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Partition Threshold Collapse and Modular Congruences in Classical Number Theory

Year: 2025

Type: article

Abstract: This study proposes that local curvature minima in the partition function p(n)p(n)p(n) are associated with modular congruence phenomena. Analyzing second discrete differences up to n=5000n=5000n=5000, we observe that known congruences (mod 5, 7, 11) align with curvature-collapse points. Furthermore, the method suggests potential hidden congruences at larger primes such as 17, 19, 23, 29, and beyond. This introduces the Partition Threshold Collapse Conjecture as a structural explanation for modular congruence behavior in combinatorial number theory.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.15285166

Author: Fernandes, Ricardo Miguel Machado

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6911902185

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