QFI–SM: Spectral Tilts, Large Deviations, and Murphy Scheduling

This paper builds the computable instrumentation layer atop the QFI program. We constructa spectral–tilt calculus for path costs on finite-state flows, define the cumulant generating function(CGF) Λ(t) as the log spectral radius of a tilted operator, and obtain rate functions I(θ) viaconvex duality. An occupancy LDP yields finite-horizon failure exponents and leads to Murphyhorizons Lc—crisp budget lengths that meet a target risk c. We prove a Level–2.5→Level–2contraction lemma for balanced flows and use it to justify Flow Centrality overlays and anaction-derived Action–Betweenness (ABα) centrality as QFI instances. The instrumentationis robust under aggregation by the gap-damped bounds proved in QFI (Primitives), and itscoverage guarantees rest on the regeneration engine developed in QFI–DF. A three-node exampleillustrates end-to-end computation of Λ, I(θ), Lc, and ABα, with an appendix checklist forreproducible toolchains.