No Crowning the Frontier: Explanation Graphs, Certification Boundaries, and Diagonal Obstruction

Every finite explanatory practice necessarily generates a frontier. This is not a deficiency to be remedied but a structural consequence of finite delivery: any successfully completed finite explanation, once its dependency structure is made explicit, takes the form of a finite directed acyclic graph, and any non-empty finite DAG contains nodes at which upward ascent stops. Frontiers are not occasional failures of inquiry. They are what finite explanation necessarily produces.This paper establishes that no such frontier can be crowned—that is, no finite maintaining community can complete, from any finite historical position, the certification procedure that would convert a current frontier node into a principled, finally authorized explanatory terminus. This result now holds, given premises that currently stand undefeated, with deductive force. It is not a recommendation toward epistemic humility. It is a present-tense structural prohibition.The argument proceeds in two tiers, each issuing a no-go result of determinate character and independent source.Tier I (Branching No-Go under Physical Interpretability) establishes that for any physically interpretable practice, no finite historical prefix can clear the whole of future witness space with respect to a frontier node. This follows deductively from two empirical premises—recurrent interpretive divergence across multi-generational practices, and the historical displaceability of interpretive authority—neither of which has been defeated by any known case. Because the deduction is valid and the premises currently stand, the no-go holds with full present force. Its force does not depend on further philosophical endorsement. It depends only on whether its stated premises can be defeated. The label ‘Tier I’ marks the source of obstruction—branching-historical rather than diagonal-internal—not its current force.Tier II (Diagonal No-Go in Sealed Fragments) establishes that once a community installs a commitment bridge over a fragment satisfying a minimal fixed-point condition, no consistent internal certification regime can cover that fragment completely. This follows from the structure of the diagonal lemma and is independent of Tier I. It does not require the frontier to be contested from outside. The sealed structure contains something it cannot certify from within, regardless of what happens in future interpretive history.Applied first to grounding theory, and then extended diagnostically to broader institutionalized forms of genealogical, textual, experiential, and historical totalization, the framework shows how both tiers bear on attempts to convert upstream explanatory position into principled terminus. The paper identifies precise trigger conditions for Tier II, supplies practical criteria for recognizing when those conditions are live, and marks the boundary cases in which the trigger is absent.Grounding may redraw the frontier. No finite practice can crown it. That is not advice. It is the present situation, described with as much precision as the subject permits.