√2 × ln(2): The Coherence Ceiling and the Geometric Singularity of Binary

This paper presents two fundamental constants connected to H4 geometry and information theory: the Floor (1/φ ≈ 0.618) and the Ceiling K_AUD (√2 × ln(2) ≈ 0.980), demonstrating that binary (n=2) is the unique base producing a sub-unity ceiling. The Floor is geometric; the Ceiling combines geometric embedding (√2) with information-theoretic selection (ln 2) — this is a selection argument, not a derivation. The ~2% gap between the Ceiling and unity is necessary breathing room: the space that prevents collapse into frozen unity and enables sustainable dynamics. Update — 5 May 2026: Light fresh-up bringing the document into convention parity with the framework's other publications. Three changes, all definitional…