Does "from the Planck Length and Planck Time to the Observable Universe and Age of the Universe" satisfy a proper definition of boundaries?
Does it satisfy “…from the smallest to the largest units of space and time”?
If I could, I would ask Minhyong Kim. Now at the University of Warwick, at the time he was at Oxford, Merton College, and a full professor of number theory at the Mathematical Institute within the Radcliffe Observatory Quarter.
Kevin Hartnett, Senior Writer for Quanta Magazine, has a very fine introductory article, “Secret Link Uncovered Between Pure Math and Physics” about Prof. Dr. Kim’s work. Of course, if Prof. Dr. Kim is just too busy, the young mathematics professor, Jordan Ellenburg, of the University of Wisconsin (mentioned in the article) might have a quick and complete answer!
Natural boundary conditions. See DeepAI, In the calculus of variations, the term natural boundary conditions refers specifically to boundary conditions appearing in the Euler-Lagrange equation* (see Gelfand and Fomin, 1963, p. 26 or Giaquinta and Hildebrandt, 1996, p. 34).* Of an energy minimization problem that was not imposed beforehand.