What question did this study set out to answer?

This manuscript aims to propose a framework linking the observable universe to a mirror universe through geometric interactions.

May 26, 2026Open Access

Speculative Model of Coupled Mirror Universes: Algebraic Structure, Recursive Compression, and Human–AI Collaborative Process

Key Points

This manuscript aims to propose a framework linking the observable universe to a mirror universe through geometric interactions.
Developed a mathematical model using quaternionic algebra to describe the dynamics between the universes.
Analyzed the implications of the cosmological constant as an emergent effect without the need for exotic substances.
Documented the collaborative process between humans and AI over seven months in developing this model.
Identified the coupling between the two universes as antisymmetric, preserving the Friedmann equations.
Reinterpreted the Big Bang as a phase transition from natural numbers to real numbers.
Established a hierarchical structure mapping physical concepts onto mathematical sets.

Abstract

Abstract: This manuscript presents a speculative cosmological framework proposing that the observable universe (A) is globally coupled to a complementary mirror universe (B) through a non-local geometric interaction. The cosmological constant Λ is reinterpreted as an emergent geometric effect of this antisymmetric coupling, requiring no exotic substance. The Friedmann equations remain unmodified. The model's natural algebraic structure is identified as quaternionic (ℍ): the antisymmetric dynamics A↔B correspond to quaternionic non-commutativity, where the inter-universe membrane emerges as the element k = i·j. The mathematical hierarchy ℕ⊂ℝ⊂ℂ⊂ℍ⊂𝕆 maps onto the physical structure of the model. The Big Bang is interpreted as the ℕ→ℝ phase transition. The manuscript maintains explicit boundaries between rigorous, empirical, speculative, and poetic content. This deposit also documents a seven-month human–AI collaborative process as part of the scientific result. Author: Tarek Antonio Ocaña Sanz — May 2026

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