Generation of Fermionic Structure Is Induced, Autocatalytic, and Pair-Correlated: Assumptions and Consequences of a Universal Inelastic Map Acting on Waveforms Alone

For a two-wave relational wave system, we design a single inelastic interaction operation that takes only the waveforms as input and contains no discriminating branches (no IF statements). Within the assumed class (two-wave, pointwise, cubic, common-phase invariant, no self-scattering, strength reusing the existing readout R = sin^2(theta)), conservation of the zero-square-sum closure (axiom) uniquely fixes the relative coefficient. The uniquified vertex rewrites exactly as an exchange flow driven solely by the imaginary part of the relative phase, is a pointwise two-channel rotation, and is exactly solvable in closed form (closure and power are conserved identically pointwise; measured drift 4e-14 over 3000 collisions). Measured consequences: (1) a parity theorem (generation is necessarily induced; a Z2 class conserved by the exponent arithmetic), (2) autocatalytic ignition rate = C f^2 with C = 11.45 constant to 0.4% over four decades of seed fraction, (3) no runaway: oscillatory relaxation to a statistical equilibrium f* = 0.4690, close to the mask phase-space fraction 0.494, (4) although no antiparticle degrees of freedom are input, products appear only in sum-rule partner bins (485 unpredicted bins at machine zero, ratio 1e-27), as correlated pairs settling the winding-number ledger (coherence 0.83), rising simultaneously from exact zero. This paper does not claim the interaction is the one realized in nature; assumptions, conditional derivations, and measurements are strictly separated, and the value of the assumption is measured by consistency and productivity. Japanese and English full texts included.