Not everything exists at every scale. Not in the trivial sense that atoms don't look like galaxies — in the precise sense that a phenomenon can be rigorously present at one measurement scale and rigorously absent at another. The question isn't how the thing changes with scale. It's whether it's there at all.
Tarjus, Ozawa, and Biroli (2026, arXiv:2602.19299) study plastic rearrangements in amorphous solids. Each localized yielding event produces a quadrupolar singularity in the displacement field — a directional distortion pattern that decays as 1/r². These quadrupoles are real: they're measured in simulations, they have characteristic orientations, they couple to stress fields. But in the thermodynamic limit, their density is exactly zero. Not approximately zero. Zero. The quadrupolar defects exist at the scale of the perturbation that created them, within a region set by the perturbation's spatial extent, and are absent at every larger scale. This isn't a matter of signal washing out. The mathematical object that describes the system at macroscopic scales has no room for these defects. They exist only where the perturbation is.
Eskin, Nguyen, and Vural (2026, arXiv:2602.18942) show that fluctuating species interactions produce a universal power-law abundance distribution. The equilibrium itself is a well-defined mathematical object — it can be computed, analyzed, perturbed. But the equilibrium can wander into regions where species abundances are negative, which is biologically meaningless. The equilibrium exists mathematically but not biologically. Whether it's real depends on which space you're measuring in — the linear algebra of the interaction matrix, or the positive orthant of abundances. At the scale of the equations, the equilibrium is always there. At the scale of the ecosystem, it appears and disappears depending on whether the noise has displaced it into feasibility.
Caupin et al. (2026, arXiv:2602.18785) observe phase flipping in confined fluids. In small enough volumes, a system oscillates between states — bubble present, bubble absent — because finite size means phase coexistence isn't a stable condition but a fluctuating one. At macroscopic scale, phase coexistence is a stable thermodynamic state. At the scale of a few hundred molecular diameters, it's an oscillation between two states that the system visits but cannot permanently occupy. The coexistence exists at one scale and not the other.
Voits and Schwarz (2026, arXiv:2602.18265) prove that first-passage time distributions in large Markovian networks converge to exactly two universal forms: exponential (the generic outcome) or delta-function (deterministic, requiring special structure). Intermediate distributions — gamma, Weibull, anything in between — exist only at finite network size. As the network grows, the distribution snaps to one extreme or the other. The intermediate forms aren't approximations of the limiting behavior. They are phenomena that exist at finite scale and do not exist at infinite scale.
Chen et al. (2026, arXiv:2602.18855) demonstrate that stacking identical trivial photonic layers produces topological bound states — but only when the number of layers is odd. Even layers: trivial. Odd layers: topological. The topological states exist or don't depending on a single integer, with no continuous parameter connecting the two cases. This isn't a threshold (above which the effect appears). It's a parity condition: the phenomenon blinks in and out of existence as you add one layer at a time.
The pattern across these five results: existence is conditional on scale, and the condition isn't always a threshold. Tarjus's quadrupoles vanish above a spatial scale. Eskin's equilibrium vanishes outside a positivity domain. Caupin's coexistence vanishes below a volume. Voits's intermediate distributions vanish above a network size. Chen's topology vanishes at even counts. What distinguishes this from ordinary scale dependence is the binary character. The phenomenon is either there or not — present or zero, feasible or infeasible, topological or trivial. There's no regime where the quadrupolar defect density is "a little bit above zero." There's no regime where the ecosystem equilibrium is "slightly infeasible." The transition between existence and absence is sharp. This has practical consequences. If you're measuring at the wrong scale, you don't see a weaker version of the phenomenon. You see nothing. And if you're theorizing at the wrong scale, you don't get a blurred description. You get a description that's exactly correct about a phenomenon that doesn't exist where you're trying to apply it. The equilibrium analysis of the ecosystem is mathematically perfect. It just happens to describe a point in a space the biology can't reach.