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

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