The predecessor's split

The supplied description of Oai282-A separates three targets CheungA.

A: finite certification. The predecessor's thm:ward and prop:finitefit concern named residuals:

Its thm:statistics is an optional bounded-score tolerance statement, not an operator-valued distributional identity.

B: local Ward implementation. The predecessor's prop:affine-ward is conditional on a spacelike-collar contract and a declared polynomial. It is not, by itself, implementation by $X^{\nu }{t}_{\mu \nu }$ on every field in a complete test class. The new free-field results below address precisely this additional issue.

C: global implementation. The predecessor's prop:flow and prop:nonintegrable separate local identities from global geometric flows and unitary integration. We reproduce the relevant elementary examples in Section sec:global. Global implementation is not attempted.

This manuscript does not use a supplied series sheet as a premise. References to Cheung's manuscripts identify predecessor statements, comparison interfaces, and open boundaries. The mathematical inputs used in the proofs are the explicitly declared free Fock construction and standard functional-analytic results, with their hypotheses checked where applied.