Semantic Physics II: A Drop in Field Substrate for Reliable Reasoning

Semantic Physics II (SP-II) is a reproducible, drop-in field substrate that upgrades today’s LLMs from fluent token machines to verified reasoning pipelines—without retraining. SP-II treats tokens as I/O and reasoning as dynamics in typed relational fields, guided by the constitutive law B=σ∇SB=\sigma\nabla SB=σ∇S. It ships three core deliverables: (1) a deterministic decode path that guarantees bit-identical outputs under load (E1), (2) an invariance harness with geometry-aware KPIs (ΔFold/W₂, IS, BS) plus coherence κ\kappaκ and dissipation Σ˙\dot{\Sigma}Σ˙ telemetry (E2/E4), and (3) the SFR API, a minimal “LLM-as-compiler ↔ field” interface for typed constraints and governance hooks. Two preregistered, falsifiable predictions anchor the evidence program: smoothing ∥∇S∥\|\nabla S\|∥∇S∥ monotonically lowers ΔFold on inversion tasks (RP-A), and Σ˙\dot{\Sigma}Σ˙ spikes predict drift/hallucination windows in CoT/RAG traces (RP-B, E3). What’s included: a one-file deterministic spec (deterministic.yaml), Docker/Conda images, make targets for E1–E4, leakage audits, and a single notebook that rebuilds every figure and decision table. Intended use is measurement and governance (determinism → invariance → early-warning); the base model remains untouched. If the preregistered effects hold, SP-II turns “reasoning lives in fields” into auditable, repeatable gains; if they don’t, the same stack falsifies the claim—publicly and compute-honestly.