The Informational Limits of the Universe From Planck to 𝝿 to 𝝋 to DNA

We explore the relationship between Biological Information and Universal Information Generative capacity. We dive into the underlying ties between Proton tunneling in DNA ,Error Catastrophe and Eigen, Planck, Golden ratio, Pi and certain Minimal Genome thresholds. The equations and derivations are an extension of the Universal Information limit of ~184 base pairs derived in DNA as Nanotechnology: Reassessing life’s origins by Gondal, pertaining to Origin of Life. We will focus on Mathematical architecture solely, making predictions and examining against measured empirical data. We extend this architecture by showing that the same limit recurs across independent physical domains: as the exponent of the Planck pixel count of the observable universe, in the nucleon and deuteron mass ratios relative to the electron, and in the geometric scaling of the minimal genome by π and φ. We further show that the minimal genome length, the proton tunneling maintenance ceiling, and the value of π itself are mutually recoverable through simple reciprocal and base-shift operations anchored to measured biological fidelity.