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The research aims to establish a mathematical framework for deriving constants of the Standard Model through modular arithmetic.

April 11, 20260 citationsOpen Access

Modular Time Field Theory

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RTRoger Tano

Key Points

The research aims to establish a mathematical framework for deriving constants of the Standard Model through modular arithmetic.
Developed through 32 papers on modular arithmetic and physics
Analyzed the Yang-Mills mass gap and nuclear magic numbers
Investigated gravitational bridge constructions
Employed modular minimal surface representations of lepton mass hierarchy
Included computational scripts for verification in Python and PARI/GP
Identified key structural constants related to level N = 143 and genus 13
Established relationships between the Monster group and modular methods
Demonstrated Feigenbaum constants in fractal dynamics
Validated theoretical predictions through computational analysis

Abstract

Modular Time Field Theory (MTFT): Complete Research Archive A zero-free-parameter mathematical framework deriving Standard Model constants from pure arithmetic. MTFT is built on the modular curve X₀(143), Monster group representations via Monstrous Moonshine, and Feigenbaum universality in fractal dynamics. This archive contains the complete research corpus: 32 papers developing the theoretical framework from foundational modular arithmetic through Yang-Mills mass gap analysis, nuclear magic numbers, gravitational bridge constructions, and modular minimal surface representations of the lepton mass hierarchy. Also included are computational verification scripts (Python, PARI/GP), the MTFT mathematical dictionary, constant atlas, and supporting workbooks. Key structural constants: level N = 143 = 11 × 13, genus 13, index 168, dim S₂(new) = 11, three Galois orbits 1, 4, 6, Monster dimension 196,883, Feigenbaum δ ≈ 4.669. Software implementation available at: https://pypi.org/project/mtft/ (MIT License) GitHub: https://github.com/Kaizoku-Ronin/mtft

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Modular Time Field Theory

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