Recognition Science: Unifies DNA Geometry, Elasticity, and Transcription Kinetics via a Single Energy Quantum

We show that minimal overhead and pair-isomorphism—two axioms at the heart of Recognition Physics—uniquely fix a logarithmic scale cascade rn = LP φ^n where φ = (1 + sqrt(5))/2. Quantising phase on this cascade yields a self-adjoint operator whose pure ladder spectrum En = nEcoh reveals a universal energy quantum Ecoh = 0.090 eV. From this single constant we derive (i) the canonical 13.6 A minor groove and 34.6 A helical pitch of B-DNA; (ii) bending and torsional persistence lengths (56 nm, 70 nm) that match experimental values without fitted parameters; (iii) a ceiling transcription velocity of ~50 bp s^(-1) and correct stall forces for E. coli RNA-polymerase, bacteriophage T7 RNAP, and yeast Pol II by assigning integer-multiple gating barriers; and (iv) the ubiquitous 1 s elemental and 10 s back-track pauses as direct escape times over 2 and 2.5 quanta, respectively. Sequence-specific modulation enters only through the Boltzmann weight of nascent RNA hairpin free energies, predicting the long his-leader pause and NusA-mediated shifts without altering the universal constants. The framework collapses a traditionally empirical field to a deterministic, parameter-free model and provides an executable pipeline for genome-wide pause mapping and rational transcription engineering.