AbstractEvery steady state held away from equilibrium by a throughput of energy carries, we argue, acommon structure which we name character xed by a single dimensionless ratio: the loga nity a = ln(G0/L), gain over loss. This one quantity is simultaneously the de Donder a nity(entropy production per step), the laser pump parameter above threshold, the log branching ratioof Malthusian growth, and a log-likelihood ratio. The framework's claim is not a new mechanismbut a reading: it maps these independently measured quantities onto one axis a, and the resultingover-determination is what makes the alignment a test rather than a de nition. Read closely,a non-equilibrium steady state carries two independent kinds of information a soft, erasablepopulation bit and a hard, topologically protected circulation bit (a probability current lockedon a frustrated cycle, changeable only by rewiring). All characters together form a morphospaceC whose tangent space is the deformation algebra gl(n,R) that linearizes the dynamics; thetwo bits cut this space into a metric sector, in which neighbouring characters average, and atopological sector, in which they fuse. Coupling two systems is a closure ⊗ : C × C → C thatcan mint a protected circulation neither carried alone, sustained only while the drive runs. Theframework is checked on analytically tractable substrates a rockpaper scissors replicator,a homochiral reaction triad, a distance-3 surface code and against a small family of real,measured instances: a fuel-driven DNA reaction network, two Brownian gyrators (electronicand colloidal), and a cell-free genetic ring oscillator. Each prediction is stated as a falsi ablemeasurement on a named substrate. The sharpest open test forces a single memory exponentβ to govern uctuationdissipation aging, queue-tail scaling, and the memory kernel at once;that data collapse against laboratory data has not yet been run. We present the framework,its derivations, its imported provenance, and its falsi ers, with full auditability deferred to fourcompanion documents.
Ronald Paul Viers (Sat,) studied this question.