A useful way to think about Feynman path integrals:
Do not start with “sum over all possible paths.”
Start with finite histories.
Take a finite time grid.
Take a finite set of allowed states.
Enumerate the possible histories.
Assign each history an action.
Turn the action into a phase.
Sum the phases.
Check the result.
Only after that should anyone talk about a continuum limit.
That is the reliability lesson I keep coming back to with AI, physics, and model authority:
finite shadows first
compatibility second
continuum authority last
A beautiful continuum object is not automatically trustworthy. It needs finite receipts.