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ZENODO
Dataset . 2026
License: CC BY
Data sources: ZENODO
Claim

Polynomial Time Convergence for NP-Complete Problems via Bounded Carry Algebra: A Hierarchical Reduction Algorithm for the Subset Sum Problem

Research datakeyboard_double_arrow_right Dataset 26 Jan 2026Publisher:Zenodo

doi: 10.5281/zenodo.18374114

Polynomial Time Convergence for NP-Complete Problems via Bounded Carry Algebra: A Hierarchical Reduction Algorithm for the Subset Sum Problem

Abstract

This paper presents a deterministic, polynomial-time algorithm (Hierarchical Carry Reduction: HCR) for the Subset Sum Problem, a classic NP-complete problem. By mapping integer sets into a vector space and analyzing carry transitions across hierarchical layers, we demonstrate that the number of active states is strictly bounded by O(n).

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