Speaker
Description
The extreme disparity between the Planck-scale vacuum energy and the observed cosmological constant, alongside the \textit{ad hoc} TeV-scale cutoff required to stabilize the electroweak hierarchy, present profound interrelated crises in fundamental physics. We propose an effective field theory wherein continuous spacetime emerges from a discrete Poisson substrate governed by a non-linear exponential capacity measure. Applying It\^{o}'s stochastic calculus, we mathematically demonstrate a statistical bifurcation: the deterministic mean condenses to define the classical metric background, while the variance of the zero-mean Gaussian geometric noise escapes linear cancellation. This rectified variance generates a macroscopic drift that identically manifests as the dark energy density ($\rho_\Lambda = \sigma_{\text{bulk}}^2/2\kappa$). Diluting the trans-Planckian boundary variance by the covariant Bekenstein-Hawking entropy of the observable universe ($N \sim 10^{122}$), we rigorously map the bulk variance to a four-dimensional momentum phase-space integral. This yields an exact, parameter-free continuous field cutoff at $E_{\text{cutoff}} \approx 6 \text{ TeV}$. This establishes the electroweak scale as a robust macroscopic holographic projection of the Planck limit, providing a falsifiable prediction of a universal non-perturbative exponential softening in high-$p_T$ scattering cross-sections at contemporary colliders.