decayChannel_count
plain-language theorem explainer
The theorem fixes the number of vacuum decay channels at five by enumerating false-vacuum tunneling, Coleman-de Luccia, sphaleron, instanton and thermal quench. Modelers of vacuum stability in the Recognition framework cite the count when assembling decay spectra or action ratios. The proof is a direct decidable computation over the finite inductive type.
Claim. The finite type of vacuum decay channels has cardinality five: $Fintype.card(DecayChannel)=5$.
background
The module introduces five canonical vacuum decay channels under configDim D=5: false-vacuum tunneling, Coleman-de Luccia bubble, sphaleron, instanton and thermal quench. These label the constructors of the inductive type DecayChannel, which derives Fintype, DecidableEq and Repr. An upstream result in DecaySpectrumFromPhiLadder establishes the identical cardinality statement for its own particle-decay enumeration.
proof idea
The proof is a one-line wrapper that invokes the decide tactic on the Fintype instance generated by the five-constructor inductive definition.
why it matters
The result supplies the five_channels field inside both vacuumDecayCert and decaySpectrumCert. It completes the channel-enumeration step required for J-cost tunneling certification on the phi-ladder. The count aligns with the module's explicit statement that configDim D equals five.
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