Add Phase 5: vector field audit, frozen CIFAR transfer, online pilot

Phase 5A: Audit passes — shuffle control collapses, gains are real
Phase 5B: Transfer SUCCESS — vec_M4 beats scalar CB by +0.25 Gamma, +0.31 rho on frozen CIFAR
Phase 5C: Online FAILURE — vec does worse than scalar CB online despite better frozen credit
Core finding: bottleneck is in local surrogate / co-adaptation, not estimator quality

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

1 files changed, 68 insertions, 1 deletions

diff --git a/NOTE.md b/NOTE.md
index 006496e..36e0be9 100644
--- a/NOTE.md
+++ b/NOTE.md
@@ -5,7 +5,7 @@
 - **pilot**: Controlled iteration (commits 0b9ebb2, 7baf7ae)
 - **frozen**: Code at commit 0b9ebb2 for all reported results
 
-## Status: PHASE 4 DIAGNOSTIC DISSECTION COMPLETE
+## Status: PHASE 5 VECTOR FIELD AUDIT + TRANSFER COMPLETE
 
 ---
 
@@ -262,3 +262,70 @@ The scalar V curvature problem is real and avoidable.
 2. Key concern: M=4 perturbation directions may not suffice for d=256/512 dimensions
    (signal/noise ~ sqrt(M/d) ~ sqrt(4/256) ~ 0.12)
 3. May need M=32+ for CIFAR, which is expensive but tractable
+
+---
+
+## Phase 5: Vector Field Audit + Real-Task Transfer
+
+### Phase 5A: Synthetic Audit (4 sanity checks)
+
+**Setup**: alpha=1.0, L={4,8}, d=128, 3 seeds, 80 epochs
+
+**Smoke test result (L=4, seed=42):**
+
+| Method | Gamma | rho | nudge |
+|--------|-------|-----|-------|
+| scalar_cb | 0.224 | 0.210 | -0.007 |
+| vec_eT_M4 | **0.847** | **0.951** | -0.026 |
+| vec_shuffleCtrl | 0.051 | 0.068 | -0.001 |
+| vec_noTerm | 0.955 | 0.971 | -0.027 |
+| vec_onesided | 0.832 | 0.943 | -0.024 |
+
+**Check B (shuffle)**: PASS — shuffled control collapses (5/6 near zero across full audit)
+**Check C (noTerm)**: Terminal NOT needed — perturbation target alone gives 0.95+ Gamma
+**Check D (onesided)**: PASS — one-sided ≈ central difference
+
+**Full 3-seed audit**: All 6 configs pass (delta_Gamma >= 0.49, delta_rho >= 0.55)
+
+### Phase 5B: Frozen CIFAR Vector Transfer
+
+**Setup**: CIFAR-10, frozen BP ref (L=4, d=256, 61.7%), 100 epochs estimators
+
+| Method | Gamma | rho | nudge |
+|--------|-------|-----|-------|
+| DFA | 0.005 | 0.005 | -0.000006 |
+| ScalarCB_eT | 0.115 | 0.120 | -0.000370 |
+| StateBridge_eT | 0.287 | 0.264 | -0.000957 |
+| **Vec_eT_M4** | **0.364** | **0.426** | **-0.001406** |
+
+**TRANSFER SUCCESS**: Vec beats scalar CB by +0.25 Gamma, +0.31 rho.
+Vec also beats state bridge on rho (0.43 vs 0.26).
+M=4 is sufficient (M=8, M=16 give same results).
+
+### Phase 5C: Online CIFAR Vector Pilot
+
+**Setup**: CIFAR-10, L=4, d=256, 100 epochs, seed=42
+
+| Config | Acc | Gamma | rho | S1 | S2 |
+|--------|-----|-------|-----|----|----|
+| DFA | 0.312 | 0.101 | -0.005 | 0 | 0 |
+| vec wr=0.2 tw=1.0 | 0.243 | 0.001 | 0.000 | -0.100 | +0.005 |
+| (for comparison: scalar CB wr=0.2 tgw=1.0 from Phase 4) | 0.283 | 0.179 | 0.009 | +0.079 | +0.014 |
+
+**ONLINE FAILURE**: Vector field does WORSE than scalar CB online, despite being
+much better on frozen features. No config achieves S1>0.
+
+### Core Finding of Phases 4-5
+
+**The bottleneck is NOT the credit estimator.** Improving credit quality from
+scalar CB (Gamma=0.12) to vector field (Gamma=0.36) on frozen features does NOT
+help online training. The bottleneck is in the **local surrogate update**:
+<F_l(h_l), a_l> cannot effectively exploit directional credit information,
+and co-adaptation between forward net and credit estimator rapidly degrades
+the signal.
+
+### Experiment IDs (Phase 5)
+- `vector_audit/`: Phase 5A smoke test
+- `vector_audit_full/`: Phase 5A full 3-seed audit
+- `frozen_cifar_vec/`: Phase 5B frozen CIFAR vector transfer
+- `online_vec_pilot/`: Phase 5C online CIFAR vector pilot