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June 23, 20260 citationsOpen Access

Physical Implications of the Minimal Discrete Épure

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FGFlorian Gisbert

Key Points

  • This research explores physical predictions derived from the hypothesis of Minimal Discrete Épure geometry at Planck scale.
  • Derived three falsifiable predictions from hypothesis (H).
  • Analyses include parameter-free predictions related to Lorentz invariance and black hole entropy.
  • Verifications through numerical methods to explore co-emergence of space and time.
  • Photon Lorentz-invariance-violation coefficient ξ₂=−0.028549 is testable by CTA around 2030.
  • Minimum black-hole entropy deviates from the loop-quantum-gravity spectrum, enabling tests via gravitational-wave echoes.
  • Barbero–Immirzi parameter approximated to 0.1804, distinguishing the épure from other LQG 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.

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Cite This Study

Florian Gisbert (2026) studied this question.

synapsesocial.com/papers/6a3a225d111626ef22ab6f83https://doi.org/10.5281/zenodo.20783730
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