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This work aims to analyze the boundary dynamics of a pseudo-Recamán recurrence and characterize its behavior at specific thresholds.

July 14, 2026Open Access

Boundary Dynamics of a Pseudo-Recamán Recurrence

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Preprint analyzes the Canonical Orbit of a History-Free Recurrence, highlighting implications for endpoint behavior.

This work aims to analyze the boundary dynamics of a pseudo-Recamán recurrence and characterize its behavior at specific thresholds.
Introduced a local modulo-threshold representation for the recurrence.
Developed an exact analysis of the canonical dynamics, focusing on endpoint rules and rational thresholds.
Included a reproducibility package with tools for verification and figure generation.
Proved a conditional endpoint-block rule with specific branch words at c = 1/2.
Identified a neutral endpoint ladder at c = 1/2, with specific peaks and valleys at square indices.
Established rational thresholds for the number of completed endpoint blocks across defined intervals.

Jake Foth (2026) studied this question.

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