Exact Semantic Carriers for Structured Physical Systems

Exact search states can be individuated by syntactic history, or by a smaller carrier that preserves exact continuation semantics. This paper gives a sufficient traversal criterion for deterministic polynomial-time computation: exact semantic factorisation, a polynomially bounded reachable carrier image, polynomial-length canonical encodings with efficient equality, complete exact polynomial-time successor dynamics, polynomially bounded progression, and exact readout.

The criterion is deliberately framed as an audit schema for exact dynamic-programming arguments, not as a new complexity mechanism.

Two worked examples are stated as explicit restricted transition systems. For an Ising instance with an independently supplied background and a fixed defect budget, optimising over configurations that differ from the background at a bounded number of sites yields an explicit frontier state machine that is successor-closed and retains every admissible configuration. For a fixed-cross-section tube, a finite frontier signature recording occupancy, polymer connectivity, exterior connectivity, the active endpoint and rear shielding gives an explicit transfer relation and a quadratic carrier count for the resulting longitudinally shielded polymer problem.

What stays open. The general shielded-polymer theorem remains conditional on exterior-state compression. The uniform-pairing example is presented only as an admitted transition-local normal form.