Unreasonable Effectiveness Solved

Wigner's 1960 observation that mathematics is ``unreasonably effective'' in describing nature rests on a tacit assumption: that mathematics is invented in pure abstraction and reality is a separate object onto which it is later mapped, with the success of the mapping requiring explanation. We propose that the puzzle dissolves when the assumption is dropped. In a substrate-physical framework in which a single ontological root --- the substrate exists --- is taken as the foundational hypothesis, every primitive of the mathematics that physics uses admits a substrate-physical reading: counting from event-counting, the natural numbers from extension-by-coupling-event, induction as a structural consequence of the substrate's iteration primitives, addition from linear superposition of substrate amplitudes in the free-propagation regime, multiplication capturing the substrate's nonlinear cross-term coupling in its scalar commutative special case, division as the formal inverse with binding-energy substrate tension as the unmodelled remainder, the integers from opposing-tally processes, the rationals from observed ratios of counted quantities, the reals as Cauchy-completion against measurement, sets from substrate-type formation, topologies from measurement-precision neighbourhoods, smooth manifolds from elastic local flatness, differential forms from oriented coupling events, Lie groups from continuous symmetries, Lie algebras from infinitesimal symmetry generators, root systems from quantised standing-wave charges, and Coxeter groups from the substrate's reflection structure on its mode lattice. Each construction is paired with an observable discharge whose existence in laboratory or astrophysical data licenses the construction. On this reading, mathematics is not a separate language that happens to fit physics; it is the formal description of the substrate's primitive content, and its effectiveness in physics is not a coincidence to be explained but a structural consequence of the identity between description and described. We present the bootstrap chain end-to-end, identify the empirical anchor that the framework's E₈ root system shares with the observed Zamolodchikov spectrum in CoNb₂O₆, and discuss the open work of fully discharging the chain.