What question did this study set out to answer?

The aim is to construct and analyze a new two-scale non-polynomial kinetic function that addresses specific astrophysical observations.

March 4, 2026Open Access

Multi-Scale Non-Polynomial Kinetic Completions: Existence, Limits, and the Additive Structure Problem

Key Points

The aim is to construct and analyze a new two-scale non-polynomial kinetic function that addresses specific astrophysical observations.
Constructed a non-polynomial kinetic function (S3) that reflects observed properties
Analyzed boost values and asymptotic slopes
Investigated conformal QS coupling and its additive structure
Achieved accurate boost values at a_0 and Cassini data
Correctly predicted the asymptotic slope of the function
Identified additive structure K_X = 1 + f(X) as an obstruction affecting observations

Abstract

We construct the first explicit two-scale non-polynomial kinetic function (S3) that simultaneously reproduces the observed boost at a₀ (1. 579 vs 1. 582), passes Cassini (KX = 1. 000 at Saturn), and achieves the correct asymptotic RAR slope (s -> 0. 52). However, the predicted slope at a₀ is 0. 86 vs observed ~0. 6. We trace this to the additive structure KX = 1 + f (X) inherent to conformal QS coupling, identifying it as the remaining obstruction.

Multi-Scale Non-Polynomial Kinetic Completions: Existence, Limits, and the Additive Structure Problem

Key Points

Abstract

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