Linking Kalimuthu’s Degenerated Spherical Triangles Validation Articles with Quantum Gravity: A Conceptual Bridge
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Abstract
This article revisits the author’s earlier validation studies on degenerated spherical triangles, where the sum of interior angles approaches π in the limiting procedure r → ∞ or area → 0. We situate this discrete anomaly within broader frameworks of spatio-temporal indexing and extreme-threshold behavior. By incorporating recent developments in discrete geometric indexing (STARE trixels, EGU21-1531) and modified theories of general relativity from a differential geometric perspective (arXiv:2507.04031), we provide a conceptual bridge to 3D quantum gravity models, particularly the Ponzano–Regge model. The proposed formulation is distinguished from standard continuous spherical geometry and from existing discrete Regge calculus approaches.
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SpatioTemporal Adaptive-Resolution Encoding (STARE): an indexing scheme. Meeting Organizer EGU21. EGU21-1531.
The study on modified theories of general relativity: a differential geometric approach. arXiv [gr-qc]. 2025. arXiv:2507.04031. Available from: https://arxiv.org/abs/2507.04031
Livine ER. A note on B-observables in Ponzano-Regge 3D quantum gravity. Class Quantum Grav. 2009 Jul 2.
Kalimuthu S. Earlier validation studies on degenerated spherical triangles. [Details not provided].