conservationLaws
plain-language theorem explainer
Recognition Science equates the count of conservation laws in classical mechanics to the spatial dimension D. A researcher deriving mechanics from the unified forcing chain would cite this when identifying energy, momentum, and angular momentum with D = 3. The declaration is a direct numeric assignment requiring no lemmas or reductions.
Claim. The number of conservation laws in classical mechanics is $3$, equal to the spatial dimension $D$.
background
The module presents classical mechanics through five formulations (Newtonian, Lagrangian, Hamiltonian, Poisson bracket, Hamilton-Jacobi) whose count equals the configuration dimension D. The Hamiltonian is identified with the J-cost energy function, which attains its minimum value of zero at equilibrium. Three conservation laws (energy, momentum, angular momentum) are set equal to D = 3 in RS-native units where c = 1.
proof idea
The declaration is a direct definition that assigns the natural number 3 to conservationLaws, serving as a one-line wrapper with no tactic steps or upstream lemmas applied.
why it matters
This definition supplies the three_laws field inside the ClassicalMechanicsDepthCert structure, which certifies the RS derivation of classical mechanics depth. It realizes the T8 step that fixes D = 3 spatial dimensions from the forcing chain. The companion theorem conservationLaws_eq_D confirms the assignment by reflexivity, closing the link between mechanics and the Recognition Composition Law.
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