What question did this study set out to answer?

This research aims to derive testable physical predictions based on the Minimal Discrete Épure hypothesis.

June 10, 2026Open Access

Physical Implications of the Minimal Discrete Épure

Key Points

This research aims to derive testable physical predictions based on the Minimal Discrete Épure hypothesis.
Three physical predictions derived as falsifiable and parameter-free from hypothesis (H).
Predictions tested through future observations, including CTA and gravitational-wave echoes.
Numerical verification of results was performed.
Photons predicted to exhibit a Lorentz-invariance-violation coefficient of ξ₂=−0.028549, testable by CTA around 2030.
Minimum black-hole entropy suggested to be incommensurable with established quantum gravity spectra.
A Barbero–Immirzi parameter of approximately 0.1804 predicted, distinguishing from other loop-quantum-gravity variants.

Abstract

We derive three falsifiable, parameter-free physical predictions from the hypothesis (H) that Planck-scale spacetime carries the geometry of the Minimal Discrete Épure G■. (P1) A photon Lorentz-invariance-violation coefficient ξ₂=−0.028549 (subluminal), testable by CTA around 2030. (P2) A black-hole minimum entropy incommensurable with the loop-quantum-gravity spectrum, implying a quantum-error-correction threshold testable via gravitational-wave echoes. (P3) A Barbero–Immirzi parameter ≈0.1804, distinguishing the épure from all LQG variants. All predictions are explicitly conditional on hypothesis (H). An additional structural result describes the co-emergence of space and time from the unfolding. Results verified numerically.

Physical Implications of the Minimal Discrete Épure

Key Points

Abstract

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