A classification of the applicability-status of declared mathematical application records, not a verdict on why or whether mathematics fits the world. The corpus fixes what a record is of (Paper 13), when a declared structure is objective (Paper 15), when a causal claim is entitled — including its own causal-specification applicability and model adequacy (Paper 16), what an embedded observer can recover (Paper 19), when a claim is true (Paper 20), when a postulate may be adopted (Paper 63), what a term refers to (Paper 75), the necessity-status of a commitment (Paper 76), and the objecthood-status of a token (Paper 77) — but nowhere types the history-internal, system-relative applicability-status of a declared mathematical application record. While no such layer exists, a Global Applier — an external authority who fixes, from outside a history, which mathematics really applies to the world and why it works — works by default. No corpus paper reserves this seat by name: this is a new-seat opening on displayed need, completing the reference (75), necessity (76), existence (77), applicability (78) quartet over the classical pillars of the philosophy of mathematics. Four type facts stand in print and bind the paper: "Typed is not adopted; classified is not answered. " / "An applicability-status is a type, not a world-side fit verdict. " / "A representation-status is a checked certificate, not a decided correspondence. " / "Applicability is relative to a declared system, never simpliciter. " An application record is not a fit. It is a recorded pairing of a declared mathematical structure with a declared finite record-fragment at a declared grain — never a presupposed math-world correspondence. The construction is an applicability-status grounding object A (a) = (Sdecl, Rep, Ideal, Prov, Use, gamma) — an application record's declared systems, its candidate-indexed representation-certificate store with its checker rules, its idealization/residual store, its application-provenance record, its use record, and an application-individuation grain — with a normal form and a barred-fields box. On it, a three-axis ApplicabilityProfile (a; S) = (R, M, P) is typed by a certificate-based decidable test over a finite declared obligation set: the R-axis (representation-status) is read by checking a declared certificate — a total or partial representation certificate verified obligation-by-obligation on the declared finite fragment, with an explicit total-over-partial-over-open routing priority — never by deciding real correspondence; its positive cell typed-representation-certified-at-grain-in-S always means that a declared certificate checks at the declared grain, never that the structure really corresponds to the world. The M-axis (idealization-status) is cascaded over the declared tolerance store, separating typed-exact-in-S from typed-idealized-at-declared-tolerance-in-S and from typed-uncontrolled — a routed status for a declared idealization carrying the declared no-tolerance flag, naming the gap instead of hiding it. The P-axis (application-provenance) is set-valued over the recorded entry modes (derived / imported / calibrated), with a named typed-no-provenance-record cell when the record is declared-empty. An over-declared store — a checked misfit against a checked certificate for the same candidate — halts the test at a top-level diagnostic outcome, diagnostic-fit-conflict-in-S, which is not a profile value but a failed profile-construction route. The contribution beyond "homomorphism-in-S restated" (the K0 guard, two-pronged) is, first, that the M- and P-axes are computed from the history-internal idealization store and the recorded provenance, not from the representation fact — the paper exhibits explicit non-collapse witness pairs over a fully declared setting — and, second, that those axes are status-like rather than metadata: a declared consumption/transfer condition discipline, grounded in the recorded use-classes by a non-circular admissibility rule, reads all three axes as gates on downstream consumption and transfer, and the satisfied conditions differ across exactly the witness pairs. The multi-axis profile locates the Wignerian miracle-reading, the deflationary posture, the mapping account, the inferential conception, and the idealization pressure as located displays and profile points. The ceiling is declared and patrolled: typing is not adopting; classifying is not answering. The substantive why-mathematics-works question is declined either way — neither effectiveness-mysterianism nor deflation; truth, objectivity, causation, recovery, knowledge, reference, necessity, objecthood, and adoption stay at their owners' seats; strict recovery of Paper 13's per-record semantics is exact (Lemma R-ap). The predicted landing is ApplicabilityProfile-layer = scoped, with a null via K0 an honest branch and an Applier-dependence theorem (K3) declared and patrolled. Nothing is adopted; no truth, satisfaction, or world-side fit verdict is claimed. The paper engages the applicability literature (Carnap 1950; Wigner 1960; Steiner 1998; Pincock 2012; Bueno Batterman 2002; Field 1980) as display and pressure-test only, operationalizing Carnap's internal/external relativity with a decidable test, splitting Wigner's two theses (the recorded half typed, the modal-explanatory half declined), locating Steiner's mathematics-guided discovery at the provenance axis, taking Pincock's mapping account as the nearest neighbor and net-contribution bar, locating Bueno and Colyvan's immersion/derivation/interpretation schema field-by-field, typing Batterman's ineliminable idealizations honestly as named uncontrolled statuses, and displaying Field's representation theorems as the certificate shape.
Tomoyuki Uchida (Thu,) studied this question.