Generative Calculus: Resource-Scaled Operational Envelopes, Reachable Capability, and the Limits of Apparent Expansion

Scientific theories typically compare states, experiments, resources, or algorithms inside a prespecified operational setting. We develop Generative Calculus, a framework for comparing complete resource-scaled envelopes of physically realizable capability. An embodied operational world specifies task families, protocols, observable error, composition, and vector-valued resource costs; its total envelope records joint task-scale-error-budget feasibility. We prove an envelope representation theorem, generative preorder and equivalence results, exact Blackwell-Le Cam and resource-theory reductions, computational formal-versus-feasible separation and hierarchy results, Turing-presented undecidability, and marginal incompleteness. We strengthen the framework with a proper-projection irreducibility theorem whose parity construction agrees on every strict coordinate projection while differing globally, yielding an unbounded generative-order hierarchy. For compact convex envelope trajectories, support functions give a representation-invariant reconstruction theorem from its support-function derivative. A bijective cyclic construction shows that microscopic bijectivity need not imply scalable operational reversibility. We replace unrestricted envelope conservation by a proved budgeted reachable-envelope transport law: capabilities reachable after an internal transition were already reachable before once transition cost is charged. Reproducible software validates the theory against Blackwell comparison, communication complexity, reachability, synthetic stress tests, and public MLPerf Power data. The framework claims scoped mathematical synthesis only, not established new fundamental physics, and identifies precise boundaries for future falsification.