What question did this study set out to answer?

This work aims to expand the catalog of zero-free-parameter derivations and demonstrate their structural necessity in the KUT framework.

June 23, 2026Open Access

The Geometric Ground State: The Complete Catalogue and Litigation of the Zero-Free-Parameter Derivations

Key Points

This work aims to expand the catalog of zero-free-parameter derivations and demonstrate their structural necessity in the KUT framework.
Introduced 7 new zero-free-parameter derivations, increasing ZFPDs from 13 to 20.
Highlighted the derivations of constants like the Hubble Constant and Bekenstein-Hawking Entropy using topological approaches.
Established geometric closure through the analysis of the (3,2) Torus Knot against the irrational pentagonal lattice.
New derivations effectively eliminate computational anomalies such as those seen in the muon g-2 calculation.
Confirmed the structural genesis of fundamental constants as outputs of the Abraxian Engine.
Identified residual variances against CODATA as the Celtic Knock, representing the observer's thermodynamic signature.

Abstract

This Version 2 update to The Geometric Ground State significantly expands the KnoWellian Universe Theory (KUT) catalog, increasing the number of primary Zero-Free-Parameter Derivations (ZFPDs) from 13 to 20, and adding the second foundational K-ZFPD. This document serves as the comprehensive litigation of the KUT framework, demonstrating that the fundamental constants of nature are not arbitrary empirical inputs, but necessary topological outputs generated by the Abraxian Engine rendering upon the Cairo Q-Lattice. New derivations in this version include: Weak Mixing Angle (KWMA): Derived as the Dyadic Phase-Shear of the longitudinal windings. Strong Coupling Constant (KSCC): Derived from the Topological Integrity of the nucleon, effectively eradicating the gluon. Hubble Constant (KHC): Resolving the "Hubble Tension" by reframing expansion as a Cosmological Latency Gradient. Bekenstein-Hawking Entropy (KHB): Deriving the holographic bound and the "factor of 4" from Causal Deadlock at the Ultimaton Locus. Muon Magnetic Anomaly (KMMA): Eradicating the need for supersymmetric "ghosts" in the g-2 calculation via Fractal Over-Winding. Elementary Charge (KEC): Derived as the direct geometric displacement of the vacuum substrate. Muon-to-Electron Mass Ratio (KMEMR): Derived as a hyper-dimensional harmonic resonance of the electron. KnoWellian Time (K-2: KWT): Establishing the absolute temporal pixel (Planck Time) from the duration of the i-Turn. By achieving "Complete Geometric Closure, " KUT proves that the parameters of the physical universe are structurally mandated by the friction of the (3, 2) Torus Knot grinding against the irrational pentagonal lattice. The residual variances against CODATA values are rigorously identified as the "Celtic Knock"—the irreducible thermodynamic signature of the biological observer. Keywords KnoWellian Universe Theory, KUT, Zero-Free-Parameter Derivation, ZFPD, Ontological Grammar Shift, Abraxian Engine, Cairo Q-Lattice, (3, 2) Torus Knot, KnoWellian Offset, Fundamental Constants, Hubble Tension, Muon g-2, Information Paradox, Bekenstein-Hawking Entropy, Weak Mixing Angle, Strong Coupling Constant, Elementary Charge, Planck Scale, KnoWellian Length, KnoWellian Time, Celtic Knock, Foundational Physics, Cosmological Mechanics, Unified Field Theory

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