The ln2 Informational Geometry - A Prime and Twin Prime Framework for Physical, Chemical and Biological Structure

This work presents the complete formulation of the ln 2 Informational Geometry: a unified prime–gap and twin–prime framework that describes physical, chemical, and biological structure using a single discrete information‑geometric ladder. The theory shows that particles, atoms, molecules, black holes, chemical reactions, and biological systems all evolve through fixed powers of ln 2, with compression, expansion, curvature, rotation, entropy, and information scaling in predictable discrete steps. Weak‑force transitions, chemical reaction steps, RNA rewrites, and black‑hole jet emission are all shown to correspond to the same fundamental rewrite unit ΔW = ln 2, mapped to the twin‑prime gap. At the physical scale, the framework reproduces particle identity, weak transitions, atomic shells, molecular bonding, and black‑hole evolution using a single scaling relation. At the chemical scale, reaction pathways are governed by prime‑gap compression changes and twin‑prime rewrite steps, providing a discrete legality test for chemical transformations and catalytic mechanisms. At the biological scale, the same information geometry explains digestion, respiration, detoxification, bacterial and archaeal cell walls, viral capsid architecture, RNA folding, and organ‑level function. Photosynthesis is identified as the biological analogue of black‑hole revival: a DF‑creation engine that injects ln 2 rewrite freedom into carbon and emits oxygen as structured rewrite exhaust. The result is a unified, testable, and falsifiable model in which nature is fundamentally discrete and structured by prime‑gap compression and twin‑prime rewrite dynamics. The ln 2 Informational Geometry provides a coherent architecture linking physics, chemistry, and biology under a single information‑theoretic framework.