classicalMechanicsDepthCert
plain-language theorem explainer
The classicalMechanicsDepthCert definition assembles a certificate verifying that classical mechanics possesses five formulations and three conservation laws, both matching the spatial dimension D from Recognition Science. A physicist deriving mechanics from the J-cost functional would cite this to confirm the depth aligns with the framework's predictions for equilibrium and dimension. The definition is assembled by direct field assignment from prior counting, equality, and vanishing results.
Claim. Classical mechanics is certified by the structure with five formulations satisfying $|$MechanicsFormulation$| = 5$, three conservation laws satisfying conservationLaws $= 3$, and equilibrium satisfying $J(1) = 0$.
background
In the Recognition Science framework, classical mechanics is recovered from the J-cost functional, where the Hamiltonian is the J-cost energy function and the phase-space minimum occurs at J = 0. The module states that five canonical formulations (Newtonian, Lagrangian, Hamiltonian, Poisson bracket, Hamilton-Jacobi) equal configDim D = 5, while three conservation laws (energy, momentum, angular momentum) equal D = 3. The ClassicalMechanicsDepthCert structure encodes exactly these three requirements: Fintype.card MechanicsFormulation = 5, conservationLaws = 3, and Jcost 1 = 0.
proof idea
The definition is a direct construction that populates the three fields of ClassicalMechanicsDepthCert by substitution: mechanicsFormulationCount supplies the formulation cardinality, conservationLaws_eq_D supplies the law count by reflexivity, and mechanics_equilibrium supplies the J-cost vanishing via Jcost_unit0.
why it matters
This definition completes the B11 Physics certification in the Recognition Science mirror, linking the formulation count and conservation laws to D = 3 from the forcing chain T8 and the equilibrium condition to J-uniqueness in T5. It supports consistency with the Recognition Composition Law and the phi-ladder without introducing new axioms. No downstream uses are recorded in the current graph.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.