pages/claim-5-sequential-logit-protocol/page.md

# Claim 5 - Sequential logit protocol


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**Verdict: supported.** Section 2 (PDF page 3) defines a topologically ordered DAG. Agent i sees only local features `x_{S_i}` and parent **logits** `z_j`, then minimizes expected BCE for

`z_i(x)=w_i^T x_{S_i} + sum_{j in Pa(i)} v_ij z_j(x)`,  
`p_i(x)=sigmoid(z_i(x))`.

The reproduction implements exactly this logit-span update on a path; it never substitutes probabilities for parent logits. Loss was non-increasing at every within-k trajectory transition, and the hard-instance relevant-information suffix invariant held exactly. The abstract loosely says “prediction columns,” but the formal protocol and proof use logits.