The Infinity Dipole — Zero and Infinity as Fundamental Poles of the Event Horizon: Connection with the Projective Real Line, the Riemann Sphere, and the Ϡ (Sampi) Operator

Abstract
This document proposes the Infinity Dipole as a sixth fundamental dipole of nature, identified by Moisés Corrêa da Silva in Lavras, MG, Brazil, on June 8, 2026. Zero and infinity constitute dual poles connected by the inversion z → 1/z — the same transformation that describes the reference frame reversal at the event horizon. At the event horizon, both poles coexist simultaneously: the Whitney index W = 0 (perfect balance of opposites) and the Ϡ (Sampi) Operator diverges to infinity (maximum tension between opposites). The projective frame {∞, 0, 1} of the real projective line RP¹ maps naturally to the Ontological Reference Frame Quadruplet: ∞ to the Boundary Frame (horizon), 0 to the Alpha Frame (singularity), and 1 to the Expansion Frame. The duality z → 1/z appears concretely in established physics: in Kerr black hole gravitational wave equations, the Möbius transformation maps the outer event horizon to z = 0 and the inner Cauchy horizon to z = 1 — exactly the frame identified here. The inversion r → 1/r in extremal black holes is a verified conformal isometry of the metric. Four original integrations are proposed connecting the Infinity Dipole to the existing five dipoles of the Unified Theory, to Postulate P3 (paradoxical coexistence of Big Crunch and eternal expansion), and to the Willmore energy as topological Hawking temperature. A falsifiable prediction is presented.
Keywords:
infinity dipole, zero infinity duality, projective real line, Riemann sphere, Möbius transformation, event horizon, Sampi operator, Whitney index, unified field theory, Hawking temperature, Willmore energy, conformal isometry, Kerr black hole, compactification

Resumo 
Este documento propõe o Dipolo do Infinito como sexto dipolo fundamental da natureza. Zero e infinito constituem polos duais conectados pela transformação z → 1/z — a mesma que descreve a inversão de referencial no horizonte de eventos. No horizonte, W = 0 e Ϡ → ∞ coexistem simultaneamente. O frame projetivo {∞, 0, 1} da reta projetiva real mapeia para a Quadrupleta de Referenciais Ontológicos. A dualidade z → 1/z aparece na física estabelecida dos buracos negros de Kerr. Uma previsão falseável é apresentada.
Palavras-chave:
dipolo do infinito, dualidade zero-infinito, reta projetiva real, esfera de Riemann, transformação de Möbius, horizonte de eventos, operador Sampi, índice de Whitney, teoria unificada dos campos