A Universal Tension Ladder Structured by the Fine-Structure Constant: Complementary Framework to Ultra-High-Energy Neutrino Event

We introduce a “tension” representation of physical scales, defined by F(λ) = ħc/λ² and normalized to the electron tension F_e = m_e² c³ / ħ. Using CODATA 2018 constants and published experimental data, we compute the rung index n = log_137(F/F_e) for 20 observables spanning particle physics, cosmology, molecular chemistry, and biology. Six independent observables — the dark energy scale, a collective THz mode of liquid water, a pathological tissue tension window, the hydrogen bond energy in water, the electron, the Υ(1S) meson, and the Higgs boson — fall on (or extremely close to) integer rungs n = -8, -7, -6, 0, +4, +5 with deviations |δ| < 0.05 in n. A simple binomial test yields a chance probability of p ≈ 3×10⁻⁴ for this degree of alignment in a 20-point sample, suggesting a nontrivial discrete structure in base 137. The most novel result is that the hydrogen bond energy in liquid water is quantitatively given by E_H = m_e c² α³ = 0.1986 eV, matching experimental estimates ≈ 0.2 eV at the 0.7% level and providing a closed-form expression in terms of fundamental constants. On the cosmological side, the characteristic wavelength derived from the Planck 2018 dark energy density (λ_DE ≈ 0.135 mm) shares the same rung n ≈ -8 as the 2.16 THz collective mode of liquid water, suggesting a possible spectroscopic “mirror” of the dark energy scale in condensed matter. On the high-energy side, the electron (by construction), the Υ(1S) meson, and the Higgs boson populate rungs n = 0, +4, and +5, respectively. Several important particles (e.g. proton, tau, W boson) do not lie on integer rungs, which constrains the scope of the ladder. We discuss limitations, propose falsifiable experimental tests (including precision measurements of the hydrogen bond energy and THz anomalies near λ_DE), and outline how this tension ladder framework could complement recent ultra-high-energy neutrino observations attributed to evaporating primordial black holes, which probe higher rungs (n ≳ 10) beyond the range studied here.