What question did this study set out to answer?

The aim is to investigate the inverse geometry of a pseudo-Recamán recurrence and understand the nature of its branching bands.

July 23, 2026Open Access

Linear Preimage Growth and Branching-Band Separation in a Pseudo-Recamán Recurrence

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This research note analyzes inverse geometry and branching bands in pseudo-Recamán recurrences, implying unique structural properties.

The aim is to investigate the inverse geometry of a pseudo-Recamán recurrence and understand the nature of its branching bands.
Derivation of the complete predecessor candidate set for the pseudo-Recamán recurrence.
Analytic proof of the branching band characteristics and their interactions during forward evolution.
Documentation of computational implementations and verification processes.
Proven that two distinct branching-band states at the same time never become closer over future iterations.
Established the upper limit of reverse-frontier size at depth d as U_d≤d+1.
Provided a repeatable and verified mathematical framework for the pseudo-Recamán recurrence.

Jake Foth (2026) studied this question.

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