proofofconcept
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derivation: Noether's Theorem
See https://www.youtube.com/watch?v=04ERSb06dOg and https://en.wikipedia.org/wiki/Noether%27s_theorem
principle of least action is axiomatic for symmetry.
Every continuous symmetry has a conserved quantity.
See https://en.wikipedia.org/wiki/Noether%27s_theorem#Derivations