The Shape of a Total Theory's Base: Categorial Foreclosures and What They Force

A total theory quantifies over everything, including its own theorists, and a companion paper derives the domains any such theory must address. This paper asks the successor question: what kind of thing could address all of them? A theory discharges a domain by account when the phenomenon arises from its base's general primitives — with no primitive whose sole job is that phenomenon, even a declared one. Under this criterion, a base's fundamental ontological category can close the by-account route to a domain while leaving principled denial open, and three such foreclosures hold at graded strengths. Pure structure cannot self-anchor: a theorem in a stated setting, by Newman's and Putnam's arguments. A base of third-person facts, whether static or dynamical, forecloses interiority: strong, conditional on the explanatory-gap premise and the by-account criterion. An experience-first base forecloses the determinate world: defeasible, since experience already carries rich structure. Jointly with the coherence conditions, the foreclosures yield a target specification for any theory that takes the by-account route everywhere: its base carries both an intrinsic and an extrinsic aspect in its general primitives, with the extrinsic aspect borne by genuine relations rather than coordinated parallelism; its dynamics govern the theorist's own operation; its reference is fixed by a natural relation internal to the base; and a well-defined formal object stands beneath all of it, its intrinsic aspect's granularity left open as a symmetric residue between a per-unit and a cosmic bearer. The genuine-relations requirement rests on a naturalness premise about reference that a covariational reliabilist can decline, and the paper carries that conditionality. Two worked systems occupy the unforeclosed region, Whitehead's per-unit event ontology and Spinoza's cosmic substance, and each leaves the formal object unbuilt; a formalized both-poles ontology is the outstanding construction. The specification narrows the search space for total theories. It certifies no candidate, and names none.