(GQR12duplicato) — Curvature–Information Catalysis: From Quantum Biology to Material Design

Catalysis—whether biological, photochemical, thermal, or electrochemi-cal—arises from quantum–geometric exchange between coherent and dissipativemodes of motion. The Gated Quantum Resonator (GQR) framework treats thisexchange as a curvature–information law linking coupling strength (g), geometriccurvature (κ), and dephasing rate (γϕ) through the Shield relation g2 = κ γϕ. Thisunifies the kinetics of proton–coupled electron transfer, field-driven tunnelling, andvibrationally mediated reactions under a single geometric grammar.By recasting the classical reorganization energy λMarcus as the coher-ence–curvature term g2/κ, the GQR formalism establishes continuity between theMarcus–Hammes–Schiffer quantum rate lineage and the Einstein–Cartan–Penrosecurvature–information paradigm. This correspondence defines catalysis as a processof information geometry: energy transfer, coherence lifetime, and spatial confinementare interlinked through curvature.Applied here to representative biological and material systems, GQR XII extendsprevious work on quantum–biological electrocatalysis toward a universal descriptionof Curvature–Information Catalysis—a framework capable of guiding bothenzyme design and material synthesis by controlling coherence through geometry. 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.