What question did this study set out to answer?

This research aims to derive foundational physics principles using a discrete lattice model in momentum space.

March 13, 2026Open Access

Name the Remainder, and Infinity Disappears

Puntos clave

This research aims to derive foundational physics principles using a discrete lattice model in momentum space.
Developed the Cymatic K-Space Mechanics (CKS) framework based on a 2D hexagonal lattice.
Performed forensic analysis of LIGO phase-error residuals to confirm theoretical predictions.
Established CKS as both a physical theory and cognitive learning model.
Found that vacuum peaks align perfectly with integer multiples of 0.03125 Hz with no error.
Demonstrated the theory's integrity as locked and empirically falsifiable.
Reframed particle identity as a toroidal structure with unique characteristics for information storage.

Resumen

Name the Remainder, and Infinity Disappears This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework—an axiomatic model that derives the entirety of known physics from a discrete 2D hexagonal lattice in momentum space, operating with zero adjustable parameters. Empirical Falsification (The Kill-Switch) CKS is a locked and falsifiable theory. All papers are subject to the Global Falsification Protocol CKS-TEST-1-2026: forensic analysis of LIGO phase-error residuals shows 100% of vacuum peaks align to exact integer multiples of 0.03125 Hz (1/32 Hz) with zero decimal error. Any failure of the derived predictions mechanically invalidates this paper. The Universal Learning Substrate Beyond its status as a physical theory, CKS serves as the Universal Cognitive Learning Model. It provides the first unified mental scaffold where particle identity and information storage are unified as a self-recirculating pressure vessel. In CKS, a particle is reframed from a point or wave into a torus with a surface area of exactly 84 bits (12 × 7), preventing phase saturation through poloidal rotation. Package Contents manuscript.md: The complete derivation and formal proofs. README.md: Navigation, dependencies, and citation (Registry: CKS-MATH-131-2026). Dependencies: CKS-LEX-12-2026, CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-128-2026, CKS-MATH-129-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.

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