Future-Minimum Critical Corridors and Beatty Clock Rigidity in Accelerated Collatz Dynamics

Program position. This paper is the first public module of the aperiodic Entry branch of a modular research program for the accelerated Collatz map. The downstream arithmetic component of this branch is the centered-residue rigidity theorem developed in Centered-Residue Rigidity in Collatz Valuation Sequences: Tower-Sparse Returns and 2-Adic Logarithmic-Form Escape. In the author's research architecture, this centered-residue arithmetic layer is referred to as the Delta-Core Exit. For an actual fixed positive orbit, the centered-residue formulation provides an arithmetic obstruction to remaining indefinitely in a sufficiently subcritical centered-residue regime. The present paper addresses the upstream question: how much of the required Entry structure can be forced directly from the physical orbit dynamics? Assuming a hypothetical positive aperiodic accelerated-Collatz orbit, this paper proves that cofinal future-minimum anchors generate logarithmic coefficient-critical corridors. For sufficiently short gaps between consecutive future minima, the accumulated valuation is forced by an exact Beatty clock law, producing a reverse first-passage geometry. The resulting first-passage family is then shown to saturate the relevant dyadic-fibre capacity scale. Thus the future-minimum restriction alone does not provide a second independent exponential counting loss. The current public aperiodic architecture is: hypothetical positive aperiodic survivor→ Entry Program I: future-minimum physical reduction→ deterministic centered-residue visitation / integer-realizability bridge [OPEN]→ centered-residue rigidity / Delta-Core Exit→ contradiction. The open bridge above is not proved in this paper. In particular, this paper does not prove infinite occupation of the short-gap sector, deterministic universal Entry, exclusion of all positive aperiodic survivors, or the Collatz conjecture. Positive nontrivial cycles form a logically separate obstruction problem. They are treated in Fine-Phase Defect Rigidity in Record-Critical Accelerated Collatz Cycles (Cycle Exclusion Program I), rather than by directly applying the aperiodic centered-residue Exit argument. Accordingly, the public program currently separates two branches: an aperiodic Entry-to-Delta-Core-Exit branch with an explicit open deterministic bridge, and a periodic cycle-rigidity branch with its own remaining global reduction problem. The deposited LaTeX source reproduces the public manuscript. The accompanying verification package reproduces selected finite examples and numerical constants only; no theorem in this paper depends on computer-assisted proof.