Constraint Physical Computing on Superconducting Bosonic Hardware: A Microwave-Referenced Feasibility, Native-Advantage, and Validation Roadmap

Constraint Physical Computing (CPC) asks whether engineered physical dynamics can perform useful computation directly from declarative constraint specifications. This white paper develops a feasibility, native-advantage, and validation roadmap for CPC on superconducting bosonic hardware, including cat-qubit, GKP, and multimode architectures. The central physical proposal combines stabilization dynamics protecting an admissible bosonic manifold with answer-independent, problem-dependent open-system dynamics intended to produce a declared semantic terminal sector. Rather than assuming that such a construction is computationally advantageous, the paper defines the physical, semantic, and resource-accounting conditions required to test it experimentally. These include bounded leakage, measurable convergence, control precision, robust referenced readout, fixed decoding, answer independence, provenance, and independent semantic validation. A Levinthal-Class Benchmark is introduced to distinguish large configuration-space avoidance from genuine computational advantage. Complete matched-confidence time-to-solution is compared against preregistered classical, quantum, physics-inspired, and structure-specific reference methods while accounting for compilation, physical synthesis, calibration, preparation, control, convergence, reset, readout, decoding, and validation. Four experimental outcomes are distinguished: backend conformance, physical semantic compatibility, competitive physical execution, and native CPC scaling advantage. The strongest outcome requires evidence of a growing advantage inconsistent with a constant implementation factor over the tested range. The proposal therefore treats native CPC advantage as a falsifiable experimental question rather than an assumed consequence of physical representation or engineered dissipation.