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Preprint . 2025
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ZENODO
Preprint . 2025
License: CC BY
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Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Proof of the ABC Conjecture via Ghost Drift Theory

Authors: MAEKI, HIDEMITSU;

Proof of the ABC Conjecture via Ghost Drift Theory

Abstract

This paper presents an attempt to prove the ABC Conjecture, one of the most profound unsolved problems in number theory, within the framework of the author's proposed Ghost Drift Theory. Ghost Drift Theory reinterprets natural numbers as vectors in a multi-dimensional semantic space (Log-prime Vector Map $T(n)$), modeling the additive relation $a+b=c$ as a "Semantic Jump" from an "initial nucleus $\mu_1 = T(ab)$" to an "emergent nucleus $\mu_2 = T(c)$." By quantifying the semantic coherence during this jump with a semantic energy function $\phiE(s)$ and analyzing the behavior of its minimum point, the Semantic Heart Point $\sH$, we rigorously demonstrate that the "finiteness assertion" of the ABC Conjecture is equivalent to the finiteness of energy explosions and the convergence of coherence residuals in the Ghost Drift space. Specifically, we show that the concept of the radical can be syntactically derived within Ghost Drift Theory, that the non-additivity of the semantic energy leads to an explosive structure, and that a clear geometric boundary exists in the semantic space to identify ABC Conjecture exceptions.

Keywords

IUT Comparison, Number Theory, Semantic Heart Point, Semantic Energy, Ghost Drift Theory, ABC Conjecture, Log-prime Vector Map

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average