A Functional Criterion for Observer-Systems in the Quantum Measurement Problem

A thermodynamically grounded “gap-filler” for the quantum measurement problem: it gives a physical, non-circular criterion for what counts as an observer-system. An observer is any system with a semantic variable R—an instruction-addressable internal macrostate that can be set by a control channel (ΔEᵢnst) and that gates output policy through a reconfigurable mapping, not fixed substrate relaxation. This yields an operational Semantic Signature (five measurable criteria) and a concrete lab protocol for reversible cost inversion under fixed substrate conditions. At the record level, we introduce the Section Law, a Gibbs-style reweighting over global record narratives σ: Pᵣec (σ) ∝ w (σ) · exp (−β·Gcmp (σ) ) · exp (−V (σ) ), where w (σ) is the Born weight, Gcmp (σ) is residual comparison-inconsistency (a weighted sum of post-enforcement binary entropies across record-comparison checks), and V (σ) enforces a hard noncommutativity feasibility constraint (“Heisenberg floor”). β is dimensionless and interpretable as thermodynamic stiffness (instructional work per comparison, relative to kB T). The framework preserves unitary dynamics and local Born statistics for isolated observers, while predicting a measurable network-level consistency pressure when observers compare records.