deBroglieWavelength
plain-language theorem explainer
The deBroglieWavelength definition assigns to each natural-number rung k the real value phi to the power of minus k. Physicists deriving matter-wave scaling in Recognition Science cite it when establishing the uniform phi-decay ratio across the five canonical phenomena. It is supplied directly as a noncomputable definition with no lemmas or reductions required.
Claim. The de Broglie wavelength scaling factor at rung $k$ is defined by $λ(k) := φ^{-k}$.
background
In the De Broglie Matter Wave from RS module the wavelength relation is $λ = ℏ × 2π / p$ with the RS-native $ℏ = φ^{-5}$. This definition isolates the rung-dependent factor $φ^{-k}$ from the phi-ladder, so that the full wavelength at rung k reads $λ_0 × φ^{-k}$. The module states that the five canonical phenomena (electron diffraction, neutron diffraction, atom interferometry, BEC matter wave, molecule diffraction) have cardinality 5.
proof idea
Direct definition as the reciprocal of phi raised to the power k; no tactics or lemmas are applied.
why it matters
This supplies the wavelength scaling used by deBroglieDecay, which proves the consecutive-rung ratio equals phi inverse, and by the MatterWaveCert structure that records both the five-phenomena count and the phi-decay property. It fills the rung-dependent part of the de Broglie relation inside the Recognition Science A1 QM foundation, consistent with the phi-ladder and T5 J-uniqueness. It leaves open the matching of numerical prefactors to specific experimental data.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.