One Inequality, Five Hazards: A Unified Dimensionless Screening Number and a Reporting Checklist for Reactive-Hazard Assessment

Abstract Process-safety practice screens reactive hazards with separate dimensionless criteria─the Damköhler number, the Frank-Kamenetskii and Semenov self-heating criteria, Stoessel criticality from the adiabatic temperature rise, and the atmospheric exclusion distance. Applied in isolation they hide a shared algebra and leave practitioners without a common disclosure standard. This Commentary makes one modest claim and one practical one. The modest one: these five criteria share the algebraic form N = load/threshold, hazardous at N ≥ 1, each recovered by naming its load and threshold. We do not claim a physical unification. Normalization keeps the ratio and discards the hazard dimension it came from, so equal N need not mean equal hazard; and the thresholds differ in kind─a bifurcation the equations single out (Frank-Kamenetskii, Semenov), an agreed convention (the 200 K severity cut), or an externally fixed exposure limit. The thermal Biot number shares the algebra but selects a modeling regime rather than measuring a hazard, and is excluded. The practical claim is a one-page reporting checklist fixing what any screening statement must disclose, worked through a hazardous and a safe example. Applied to twelve published reactive materials, the number and the categorical NFPA-704 instability rating disagree for 31% of strictly comparable pairs─a descriptive statistic on a small, nonindependent set (n = 12)─because a categorical rating encodes ease of initiation while N orders thermal severity. An uncertainty analysis shows classification is far more sensitive to the choice of threshold than to calorimetric error, which is why the checklist requires the threshold’s provenance.