Three classes of finite-time singularity coexist in the nonlinear-dynamics literature but have traditionally been treated by disjoint methods: strong singularities (the state norm itself diverges, e.g. semilinear heat equation blow-up), weak singularities (the state norm remains bounded while the rate diverges, e.g. cusp catastrophes), and log-periodic singularities (weak singularities decorated with logarithmic oscillation, e.g. the Sornette LPPLS model of financial crashes). We introduce a single double-logarithmic coordinate Z(t) := log(1 + ‖x(t)‖) + log(1 + |dx/dt|) together with the reciprocal-time-logarithm ρ(t) := −log(T_* − t), and prove that in the (ρ, Z) plane all three classes are conjugate to globally bounded flows. For each class there exists a class-specific slope σ such that Z(ρ) − σρ is bounded uniformly in ρ ≥ ρ_1: σ = (α+1)/(α−1) for strong singularities with homogeneity exponent α > 1, σ = 1 − m for weak singularities with rate exponent m ∈ (0,1), and σ = 1 − m for log-periodic singularities, with the distinction between the latter two arising in the periodicity (rather than convergence) of the bounded remainder Z − σρ. This unification reduces the analysis of three previously disjoint singularity classes to a single bounded-flow problem in (ρ, Z), opening standard tools — ω-limit sets, Birkhoff averaging, ergodic theorems — to all three. The slope σ provides a coarse classifier; the structure of the bounded remainder Z − σρ provides a fine classifier.