From Grounding Ancestry to an Ultimate Explanatory Order - Well-Founded Resolution, Content Coverage, and the Bearer-Neutrality of Ultimate Explanation

Abstract

A conditioned world-structure has an actual complete unconditioned grounding basis when complete grounding admits at least one set-sized, well-founded resolution network, while infinite local ancestry does not by itself establish the global explanatory sufficiency of a rival non-well-founded account. The argument distinguishes an unconditioned ancestor from a sufficient basis and a sufficient basis from an adequately specified explanatory order. A minimal-ancestor result is proved directly from a predecessor-closed ancestry with a minimal member; a resolution theorem then assembles a complete basis from local full grounds under an explicit well-founded network and substitution principle. Profile Completion requires every indispensable coordinating contribution, including law-governed structure, to be attributed within the explanatory order rather than left as an unacknowledged supplement. Against grounding infinitism, the paper accepts Billon's result that non-termination alone does not entail explanatory incompleteness and establishes a Burden-Displacement Theorem: local full-grounding relations do not by themselves establish global sufficiency; if a governing law or structure L is invoked, the additional claim that L explains the infinite ancestry as a whole must be independently warranted. The resulting positive theorem is conditional and bearer-neutral. It neither proves infinitism impossible nor derives numerical simplicity, pure actuality, personhood, goodness, or any further theological predicate.