What does this research mean for the field?

Strong constraints on admissible large-scale geometric organization in discrete SU(2)-valued substrates are derived from locality and confinement stability. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to derive constraints on possible large-scale geometries in discrete SU(2) substrates based on structural principles.

February 16, 2026Open Access

Geometric Necessity from Causality and Confinement in Discrete SU(2) Substrates

Key Points

The aim is to derive constraints on possible large-scale geometries in discrete SU(2) substrates based on structural principles.
Analyzed large-scale geometric organization within discrete SU(2) systems.
Considered factors such as locality, bounded valence, and finite propagation.
Evaluated stability of conditional confinement to identify admissible geometries.
Excluded broad classes of candidate geometries from consideration.
Characterized surviving geometries by three-dimensional organization.
Identified triadic connectivity as a key feature of admissible structures.

Abstract

This paper is the third in the Gravitype series. It derives strong constraints on admissible large-scale geometric organization in discrete SU(2)-valued substrates from locality, bounded valence, finite propagation, and conditional confinement stability. Broad classes of candidate geometries are excluded. The surviving admissible equivalence class is characterized by three-dimensional organization with triadic connectivity. The analysis is structural and pre-physical; no continuum limit, metric structure, or physical interpretation is assumed.

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