Why Enthalpy Is U + PV, Not U + ∫PdV

A uniform, unchanging density can still carry transport. The current comes from the phase gradient, and a plane wave stands for a long packet, a scattering state or a particle beam, never a single normalized particle.

We check a Master Theorem construction for f^s(x) against affine maps by hand, then see where convergence and uniqueness give out.

Replacing dx with √dx in a Riemann sum multiplies the ordinary integral by √n. A finite answer therefore needs a zero integral and a precisely tuned singularity.