Dimensionless Solvent-Energy Constraints on DNA-Based Habitability in Water, Heavy Water, Liquid Ammonia, and Water–Ammonia Mixtures

The Life-Ratios Hypothesis (LRH) is proposed as a quantitative framework for DNA-based habitability in polar-hydride solvents. The central idea is that DNA’s biological function is temperature-range constrained not by absolute molecular energies but by dimensionless ratios of those energies to the thermal scale kBT. LRH is a calibrate-then-predict approach with no free adjustable parameters. The framework is calibrated on terrestrial liquid H2O via the hydrogen-bond dissociation ratio over the observed temperature limits of terrestrial life. The calibrated ratio values are Rdiss(ℓ)≡DHB(ℓ)/kBT∈[6.0,10.4], and Rdiss(ℓ)(H2O)≈8.4 at Tbio=310K. The framework yields three falsifiable results. First, a bond-replacement self-cancellation theorem: when a Watson–Crick base pair opens in a polar-hydride solvent, the enthalpic hydrogen-bond residual cancels topologically whenever the solvent’s N or O atom matches a base nitrogen or oxygen atom. The theorem is near-exact in water, exact in ammonia (every Watson–Crick bond contains nitrogen), and preserved at every H2O–NH3 composition. Second, the cross-solvent invariance of Rdiss(ℓ) is postulated, and, when applied to D2O, the framework predicts a +7.25K shift in biological temperature, matching the observed +7.2K shift in the temperature of maximum density. Third, when applied to liquid NH3, the framework predicts a cold solvent-network window of 198–270K, optimum 226K, accessible at 0.07–3.73atm, where warm or hot ammonia-based DNA life is excluded as a negative prediction. Combined, these results give a continuous corridor of predicted optimum biological temperatures across H2O–NH3 mixtures, from 226K in pure ammonia to 310K in pure water, over wide pressure ranges in which the corresponding solvent mixtures remain liquid. This corridor defines where DNA-based or DNA-like life should be sought if such biochemistry is possible; it does not imply that such life exists.