QFI (Primitives): Idiom-Portable Invariants, FI/CRLB Transport, and Typed-Effect Contracts

We formalize the invariant backbone of the QFI program. The QFI schema is an idiom-portable assignment of an information curvature to parameterized models that is (i) invariantunder isomorphisms, (ii) monotone under partition refinement (equivalently, contractive undercoarse-graining), and (iii) stable under lumpability with explicit gap-damped error bounds. Weprove transport results for classical Fisher information (FI) under sufficient statistics and forquantum Fisher information (QFI) under completely positive trace-preserving (CPTP) maps,yielding CRLB monotonicity across idioms. We integrate these guarantees into a lightweight typed-effect contract system that indexes computations by budgets and certifies invariant preservationat compile time. A minimal three-state exponential example verifies the schema mechanically.This axiomatic pillar is companion to QFI–DF (drift/flow dynamics and ergodicity) and QFI–SM(spectral/LDP instrumentation and Murphy scheduling).