(GQR31/Math1) Geometry-Gated Catalysis Beyond Arrhenius–Marcus: Shielded Intermediates, Electronic Rationality, and Time-Structured Reactivity.

Enzymatic catalysis achieves selectivity, efficiency, and directional-ity under conditions where traditional energetic descriptions based onArrhenius activation or Marcus reorganisation struggle. We argue thatthis reflects a distinct physical regime in which catalysis is governedprimarily by geometry and time rather than equilibrium energetics.Building on a minimal demonstration of time-gated directed transportin a purely Hamiltonian quantum system, we introduce the Shield Lawand distinguish classical energetic intermediates from shielded geomet-ric intermediates that persist across femtosecond–terahertz vibrationalcycles. We show how donor–acceptor chemistry, orbital structure, andlong-range tunnelling emerge naturally from a principle of electronicrationality seeking geometric closure under dynamic constraint, and weexplain why enzyme mimics fail despite reproducing static active-sitefeatures. Full 70 article programme https://github.com/jamessutton600613-png/GQR/blob/main/Programme_Index.md The programme contains both standalone and self referencing articles. These can all be read as notes in proof of GQR1.