What question did this study set out to answer?

This work aims to establish a correspondence between the bond percolation threshold and the S8 suppression parameter in cosmology.

June 3, 2026Open Access

A Percolation Correspondence for the S8 Suppression Parameter A companion note to the Stochastic Rupture framework

Key Points

This work aims to establish a correspondence between the bond percolation threshold and the S8 suppression parameter in cosmology.
Numerical analysis of a cubic lattice model at the Planck scale.
Comparison of bond percolation threshold with observational data from DES Year 3 and KiDS-1000.
Demonstration of redshift scaling as an attractor solution in the Λ-dominated dissipation regime.
The bond percolation threshold is found to be pc = 0.2488, closely matching the cosmological parameter e0 = 0.249±0.035.
The agreement is within 0.1%, well within the 1σ observational range.
The (1+z)−2 redshift scaling is confirmed as the solution in the relevant field equation.

Abstract

The Stochastic Rupture (SR) framework models spacetime as a simple cubic lattice of square holographic sheets stacked at the Planck scale. We report a numerical correspondence between the bond percolation threshold of this lattice, pc = 0.2488, and the cosmological structure-suppression parameter e0 = 0.249±0.035 tted to DES Year 3 and KiDS-1000 data.The agreement is 0.1% well within the 1σ observational range. We additionally show that the (1+z)−2 redshift scaling follows as the attractor solution of the SR eld equation in the Λ-dominated dissipation regime, replacing the assumption in the original S8 fit.

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