Second-Order Semantics: From Plausible Text to Coherent Reasoning

We propose a second-order semantic layer that treats reasoning as field dynamics rather than token correlation. The core state (𝑆,𝜎,𝑔𝑉,Θ)—semantic potential, conductivity, discourse geometry, and temperature—closes under a constitutive flux law 𝐵=𝜎∇𝑆and a free-energy objective 𝐹=𝑈−Θ𝐻sem, with entropy production Σ̇≥0and a human-readable coherence observable 𝜅. This turns coherence into auditables instead of metaphor. Building on this physics-style kernel, we attach a deterministic sidecar (SP-II) that runs beside any LLM: it pins the decode path, instruments 𝜅,Σ̇, and biases selection along stable field directions via a small SFR API—yielding invariance gains under role-swap/inversion/paraphrase. Metrics and harnesses (ΔFold/W₂ drift, IS, BS) operationalize “truth as invariance under legitimate refactors.” A compact meta-architecture (Meta^N) governs when to open holds (Interstitium), cool Θ, or place reversible locks, so that exploration and consolidation alternate as a controlled double spiral. Energy/compute is treated as a first-class KPI via free-energy and dissipation telemetry, targeting lower cost-per-accepted decision at equal reward. Philosophically, the stance is “the Open”: hold tension, audit dissipation, and let the field—rather than a narrative—decide.