Finite Course Dosage Regimen Design in Therapeutics with LOGOS Theory B

Temporal allocation and cessation are distinct design freedoms in finite treatment courses. We study Theory B, the finite-course special case of the LOGOS framework, under matched resource and safety assumptions. We establish an endpoint-specific timing null, a global solution for a concave linear-elimination benchmark, and a policy-conditional stopping contrast. The analytical solution has no-treatment, bolus–coast, and loading–maintenance–coast regimes. At the canonical matched dose, flexible allocation improves integrated benefit over an optimal no-loading constant reference by 13.218%; removing the declared continuation floor contributes a separate increment of 0.139 benefit units. A delayed-injury counterexample shows why safety assessment may need to extend beyond the efficacy horizon. An analytical constant-family ceiling and a conservative flexible witness establish restoration of target feasibility for 11.271 < J_req ≤ 13.689. Fixed-target calculations distinguish about 20% dose savings at targets 10 and 11 from restored feasibility at targets 12 and 13. Analytical certificates, feasible witnesses and floating-point bounds within a finite-dimensional family have different scopes. Together, these results provide an attribution framework that separates temporal allocation, policy-conditional cessation, resource savings and target feasibility. They support conditional model-based results and do not demonstrate clinical efficacy or safety gains.