Form-Invariant Resolution Calculus: A Typed Proposal-Resolution Framework for Constrained Evolution and Partial Differential Equations

We introduce Form-Invariant Resolution Calculus (FIRC), a typed framework for constrained evolution in which a proposed change is distinguished from the change actually realized. The state is decomposed into structural and accounting coordinates. Structural motion is resolved against a fixed closed convex legality set, while the associated reaction has no direct accounting component. Continuous proposals admit an orthogonal tangent-normal resolution, whereas finite jumps are resolved by metric projection and are generally nonorthogonal. The two regimes are connected through a single-packet infinitesimal limit. Internal events use a shared source for structural and accounting effects, and simultaneous and serial execution are distinguished explicitly. For absolutely continuous flow, observables evolve along the lawful velocity rather than along the raw proposal. For finite hybrid executions, total proposal equals actual state change plus net reaction. A minimal strong-form PDE realization is provided. The term form-invariant refers to recurrence of the same resolution structure as the state evolves. It does not imply invariance of the state, event commutativity, or geometric fractal self-similarity. Classical projection, convex-analysis, chain-rule, and hybrid-evolution results are treated as donor mathematics. The object reserved for later audit is the combined typed resolution architecture.