A classification of the necessity-status of declared logical, mathematical, and modal commitments, not a verdict on what is in fact necessary. The corpus fixes when a law is nomologically necessary (Paper 17), when a claim is true or modal-cf-satisfied given a modal base (Paper 20), when a belief is knowledge (Paper 21), how inquiry revises (Paper 22), when a norm has standing (Paper 27), when a postulate may be adopted (Paper 63), and what a theoretical term refers to (Paper 75) — but nowhere types the history-internal, system-relative necessity-status profile of a logical, mathematical, or modal commitment. While no such layer exists, a Global Formalizer — an external authority who fixes, from outside a history, whether a commitment is necessary, a priori, or provable, and which axiom system is the correct one — works by default. Paper 27 reserved this exact seat by name. This paper types that layer. Four type facts stand in print and bind the paper: "Typed is not adopted; classified is not answered. " / "A necessity-status is a type, not a world-side verdict. " / "A certificate-status is a checked certificate, not a decided theorem. " / "Necessity is relative to a declared system, never simpliciter. " The construction is a necessity-status grounding object N (phi) = (Sdecl, Cert, Warr, Adopt, Use, gamma) — a commitment's declared systems (each with a declared modal role), a declared certificate store with its checker rules, a warrant-provenance graph, an adoption record, its derivation-usage, and an individuation grain — with a normal form and a barred-fields box. On it, a three-axis NecStatusProfile (phi; S) = (P, A, D) is typed by a certificate-based decidable test: the P-axis (certificate-status) is read by checking a declared certificate against declared checker rules — never by deciding theoremhood — with a positive cell typed-certified-in-S that retains its certificate subtype (a syntactic proof-certificate or a declared model-class validity-certificate) ; the A-axis (a-priori-attribution) is read over an explicit warrant-provenance graph, typing the recorded provenance and never a world-side analyticity verdict; the D-axis (adoption-status) reads a declared adoption record and licenses nothing. The derived modal label typed-necessary-relative-to-S fires only for the validity certificate subtype (validity over a declared modal model class) under a system declared a modal base, so mere derivability or axiom-hood does not promote a commitment to necessity. Certificate conflicts route to a diagnostic outcome, not a status. The contribution beyond "provability-in-S restated" (the K0 guard) is that the A- and D-axes are computed from history-internal warrant and adoption records, not formal-system facts: two commitments both typed-certified-in-S can carry different profiles, and the paper exhibits explicit non-collapse witness pairs over a fully declared propositional Hilbert system. The multi-axis profile locates the necessary-a-posteriori and contingent-a-priori square as distinct typed points, so the output is a necessity-status profile, not only a proof bookkeeping. The ceiling is declared and patrolled: typing is not adopting; classifying is not answering. The substantive what-is-in-fact-necessary question is declined, not refuted; the object-ontology of mathematics is a future seat; truth, modal-cf, knowledge, nomological necessity, revision, value, adoption-licensing, and reference stay at their owners' seats; strict recovery of Paper 13's per-record semantics is exact (Lemma R-nec). The predicted landing is NecStatusProfile-layer = scoped, with a null via K0 an honest branch and a Formalizer-dependence theorem (K3) declared and patrolled. Nothing is adopted; no truth, modal-satisfaction, or world-side modal verdict is claimed. The paper engages the philosophy-of-mathematics literature (Carnap 1950; Kripke 1980; Quine 1951; Benacerraf 1973; Lakatos 1976; Wittgenstein 1956; Kitcher 1984; Field 1980) as pressure-test and boundary only, operationalizing Carnap's internal/external relativity, answering Quine's analytic/synthetic critique by typing recorded warrant-provenance, side-stepping Benacerraf's access problem by declining the world-side question, locating Kripke's necessary a posteriori as a typed profile point, taking Lakatos/Wittgenstein/Kitcher's proof-as-practice as the grounding-object stance, and marking Field's nominalism as the withdrawn object-ontology boundary.
Tomoyuki Uchida (Thu,) studied this question.
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