Energy
plain-language theorem explainer
Energy is supplied as the native type for energy values in the Recognition Science unit system, scaled to the coherence quantum φ^{-5} with c fixed at unity. Researchers deriving conservation laws or Hamiltonian dynamics from the action principle cite this definition to keep calculations inside the phi-ladder. The declaration is introduced as a direct abbreviation with no further structure or computation.
Claim. In the Recognition Science native units, an energy value is an element of the real numbers $ℝ$, with the fundamental scale set by the coherence quantum $φ^{-5}$.
background
The RS-native system takes the tick (discrete time quantum) and voxel (spatial step with c=1) as base units. Derived quantities include the coherence quantum coh = φ^{-5} for energy and the action quantum act = ħ = coh · tick. All physical quantities sit on the phi-ladder φ^n for integer n, fixing dimensionless ratios by the golden ratio alone.
proof idea
The declaration is a direct abbreviation that identifies the energy type with the real numbers.
why it matters
This definition is used in forty downstream declarations, including the proof that energy is conserved along Newtonian trajectories under time-translation symmetry and the derivation of Hamilton's equations from the Euler-Lagrange equation. It provides the type for total energy in the Hamiltonian formulation and for photon energies on the phi-ladder in applied calculations such as photobiomodulation. The setting realizes the framework landmark that c = 1 and ħ = φ^{-5} in native units, with no external anchoring required.
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