For a rational parameter c=P/Q with 0<c≤1/2, this research note studies the exact inverse geometry of a nonautonomous pseudo-Recamán recurrence on time-stamped integer states. It derives the complete predecessor candidate set and the exact two-predecessor branching band. Although reverse paths may leave the band, later re-enter it, and branch again, the reverse frontier remains thin. The central theorem proves that two distinct branching-band states at the same time never become closer under future forward evolution. Consequently, every reverse layer contains at most one branching state. If Ud is the reverse-frontier size at depth d, then U₃+₁≤Ud+1 and therefore Ud≤d+1. The record includes the final paper, searchable manuscript source, authoritative exact-integer implementation, reproducibility notes, checksums, theorem-verification code and results, and the accepted Tier 2. 5A finite-search implementation and aggregate results. The universal mathematical conclusions rest on the analytic proof; computation is redundant finite verification. This work is a sequel to “Boundary Dynamics of a Pseudo-Recamán Recurrence, ” DOI 10. 5281/zenodo. 21328138. Version 2. 0 repairs an omitted hypothesis verification in the round induction of Theorem 5. 4. The proof now explicitly maintains and propagates the upper-path cascade bounds through every active block. This closes a proof-presentation gap and does not change the theorem statement, any corollary, or any computational result.
Jake Foth (Tue,) studied this question.