What question did this study set out to answer?

The aim is to derive the Bekenstein-Hawking entropy formula from first principles without complex background theories.

March 28, 2026Open Access

Universal Processing Law (UPL) Track 4: Derivation of the Bekenstein-Hawking Entropy from Discrete Pixel Geometry

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This derivation shows exact Bekenstein-Hawking entropy from discrete computational geometry, suggesting new insights in physics.

The aim is to derive the Bekenstein-Hawking entropy formula from first principles without complex background theories.
Developed the theorem based on Planck-scale discrete computational geometry
Introduced the Cascade Freeze Mechanism at the event horizon
Applied Cauchy's surface projection theorem for area calculation
Performed computational verification using discrete voxel spheres from radii 3 to 50 Planck lengths
Confirmed the exact formula for Bekenstein-Hawking entropy as $S = A/(4l_P^2)$
Verified convergence to the $1/4$ factor in the macroscopic limit
Predicted finite-size lattice corrections for microscopic black holes
Achieved 97.3% accuracy in deriving the cosmological constant

Ahmed Lahmidi (2026) studied this question.

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