DecaySpectrumCert
DecaySpectrumCert packages the three properties that certify a decay spectrum on the phi-ladder: exactly five channels, consecutive lifetimes in geometric ratio phi, and strictly positive values. A physicist constructing exotic-decay models inside Recognition Science would cite the certificate to assert that the spectrum matches the required ladder structure. The declaration is a bare structure definition that introduces the bundled fields with no computational content or lemmas.
claimA structure certifying that the set of decay channels has cardinality 5, that lifetimes satisfy $lifetime(k+1)/lifetime(k)=phi$ for every natural number $k$, and that $lifetime(k)>0$ for every $k$, where the five channels are alpha, beta-minus, beta-plus, electron-capture and spontaneous-fission and $lifetime(k)=phi^k$.
background
The module defines five canonical exotic decay channels (alpha, beta-minus, beta-plus, electron-capture, spontaneous-fission) that realize configDim D=5. The lifetime function is supplied by the sibling definition lifetime(k) := phi^k. The upstream phi_ratio definition from Quasicrystal supplies the inverse 1/phi, while the present phi_ratio field asserts the forward ratio phi itself. The local setting is that each lifetime occupies one rung of the phi-ladder, furnishing a discrete spectrum for decays.
proof idea
The declaration is a structure definition with an empty proof body. It simply declares the three field types; no lemmas are applied and no tactics are invoked.
why it matters in Recognition Science
The structure is instantiated downstream by decaySpectrumCert, which supplies the concrete witnesses decayChannel_count, lifetime_ratio and lifetime_pos. It thereby certifies the phi-ladder decay spectrum required by the Recognition Science physics module and links the five channels to the self-similar fixed point phi (T6). The certificate closes one link in the chain from the J-cost functional equation to observable decay lifetimes.
scope and limits
- Does not derive phi from the J-cost equation or Recognition Composition Law.
- Does not prove that the five listed channels are the only possible decay modes.
- Does not compute numerical lifetime values or match them to experiment.
- Does not relate the present channels to the vacuum-decay channels defined in a separate module.
formal statement (Lean)
38structure DecaySpectrumCert where
39 five_channels : Fintype.card DecayChannel = 5
40 phi_ratio : ∀ k, lifetime (k + 1) / lifetime k = phi
41 lifetime_always_pos : ∀ k, 0 < lifetime k
42