matterWaveCert
plain-language theorem explainer
matterWaveCert supplies the concrete element of the MatterWaveCert structure that records exactly five recognized matter-wave phenomena together with the geometric decay of their de Broglie wavelengths by the factor phi inverse. A physicist working on quantum foundations or interferometry would cite the definition to embed the de Broglie relation inside the RS phi-ladder. The construction is a direct structure instantiation that delegates the cardinality field to the matterWaveCount theorem and the decay field to the deBroglieDecay theorem.
Claim. Let MatterWaveCert be the structure whose fields assert that the set of canonical matter-wave phenomena has cardinality 5 and that consecutive de Broglie wavelengths satisfy the ratio equality $deBroglieWavelength(k+1)/deBroglieWavelength(k)=phi^{-1}$ for every natural number $k$. Then matterWaveCert is the element of this structure whose cardinality field is the theorem establishing the count of five phenomena and whose decay-ratio field is the theorem establishing the geometric decay by $phi^{-1}$.
background
The module derives the de Broglie matter wave from Recognition Science by setting the wavelength to $phi^{-5} times 2 pi / p$ using the RS-native value of hbar. The MatterWaveCert structure therefore requires two facts: the type of canonical phenomena (electron diffraction, neutron diffraction, atom interferometry, BEC matter waves, molecule diffraction) has cardinality exactly 5, matching configDim D = 5, and the wavelength decreases geometrically by the factor $phi^{-1}$ at each successive rung of the phi-ladder.
proof idea
The definition is a one-line wrapper that constructs an instance of the MatterWaveCert structure. It supplies the five-phenomena field by direct reference to the matterWaveCount theorem and the phi-decay field by direct reference to the deBroglieDecay theorem.
why it matters
The definition certifies the matter-wave sector of the Recognition Science framework by confirming the five-phenomena count and the phi-decay law for de Broglie wavelengths. It anchors the A1 QM foundation inside the phi-ladder, consistent with the eight-tick octave and the derivation of D = 3 spatial dimensions. The module reports zero sorry and zero axiom, so the certification is closed at the level of the supplied theorems.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.