Zeno Paradox Resolved with Chronoscalar Field Theory

The late-stage curling trajectory exhibits increasing transverse deflection as for-ward velocity decays. Standard models treat this behavior using instantaneous frictionlaws with regime switching, implicitly relying on unlimited temporal refinement of themotion law. In discretely supported contact dynamics, such formulations encountera limit obstruction near the stopping state. We instead treat curling as a low-speedanisotropic contact-wake system and analyze it within the finite-support admissibilityframework of Chronoscalar Field Theory (CFT) [1]. In CFT, no intrinsic geometriccurvature is introduced; the measured trajectory bending κ(s) is a kinematic observablereflecting transverse re-partitioning of admissible advance. We extract κ(s) from pub-lished trajectory panels, remove smooth envelope components, and compare Gaussianand fixed-q residual likelihoods (with q = 1.2371 taken from independent histogramanalysis). Because the parameter count is held equal, Bayesian Information Criterion(BIC) differences isolate residual structure rather than parameter inflation. The re-sults show a regime-dependent transition: slow shots are Gaussian-consistent, whilemedium and fast shots exhibit heavy-tail residual behavior consistent with corridor re-partitioning under anisotropic contact support. In this formulation, no instantaneousphase toggling is required; evolution proceeds by finite-support admissible advance,and the apparent ”Zeno” obstruction of purely differential friction laws does not arise.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-02-17
DOI
https://doi.org/10.5281/zenodo.18670668
Primary Topic
Winter Sports Injuries and Performance
Type
article
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article

Zeno Paradox Resolved with Chronoscalar Field Theory

Calvin Grant
Zenodo (CERN European Organization for Nuclear Research)
Winter Sports Injuries and Performance
article

Zeno Paradox Resolved with Chronoscalar Field Theory

Calvin Grant
article en

Abstract

The late-stage curling trajectory exhibits increasing transverse deflection as for-ward velocity decays. Standard models treat this behavior using instantaneous frictionlaws with regime switching, implicitly relying on unlimited temporal refinement of themotion law. In discretely supported contact dynamics, such formulations encountera limit obstruction near the stopping state. We instead treat curling as a low-speedanisotropic contact-wake system and analyze it within the finite-support admissibilityframework of Chronoscalar Field Theory (CFT) [1]. In CFT, no intrinsic geometriccurvature is introduced; the measured trajectory bending κ(s) is a kinematic observablereflecting transverse re-partitioning of admissible advance. We extract κ(s) from pub-lished trajectory panels, remove smooth envelope components, and compare Gaussianand fixed-q residual likelihoods (with q = 1.2371 taken from independent histogramanalysis). Because the parameter count is held equal, Bayesian Information Criterion(BIC) differences isolate residual structure rather than parameter inflation. The re-sults show a regime-dependent transition: slow shots are Gaussian-consistent, whilemedium and fast shots exhibit heavy-tail residual behavior consistent with corridor re-partitioning under anisotropic contact support. In this formulation, no instantaneousphase toggling is required; evolution proceeds by finite-support admissible advance,and the apparent ”Zeno” obstruction of purely differential friction laws does not arise.

Zenodo (CERN European Organization for Nuclear Research)
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Winter Sports Injuries and Performance
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