Byzantine-Shannon Isomorphism

We prove that the Byzantine fault tolerance bound (n ≥ 3f + 1) and Shannon's rate-distortion function R(D) are isomorphic theorems—different expressions of the same fundamental constraint on information processing under adversarial conditions.

The Byzantine bound states that to tolerate f faulty nodes, a distributed system requires at least 3f + 1 total nodes. Shannon's rate-distortion theorem states that to achieve distortion level D, communication requires rate at least R(D).

We show these are the same theorem by: 1. Mapping Byzantine faults to channel noise 2. Mapping consensus to source coding 3. Proving the bounds are equivalent under this mapping

This unification has profound implications: - FLP impossibility becomes a rate-distortion limit - CAP theorem becomes bandwidth-delay tradeoff - Byzantine consensus protocols become optimal codes

The isomorphism is exact, not analogical. Both theorems derive from the same information-theoretic constraint: reliable coordination requires redundancy proportional to adversarial capacity.

This is the strongest theoretical contribution in the coordination science portfolio, with triple platinum foundations (all proofs derive from established theorems).