gates (Phase 4-A3):
* G_mechanism: PASS (exit 0, no NaN)
* G_positions_become_nonzero: PASS (88/128 non-zero)
* G_trade_recovery: PASS (1911 ∈ [500, 8000]) ← PRIMARY
* G_no_regression: PASS (-$794k > -$8M)
* G_band_active: PASS (frac_masked 0.797 ∈ (0, 0.85))
* G_action_diversity: FAIL (action_entropy 0.65 < 1.0) — see below
The action-diversity gate fails because the policy still concentrates
on Hold (action 2) + TrailLoosen (action 8). However this is NOT the
4-A2 "band can't train" collapse: trades flow, band trains, positions
move. The bimodal pattern toward TrailLoosen is a separate Q-distill
or controller side-effect that pre-existed the band — surfaced by the
spec's STOP-on-surprise rule #2 for follow-up rather than fixed here.
Spec: docs/superpowers/specs/2026-06-03-no-transaction-band-architecture.md §10.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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