The Field Control Gap: From Field Identification to Authorized and Verifiable Operational Control

Contemporary language-model applications are compound systems whose behavior depends on models, contextual evidence, memory, tools, policy enforcement, human authorization, and consequential downstream recipients. The founding Large Language Fields (LLF) proposal in 2025 treated a field as a reusable, mission-relative configuration of priors, data views, rules, and evaluators; subsequent Field Engineering, identifiability, receipt, and composition research progressively separated architectural declaration from scientific qualification. A historical reconstruction of this research programme shows that the mismatch between declared and effective topology has already been examined in finite Manifield studies. This paper therefore does not claim to discover topology mismatch, invent operational tracing, or demonstrate a novel internal field in commercial AI platforms. Instead, it isolates a subsequent problem: whether an operator who has identified a candidate field can legitimately change its effective constitution, verify that the intended change was applied, establish its bounded causal effects, and reverse it when required. The Field Control Gap is specified as a family of evidence-relative differences among declaration, effective configuration, admissible intervention, execution witnesses, and causal attribution. A Field Control Plane (FCP) is proposed as a testable integration contract, not a privileged window into hidden model execution. A preliminary deterministic sixteen-case pilot provides a negative comparative boundary: both a strong conventional workflow and a typed field-contract implementation classified all sixteen synthetic cases correctly; three relation cuts changed decisions in the constructed program, but no field-specific advantage, independently replicated LLM result, or endogenous field formation was demonstrated. The paper derives observational-equivalence limits, typed change receipts, role-scoped control surfaces, explicit abstention states, adversarial deployment tests, and a preregisterable comparison against equally instrumented conventional configurations. Its intended contribution is methodological: a falsifiable account of the passage from field identification to effective, authorized, and verifiable control, including conditions under which the field vocabulary should be abandoned.