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@@ -528,3 +528,13 @@ stage1b_f3e3cont (floor 3e-3 from s45000): **1.2883** vs stage1b 1.2808 (floor 1
competitive at full ImageNet by Kerjan-Hoier-Scellier) then centered (2x nudge) if needed;
(b) fb K=3 finite-relaxation bias; (c) Muon x gradient-noise interaction; (d) ~0.02-0.03 of the 0.05
is metric-noise band. Recipe note: random-sign is a one-line trainer change (sign of beta_t per step).
+
+### RESULT 13 (2026-07-12): bsign (random-sign beta) NEUTRAL at 4k — 42M gap-chasing has hit the noise floor. THREAD CLOSED.
+bsign 3-seed: 1.7031/1.7562/1.7552 (mean 1.7382) vs single-sided 1.7314 vs BP+Muon 1.7098. The bias
+reduction is cancelled by injected update-direction variance at this horizon (seed spread now dominates:
+s1 alone beat the BP mean). Ledger of the residual-0.05 epoch gap after three probes: NOT late-beta-SNR
+(f3e3cont), NOT K (K5 probe), NOT first-order sign bias at short horizon (bsign). Remaining mass:
+~0.02-0.03 metric-noise band + small unattributed accumulation. **Decision: stop polishing 42M.**
+Carry `--bsign_rand` and a future centered mode as Stage-2 A/B flags; the gap question re-opens at
+300M/real-corpus where it means something. Effort pivots to: (1) Stage-2 data pipeline (FineWeb-Edu +
+32k tokenizer), (2) E-tier tolerance suite on the idle farm (hardware track / UIUC outreach feed).