Documento de Revisão e Extensão O Operador Ϡ (Sampi) Dentro do Horizonte de Eventos

Abstract

This work extends the Ϡ (Sampi) Operator beyond its original formulation by introducing an imaginary continuation within the Schwarzschild event horizon. The proposed extension interprets the emergence of the imaginary domain as the mathematical signature of a referential inversion between radial and temporal causal structures, consistent with the Mass–Space Inversion Postulate. From this extension, a generalized family of transition operators, Ϡᵣ₀, is derived, allowing arbitrary referential horizons and establishing a broader framework for causal and topological transitions.

The work further demonstrates that the tunneling operator Υ requires the extended form of Ϡ in order to remain defined inside horizon regions, revealing a direct structural correspondence between horizon crossing and quantum tunneling processes. The event horizon is consequently reinterpreted as a genuine referential transition surface, where causal orientation, topological character, and observational accessibility undergo simultaneous transformation.

Additional developments introduce the concepts of thermodynamic horizon memory, causal holographic organization, and a dual reflective–refractive information pathway in which information is partitioned into complementary conserved channels analogous to transmission and reflection coefficients in quantum mechanics. Together, these results provide an integrated mathematical framework connecting horizon topology, tunneling dynamics, causal inversion, and information organization within the author's Unified Theory.

Keywords: Sampi Operator (Ϡ); Tunneling Operator Υ; Referential Transition; Event Horizon; Mass–Space Inversion; Topological Eversion; Horizon Memory; Unified Theory.