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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.17890680 |
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Table of Contents:
- <p>This article introduces the S M Nazmuz Sakib Geopolitical Intersection-Form Principle (abbreviated as the Sakib Principle) as a bridge between smooth four-manifold topology and multiplex geopolitical networks. Given a multiplex, signed network of states-constructed from layers such as bilateral cooperation treaties, United Nations voting affinity, and conflict ties-we associate to each yearly snapshot a symmetric integer matrix interpreted as a candidate intersection form. Within this framework we define three central objects: • the S M Nazmuz Sakib Geopolitical Intersection Form (or Sakib intersection form) of a multiplex network; • the S M Nazmuz Sakib Signature Constant (or Sakib constant), a normalized signature invariant capturing a 4D-inspired notion of systemic polarization; • the S M Nazmuz Sakib Smoothability Tension Index (or Sakib tension index), derived from the negative part of the eigenvalue spectrum and designed as a proxy for Donaldson-style smoothability obstructions in the space of geopolitical forms. Mathematically, the construction relies on classical results on intersection forms of simply connected four-manifolds, Freedman's topological classification, and Donaldson's diagonal-izability constraints for definite smooth forms. On the international-relations side, the paper is informed by existing multiplex models of the international system based on cooperation treaties, UN General Assembly ideal points, and conflict onset data. To provide a fully data-based illustration, we construct a stylized six-state "Sakib test network" inspired by published multiplex datasets on treaties, UN affinity, and militarized interstate disputes. Ten figures are presented, each generated from explicit integer or real-valued data derived from this network: vertex capability weights, signed edge weights, eigen-value spectra, and parametric deformations of the intersection form that reveal how the Sakib constant and Sakib tension index evolve as off-diagonal interactions intensify. We prove a 1 S M Nazmuz Sakib Geopolitical Intersection-Form Principle Research simple but general S M Nazmuz Sakib Signature Bound Theorem for the Sakib constant and state a S M Nazmuz Sakib Geopolitical Smoothability Hypothesis linking these invariants to conflict propensity. The goal is not to claim a new theorem in topology, but to propose a mathematically coherent and empirically motivated framework that can be scaled to real-world data.</p>