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 (ΔE_inst) 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:P_rec(σ) ∝ w(σ) · exp(−β·G_cmp(σ)) · exp(−V(σ)),where w(σ) is the Born weight, G_cmp(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 k_B 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.