Result: Partition Threshold Collapse and Modular Congruences in Classical Number Theory

Title:
Partition Threshold Collapse and Modular Congruences in Classical Number Theory
Authors:
Fernandes, Ricardo Miguel Machado
Publisher Information:
Ricardo Miguel Machado Fernandes
Publication Year:
2025
Collection:
Zenodo
Subject Terms:
Partition Function, Modular Congruences, Curvature Collapse, Number Theory, Discrete Analysis, Structural Heuristics, Ramanujan Congruences
Document Type:
Academic journal text
Language:
unknown
Relation:
https://zenodo.org/records/15285167; oai:zenodo.org:15285167; https://doi.org/10.5281/zenodo.15285167
DOI:
10.5281/zenodo.15285167
Availability:
https://doi.org/10.5281/zenodo.15285167
https://zenodo.org/records/15285167
Rights:
Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode
Accession Number:
edsbas.847EE219
Database:
BASE

Further Information

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.