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Background-Free Candidates Without a Global Gatekeeper: The Candidate-Class Normal Form for the Background-Free Support Functor, the Admission Test, and the Literature Families Typed

Uchida, Tomoyuki
PhilArchive · Papers
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philosophy
When a research program registers an open frontier that "closes only by a successor's exhibited construction," a quiet authority takes office in the meantime: whoever decides which frameworks count as candidates for that construction. In practice the decision runs on prestige, community momentum, and a referee's sense of seriousness — an admission authority this paper personifies as the Global Gatekeeper and retires constructively. The paper is the sixty-ninth in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates. Its fifty-seventh installment had built a dressed region algebra on a fixed ambient net and scored its own ceiling honestly — anchor-carried is not background-free — registering full background independence as an open conjunct that no paper has attempted. This paper does not attempt it either. It builds the layer the frontier was missing: a checkable answer to what counts as a candidate. The instrument is a normal form for candidate declarations. A background-free support-functor candidate is a finite declaration text with seven fields: a source category of relational region data whose type constraint bars externally fixed background structure (ambient nets, fixed metrics, cell assignments) while allowing internally supplied relational geometry — with a renaming test, run as three finite scans of the declaration itself, that catches fixed background smuggled under relational names; a target algebra category with a label check; the support functor, declared on a finite presentation; axioms at declared strengths; a reduction map onto the fixed-net package of the parent construction, whose codomain is the only place a fixed net may appear; strict-recovery proof targets, required at declaration grade now with proofs the successor's obligation; and explicit failure criteria. Admission is then decidable — four finite checks with a fixed verdict routing — and the paper's vocabulary enforces its anti-authoritarian point: verdicts are admissible-as-typed, conditionally admissible-as-typed pending named fields, or outside the declared candidate type. Admission is not permission; it is a finite type check against declared fields. The declared candidate table — four literature families (crossed-product and modular-theoretic constructions; edge modes and boundary charges; dressed observables; the locally covariant functor) plus one corpus-internal boundary-data row — is typed under an extraction protocol that reads displayed structure only, with a setting/input rule separating a source's presentation arena from its input signature. Two families land conditional with their pending fields named; two land outside as published, each with its achievements and its re-basing route displayed — the locally covariant functor's landing crystallizing the paper's sharpest distinction: background-covariant is not background-free, a defined and scoped typing result rather than a criticism. Nothing is constructed, no family is selected or ranked, the frontier remains exactly as open as its owner left it, and the completeness of the preparation artifact is recorded without opening, numbering, or reserving any successor program. The philosophical moral is carried by the paper's registered pair: typed is not constructed; admissible-as-typed is not selected.
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