The Declaration Boundary: Forceable Form, Irreducible Content, and the Recursive Limit of Bounded Judgment

This paper develops a formal account of declaration in bounded judgment. It asks what remains when a regime has exhausted the distinctions available through its licensed evidence and inference, yet consequential judgment still requires content that has not been certified as derived. The central distinction is between derivation and declaration. Derivation consists in outputs that factor through the information quotient already licensed by the regime. A resolving declaration does not override that logic; it supplies an authorized informational enrichment that refines the distinctions available to subsequent derivation. The paper separates declaration content, informational enrichment, induced quotient refinement, newly derivable consequences, and authority to commit, preventing these layers from being identified. At fixed-carrier set scope, the paper characterizes the exact obstruction to a desired target, the canonical minimal informational refinement sufficient to remove that obstruction, and the corresponding target-completion law. For finite carriers, a specialization of the Minimum Repair Alphabet theorem from The Gate Between Constraint and Identification gives the minimum auxiliary alphabet width required by any informationally sufficient realization. This yields a four-level boundary: the obstructing identifications, their canonical minimal structural repair, the minimum finite realization width, and the authority required to lawfully supply such a realization. The paper further develops recursive provenance, declaration relativity, capability–authority separation, declaration lifecycle and retirement, and operational termination without self-certifying finality. Higher-order selection can relocate the declaration boundary by introducing additional distinctions, but it cannot erase the provenance requirements of those distinctions for free. The resulting architecture is: derive what the licensed distinctions determine; expose what remains unresolved; introduce additional distinctions only through declared authority; preserve their provenance; and independently verify the consequences that follow. The mathematics can determine what resolution is missing and, at finite scope, how much discriminating capacity a realization requires. It does not thereby manufacture the realization or the entitlement to install it.