What question did this study set out to answer?

The aim is to present a comprehensive theory of forward dynamics, inverse geometry, and growth rates in a pseudo-Recamán recurrence.

July 23, 2026Open Access

Threshold Geometry and the Pronic Backbone: Forward Dynamics, Exact Inverse Geometry, and Sharp Preimage Growth in a Pseudo-Recamán Recurrence

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Authors

JFJake Foth

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Implication

This preprint presents a unified theory on dynamics and geometry of a pseudo-Recamán recurrence, suggesting broad implications for mathematical structures.

Key Points

The aim is to present a comprehensive theory of forward dynamics, inverse geometry, and growth rates in a pseudo-Recamán recurrence.
Developed a unified theory integrating forward dynamics and inverse geometry of threshold c = 1/2
Established sharp deficit formulas and critical frontier maxima
Underwent integer verification and external review to support findings.
Identified three regimes based on threshold values, influencing dynamics and geometry
Discovered a pronic backbone linking various mathematical structures with specific growth rates
Verified growth order of Θ(sqrt(N)) and cumulative maxima of Θ(N^(3/2)).

Cite This Study

Jake Foth (2026) studied this question.

synapsesocial.com/papers/6a61afe0faa9903c5116a99c https://doi.org/10.5281/zenodo.21475061

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Implication

This preprint presents a unified theory on dynamics and geometry of a pseudo-Recamán recurrence, suggesting broad implications for mathematical structures.

Threshold Geometry and the Pronic Backbone: Forward Dynamics, Exact Inverse Geometry, and Sharp Preimage Growth in a Pseudo-Recamán Recurrence

Discussion

Member takes

Implication

Key Points

Cite This Study

Threshold Geometry and the Pronic Backbone: Forward Dynamics, Exact Inverse Geometry, and Sharp Preimage Growth in a Pseudo-Recamán Recurrence

Discussion

Member takes

Implication

Key Points

Cite This Study

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