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This work aims to define the signalling capacity in binary latent-variable models during repeated interactions.

March 28, 2026Open Access

Multi-Round Correlational Signalling and Corner Reduction

Key Points

This work aims to define the signalling capacity in binary latent-variable models during repeated interactions.
Developed a structural analysis to explore signalling capacity.
Utilized reduction to extremal states and posterior freezing techniques.
Established a strict per-round mass conversion bound and no-dual-lock constraint.
Derived the law for n-round signalling capacity as C^{(n)} = 1 - 2^{1-n}.
Provided a constructive proof aligning with a canonical branch-and-lock strategy.

Abstract

This paper establishes an exact law governing signalling capacity under repeated interaction in binary latent-variable models. We prove that the n-round signalling capacity satisfies: C^ (n) = 1 - 2^1-n The result is derived through a structural analysis based on: reduction to extremal states, posterior freezing, a strict per-round mass conversion bound, and a no-dual-lock constraint. The proof is constructive and matches a canonical branch-and-lock strategy. This work completes a three-part series on operational signalling: Paper I: Non-identifiability and control parameter Γ Paper II: Emergent signalling under repeated interaction Paper III: Exact multi-round amplification law

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Bob Jefferson (Thu,) studied this question.

synapsesocial.com/papers/69c771f08bbfbc51511e2180 https://doi.org/https://doi.org/10.5281/zenodo.19240782

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