√2 × ln(2): GEOMETRIC CONSTANTS FROM H4 Mathematical Framework and Discovery Context Version 2.0

This project presents a mathematical framework connecting H4 geometry (the 120-cell polytope) to information-theoretic constants. The ceiling constant K_AUD = √2 × ln(2) ≈ 0.980 combines geometric embedding (√2) with binary distinction cost (ln 2). The factor √2 has multiple independent origins (H4 circumradius, L2 norm, tesseract geometry, algebraic structure) — H4 is one candidate among several. The floor constant 1/φ ≈ 0.618 emerges from golden ratio self-similarity in H4 vertex coordinates. The gap G = 1 − K_AUD ≈ 0.0197 is constitutive, not error. The framework includes identities (Corridor = 1/φ² − G, Golden Partition: 1/φ + 1/φ² = 1), a Binary Tower showing G scales through powers of 2 to track golden…