Arithmetic unification of masses and energies in physics, chemistry, biology and artificial intelligence via the exceptional lattice ₇₂

Experimental data for atomic masses (AME2020), ionization energies (NIST), covalent bond energies, semiconductor band gaps, DNA base pairs, protein interactions, fundamental biochemical reactions, as well as the training of a ternary neural network, admit a compact arithmetic representation of the form: E = 4^m ₊=₀^14 ₖ ₖ where is a scale constant (7. 726 MeV for masses, 5. 950 eV for chemistry and biology), m an integer, ₖ \-1, 0, 1\, and ₖ are 15 universal constants of empirical origin. For 5811 ionization energies, the mean relative error is 0. 00065% and 78. 5% of the points are predicted with an error better than 0. 001%. The mean relative error for 295 nuclear masses is 0. 0287%. The ₖ numerically coincide with 15 of the 48 non‑degenerate roots of the exceptional lattice ₇₂, suggesting a deep geometric link that remains to be elucidated.