Bounded Reasoning Under Energy and Stability Constraints

This work defines the structural conditions under which reasoning is a well-posed operation in constrained execution environments. Rather than treating energy, latency, and termination as optimization targets, the framework characterizes them as validity conditions that determine whether reasoning may legitimately proceed. Reasoning is formulated as an admissible operation whose permissibility is evaluated prior to execution. Admissibility is determined through non-semantic invariants that summarize reasoning structure without inspecting content, enumerating execution paths, or modifying underlying inference models. These invariants enable deterministic certification of admissible closure or explicit refusal before any computational resources are committed. The framework establishes refusal as a first-class semantic outcome, not a failure mode. When admissibility cannot be certified under defined resource and stability constraints, explicit refusal is the only correct result. Retry-based or post-hoc moderation approaches are shown to be structurally ill-defined in constrained environments because they conflate evaluation with actuation. The contribution is structural rather than procedural. This work does not propose a new model, algorithm, agent architecture, or optimization technique. It specifies the coordinate system within which bounded reasoning systems must operate to be well-defined under physical, temporal, and auditability constraints. Implementation, estimation, and calibration are intentionally deferred. The framework is architecture-independent and compatible with on-device, hybrid, and cloud execution. Because admissibility decisions are computed from non-semantic invariants, the approach supports privacy-preserving reasoning, deterministic auditability, and deployment in safety-critical or resource-constrained environments. This record establishes definitional precedence for admissible reasoning under constraint.