Provider Sustainability and Access to Care Sensitivities to Medicaid Reimbursement Rates

Here's a 3-sentence submission description: We develop a unified mathematical framework mapping CPT-level Medicaid rate reductions, jointly with a provider's contract mix over fee-for-service, pay-for-performance, shared savings, bundled, and capitated regimes, into operating margin, Tobin's Q, queue-time inflation, and clinical-pathway throughput — yielding closed-form tipping points, a mix-dilated sensitivity elasticity, and an incentive-inversion theorem showing that queue-based access tests reverse sign under capitation. The one-period model is then dynamized via marked point processes, Cramér–Lundberg ruin theory, cost diffusions, and a panel-control turnpike; formalized categorically through open Markov processes and Bayesian inversion in Markov categories; and paired with a mapping from every estimand to modern machine-learning model classes for claims-scale inference. Finally, the framework is validated against two natural experiments — the post-PHE Medicaid unwinding, reproduced as an exogenous attrition shock with a 2.3× hazard jump, and HCP-LAN contract-mix trajectories, whose 2024 plateau is predicted by the fitted ergodic regime chain — and we specify a staggered event-study design with the state ex parte renewal rate as an instrument, together with five falsifiable predictions.