What question did this study set out to answer?

To derive the universal coherence parameter C_univ as a function of spacetime dimensionality.

February 25, 20260 citationsOpen Access

First-Principles Derivation of Cᵤniv = 1/ (d+1) from Tensor Network Architecture and Spacetime Dimensionality

Key Points

To derive the universal coherence parameter C_univ as a function of spacetime dimensionality.
Derived C_univ = 1/(d+1) from the dimensional structure of spacetime.
Used the HaPPY holographic code as a proof of concept.
Analyzed the partitioning of degrees of freedom between dimensions.
Confirmed C_univ = 0.20 ± 0.08 for d = 3, consistent at <1σ.
Established that global unitarity is maintained across cosmic bounces.
Demonstrated relevance of AdS/CFT kinematic structure in cosmology.

Abstract

We derive the universal coherence parameter Cᵤniv = 1/ (d+1) = 1/4 (for d = 3 spatial dimensions) from the dimensional structure of spacetime, independent of any specific tensor network architecture. The key argument is that degrees of freedom partition between the cyclic (temporal) dimension and the d spatial dimensions, yielding Cᵤniv = 1/ (d+1) universally. We verify this result using the HaPPY (Harlow-Pastawski-Preskill-Yoshida) holographic code as a proof of concept, obtaining CᵤnivHaPPY = 0. 20 ± 0. 08 (consistent at <1σ). We prove that global unitarity is preserved across bounces via a unitary rotation in the full Hilbert space, and justify the use of AdS/CFT kinematic structure in cosmological context. This eliminates the last parameter in the framework. Part VII of VII.

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