Abstract This paper introduces the Reconstruction Calculus of the Foundations Program. Paper IV specified the Reconstruction Procedure: the constitutional procedure by which foundational commitments are identified, isolated, functionally characterized, dependency mapped, audited, tested, and assigned provisional constitutional status. The present paper formalizes that procedure. The Reconstruction Calculus defines the formal language, object system, state system, relations, operators, metrics, inference rules, proof obligations, failure structures, decision functions, closure conditions, and machine-verifiable representations required for constitutional reconstruction. Its purpose is not to propose a scientific theory, determine empirical truth, resolve ontological questions, or replace domain-specific inquiry. Its purpose is to make foundational reconstruction formally expressible, comparable, measurable, and provable. Within this calculus, foundational commitments become formal objects; dependencies become typed relations; protected functions become preservation constraints; reconstruction candidates become testable structures; failures become constitutional information; and primitive status becomes a formally derivable methodological state rather than an inherited assumption. The Reconstruction Calculus constitutes the formal layer of the Foundations Program.
Israel Don (Thu,) studied this question.