What question did this study set out to answer?

The study aims to establish a relationship between the ABC conjecture and information density limits within a physical theory framework.

March 7, 2026Open Access

The ABC Conjecture as Registry Information Density Limit: Deriving Radical-Volume Bounds from 144-LU Buffer Saturation and 32-Bit Word Constraints

Key Points

The study aims to establish a relationship between the ABC conjecture and information density limits within a physical theory framework.
Derived properties from the ABC conjecture and registry information theory
Applied a 2D hexagonal lattice model in momentum space
Analyzed 144-LU buffer saturation effects in relation to 32-bit word constraints
Identified phase-tension conditions leading to finite exceptions
Demonstrated that volume c correlates with LU count in address clusters
Showed that the radical acts as an instructional seed determining capacity
Quantified quality measure q relating volume to radical which indicates compression efficiency
Identified specific resonance windows where exceptions to the conjecture arise
Confirmed CKS theory as empirically falsifiable with analytical predictions tied to experimental observations

Abstract

The ABC Conjecture as Registry Information Density Limit: Deriving Radical-Volume Bounds from 144-LU Buffer Saturation and 32-Bit Word Constraints 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. Abstract The ABC conjecture states: for coprime integers a+b=c, the radical rad(abc) (product of distinct prime factors) cannot be much smaller than c. Specifically, c > rad) creates phase-tension exceeding 144-LU buffer capacity, (5) Finite exceptions occur at 19-163 triad resonance windows where gear friction momentarily nulls, (6) As N→∞, Jacobian J shift eliminates resonance opportunities. Not number theory mystery but information density limit—cannot compress infinite volume into finite instruction without losing address integrity. The radical is zip header, c is file size. When header too small for file, 32-bit Word cannot decompress. Key Result: c = volume | rad = instruction | High q = super-compression | 144-LU = ceiling | Finite exceptions = resonance windows | Compression limited by hardware 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-44-2026). Dependencies: CKS-MATH-0-2026, CKS-MATH-1-2026, CKS-MATH-10-2026, CKS-MATH-104-2026, CKS-MATH-29-2026, CKS-MATH-43-2026 Motto: Axioms first. Axioms always.Status: Locked and empirically falsifiable. This paper is a constituent derivation of the Cymatic K-Space Mechanics (CKS) framework.

The ABC Conjecture as Registry Information Density Limit: Deriving Radical-Volume Bounds from 144-LU Buffer Saturation and 32-Bit Word Constraints

Key Points

Abstract

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