Descriptive differential dynamics: infinite completions and matching scaffolds

Series and infinite series, completions, quantities in derivations, symbols and notation, terms that are variables in continuum limits, Fejer and Dirichlet kernels, infinite series and their arithmetic, telescoping and scaffolding, scaffolding and derivations, discardable and non-discardable scaffolding, derivative-stopping and smooth operator calculus across zero in ranks, integrating Fourier series and the inverse or hyperbola in derivational quantities, uniqueness or multiplicities of functions under antiderivation and integrals, Dirichlet function and checkerboard function, models of integrating the Dirichlet function and signal-continuity, limit points or critical points.