Semantic Gravity as a Tensor Field over Stochastic Flows: Invariant Diagnostics, QFI Transport, and Murphy-Scheduled Probes

We develop a tensorial field theory of Semantic Gravity over stochastic discourse flows. Ascalar potential Φ defined on a quotient flow graph induces a vector field g= GradΦ and asemantic stress tensor Σ whose divergence yields force balances for meaning transport. Theconstruction is invariant to admissible quotients and is stable under near-lumpable mergeswith explicit gap-damped error bounds. We tie the calculus to information geometry via QFItransport: Fisher-type curvature serves as a Lyapunov functional under drift/flow and contractsunder coarse-graining, providing typed-effect contracts and compile-time safety guarantees. Onthe instrumentation side, spectral tilts give cumulant generating functions Λ(t), rate functionsI(θ), and Murphy horizons Lc that budget probe lengths to elicit rare composites. We thendefine Action–Betweenness ABα as the sensitivity of Λ to node/edge restrictions, yielding tensor-aware chokepoint diagnostics. The theory explains three empirically observed failure modes aslawful phenomena: category collapse, constraint collapse, and semantic collapse. We providealgorithms (sparse perturbation, power methods, streaming estimators), complexity analyses,and on-line calibration procedures. A suite of experiments demonstrates predictive power forcomposite-phenotype elicitation, irony/humor detection, and long-horizon reasoning. The resultis a field-theoretic upgrade of measure-theoretic flow diagnostics with QFI-grounded guaranteesand scheduler-ready budgets.