Papers

Ternary Conservation in Distributed Systems

Distributed systems lack a native concept of resource balance. Binary health checks—alive or dead—discard information about the neutral or transitional states that dominate real system behavior. This paper introduces ternary conservation, a structural invariant for distributed agents based on three-valued classification. Every signal is classified as {−1, 0, +1}, and a conservation law requires the sum of ternary values to be preserved across any closed set of operations. The invariant is structurally isomorphic to Gauss's law in Z₃ lattice gauge theory. We present the mathematical foundation, a multi-scale ternary Haar decomposition, the Bottle Protocol for cross-boundary ternary state, and a Rust implementation that enforces conservation at the type level.