What question did this study set out to answer?

The goal is to explore the nature of prime-factorization potentials and their implications in multiplicative number theory.

March 27, 2026Open Access

Prime-Factorization Potentials Construction, Boundedness, and Spectral Analysis - Universal Tool for Multiplicative Number Theory

Puntos clave

The goal is to explore the nature of prime-factorization potentials and their implications in multiplicative number theory.
Developed bounded fractal functions to represent integers' multiplicative structures.
Conducted a variational analysis to derive scaling properties.
Examined the gcd structure through resonance phenomena.
Demonstrated the boundedness of prime-factorization potentials.
Identified complete scaling properties from the analysis.
Uncovered spectral signatures indicating resonance phenomena in multiplicative structures.

Resumen

Theory of prime-factorization potentials encoding multiplicative structure of integers into bounded fractal functions on ℝᵈ. Proves boundedness, establishes complete variational derivation of scaling properties, analyzes spectral signature of gcd structure through resonance phenomena. Self-contained, applicable to any problem involving prime factorizations: abc conjecture, Catalan-type equations, general multiplicative constraints.

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