From Processual Crossing to Temporal Relevance: A Comparative Clarification for GOCD

This paper identifies and defends a missing middle layer in debates over temporal relevance within pre-physical generative theory. Much existing discussion moves too quickly from bare sequence, asymmetry, or generic process to claims about temporal direction, or else begins only after spacetime, physical systems, and readout-level temporal articulation are already in place. Against both tendencies, the paper argues that temporal relevance arises neither from order as such nor from process in a merely generic sense, but from what it calls processual crossing: a process-internal threshold transition by which a candidate acquires a standing-difference that is determinable within the route itself and consequential for later admissible organization. Drawing on the minimal-conditions framework for pre-physical generation LiLi2026a, the paper first argues that any viable account of such crossing must involve internal status-bearing transition, thresholded decisiveness, retained downstream consequence, and exclusion of same-level reopening. It then shows that the local GOCD route satisfies these burdens through the relation among closure, freezing, and obtained standing LiLi2026b, LiLi2026c. Closure makes settlement answerable; freezing provides second-threshold retention; obtained standing names the status borne by what successful retention yields, namely an already obtained predecessor available for higher-level inheritance but barred from same-level reconstitution. On that basis, the paper argues that processual crossing is not reducible either to mere order, as illustrated by contrasts with logical derivation and mathematical induction, or to generic process philosophy, as shown through comparison with Whiteheadian becoming Whitehead1978, Bickhard2011. The paper concludes by formulating the necessary conditions for minimal temporal relevance and the corresponding local sufficient condition in the GOCD case. What is thereby established is not metric time, thermodynamic irreversibility, or a full theory of temporal order, but a more primitive criterion: the condition under which a generative transition becomes a retained predecessor-bearing crossing and thereby becomes capable of grounding a structural arrow claim.