RESULT 25: bias decomposition probe — 100% between-block transmission (TRANS=EP 0.9987, ANCHOR=1.0000, K1=BP exactly, K3=K8 saturated)

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014FAPDWQ49M5Ye3NpTndTpn

1 files changed, 29 insertions, 0 deletions

diff --git a/docs/campaign/CASCADE_ABLATION_PLAN.md b/docs/campaign/CASCADE_ABLATION_PLAN.md
index 74eb7c8..b958574 100644
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+++ b/docs/campaign/CASCADE_ABLATION_PLAN.md
@@ -568,6 +568,35 @@ direction), not training-under-fault; wave-2 = co-training with faults injected
 
 
 
+### RESULT 25 (2026-07-15): ERROR-SOURCE DECOMPOSITION — the bias lives ENTIRELY in between-block transmission; within-block reads are exactly lossless.
+Probe: probe_blockcos.py (GPU0, s45000 C512 ckpt, 4 batches, fp32). Exact factorization
+{anchor: free/nudged} x {cotangent: exact-c/EP-transmitted-d}; all four corners share one code
+path (selfcheck (free,c) vs BP = 1.000000).
+| corner | meaning | cos vs BP (beta 1e-3) |
+|---|---|---|
+| (nudged, d) = EP | the training estimator | 0.9987 |
+| (free, d) = TRANS-only | transmission error alone | 0.9987 (== EP, per-block profile identical) |
+| (nudged, c) = ANCHOR-only | local-read displacement alone | 1.0000 (1.000 x12 blocks) |
+Depth profile (0=bottom..11=top): 1.000 at top -> 0.997 at bottom, ~3e-4 loss per hop,
+monotone compounding — the between-block fingerprint (also explains why L3->L12 gates barely
+differ: 12 hops x 3e-4).
+K-sweep twist: K=1 -> EVERYTHING 1.0000 (d derived at free states = exact vjp chain = BP
+reproduced through block-local ops). K=3 = K=8 = 0.9987/0.9988 -> the error is the O(beta)
+DISPLACEMENT OF THE SELF-CONSISTENT nudged solution (saturates immediately; NOT settling
+truncation — K8 doesn't help; NOT local curvature — ANCHOR=1). beta 1e-3 vs 3e-3: 0.9987 vs
+0.9989 (insensitive — this bias term is far below the noise term's beta-sensitivity).
+Readings:
+- ANSWER to "block内EP过程 vs block间PC连接": the bias is 100% transmission (PC-connection side);
+  the within-block theta-read at displaced anchors is exactly free. (Digital-twin statement; on
+  analog hardware within-block reads acquire device noise instead.)
+- WHY CENTERED WINS, mechanistically: +/-beta averaging symmetrizes the self-consistent
+  displacement — kills the odd O(beta) term of exactly the one error source that exists.
+- The K=1 degeneracy is a digital-only shortcut (free-state vjp chain = BP-with-local-ops; a
+  referee would rightly kill the BP-free claim for K=1). K>=2 = the physically-faithful
+  self-consistent settle; its bias price is 0.9987 = not the binding constraint (noise is).
+- C128's gate cos 0.805 (ladder) is the NOISE term at small gn, not this 0.999-level bias;
+  RESULT 23: that noise only costs CE at deep fit.
+
 ### RESULT 24 (2026-07-14): fw72m_cent LAUNCH — window-aware centered crown rerun (pre-registered).
 User call: "72m从头跑centered试试看". From-scratch 234k-step FineWeb rerun applying RESULT 22:
 original fw72m flags EXCEPT --est centered, --bf_late 3e-3 --bf_late_at 20000 (ride the arms-winner