The Field Correspondence Principle: Toward a Shared Mathematical Foundation for Quantum, Language, and Signal Fields

The recurrence of field descriptions in quantum physics and artificial-intelligence systems raises a legitimate mathematical question but not, by itself, a legitimate unification claim. Quantum field theory (QFT) concerns physically constrained quantum observables and states, whereas Large Language Fields (LLFs) and Large Signal Fields (LSFs) are candidate operational descriptions of distributed language- and signal-processing regimes. This paper proposes the Field Correspondence Principle (FCP) as a defeasible research hypothesis: ontologically distinct field regimes may admit nontrivial, typed correspondences among contexts, states, observables, transformations, composition and selected invariants without sharing physical substance, causal laws or measurement semantics. We formulate a minimal comparative contract, distinguish covariant observables from contravariant state restriction, describe correspondence through a shared test signature rather than an assumed identity map, and define translation defects, information-loss obstructions and domain-specific axiom guards. Three bounded propositions clarify what cannot be recovered from observational quotients, why local component agreement fails to certify relational composition, and why categorical structure alone cannot imply relativistic locality. A finite operational example and a prospective quantized-lattice test bed illustrate the method without claiming an executed QFT experiment. We develop a falsifier-first protocol with matched-information conventional baselines, held-out interventions, independent physical validity checks, negative controls and explicit refusal outcomes. The proposal is not a new quantum theory, a proof that LLFs or LSFs constitute physical fields, or evidence of a universal field ontology. Its intended contribution is a precise, auditable boundary between useful mathematical correspondence and unsupported physical equivalence, together with a research architecture in which positive, negative and null results remain publishable.