Round 40 §4 update: cos-vs-acc 3-part proposition (Observation / Inference / Mechanism hypothesis)

Codex round 40 recommended turning the Mode 2 dissociation from empirical
curiosity into a methodological claim via a 3-part proposition:

1. Observation: CB+pen and DFA+pen reach same acc despite 4x deep-cos gap;
   SB+pen best acc with intermediate cos
2. Inference: layerwise BP-cosine is NECESSARY to rule out grossly wrong
   credit signals but NOT SUFFICIENT to certify usable credit for depth
3. Mechanism hypothesis: usefulness depends on whether local updates induce
   coordinated forward-state change across blocks, not just angular agreement
   with BP

Method framing (codex-approved safer versions):
- CB = 'gradient-direction surrogate' (high angular agreement, low functional
  credit)
- SB = 'state-level downstream teaching signal' (lower angular agreement,
  higher functional credit)
- Explicitly framed as HYPOTHESIS not theorem

Main content still 9 pages exactly (within E&D limit).

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

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