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  17theorem applied to time-translation symmetry.
  18
  19## What it bundles
  20
  21- (1) Energy conservation: `H(γ(t₁), p(t₁)) = H(γ(t₂), p(t₂))` for any
  22  Newtonian trajectory under the standard regularity hypotheses
  23  (`hV_diff`, `hγ_diff`, `hγ_diff2`, `h_dE_factored`).
  24- (2) Hamilton's equations from the EL: the pair `(γ̇ = p/m, ṗ = -V'(γ))`
  25  is forced by the EL of the standard Lagrangian.
  26
  27## Falsifier
  28
  29A closed-system mechanical trajectory with potential `V` differentiable
  30on the trajectory image, regular accelerations, and EL satisfied, yet
  31total energy `H(γ, p)` measurably non-constant in time. This would
  32falsify clause (1) and therefore Noether's theorem on time-translation
  33symmetry of the J-action.
  34
  35Paper companion: `papers/RS_Least_Action.tex` (Paper A), §"Hamiltonian
  36Formulation as a Corollary".
  37-/
  38
  39namespace IndisputableMonolith
  40namespace Action
  41
  42open IndisputableMonolith.Action
  43
  44/-- Domain certificate for energy conservation along Newtonian
  45trajectories of the small-strain J-action. -/

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