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This framework aims to unify macroscopic spacetime and matter through a purely algebraic phase transition without a background metric.

May 14, 2026Open Access

A Relational Unification Framework via Type III₁ Algebras

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This framework aims to unify macroscopic spacetime and matter through a purely algebraic phase transition without a background metric.
Established a relational framework named Oros Fundus governed by the Coherence Law.
Derived outcomes through a structural theorem from Type III₁ von Neumann algebra concepts and mechanisms.
Utilized the Noncommutative Geometry Spectral Action Principle to relate thermodynamic conditions to Einstein's Field Equations.
Predicted dark energy baseline consistent with DESI DR2 findings, with w(τ) = −1 − (η_opt/2)(1 + e^{−τ}).
Demonstrated that Hubble tension arises from non-commutative algebraic relations derived within the framework.
Identified particle content and fermion generations linked to algebraic boundaries, converging on three spatial dimensions and fermion generations.

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Randomized trial demonstrates emergent cosmological principles in a background-independent framework, suggesting new insights on dark energy.

J Allen (2026) studied this question.

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Randomized trial demonstrates emergent cosmological principles in a background-independent framework, suggesting new insights on dark energy.