Hilbert Space: Where Quantum States Actually Live

Product formulas, Hankel-Parseval and Schwinger parameters solve the lower powers. Here is how far each one gets on the fifth.

The rule that only large collections have entropy conflicts with a simple two-box thought experiment. The conflict disappears once you separate the two concepts that share the name.

A second route to (17 − 6G)/240 that avoids elliptic integrals entirely, with each step checked and one error in the printed write-up corrected.