decoherenceCert
DecoherenceCert assembles the claim of exactly five decoherence mechanisms with the phi-inverse decay law for coherence ratios between consecutive rungs. Physicists modeling quantum systems in the Recognition Science framework cite it to confirm the configDim match to D=5 and the decay behavior derived from the J-cost. The definition is a direct record that supplies the mechanism cardinality theorem and the coherence decay theorem as its two fields.
claimA certificate asserting that the set of decoherence mechanisms has cardinality 5 and that the coherence ratio satisfies $C(k+1)/C(k) = phi^{-1}$ for every natural number $k$.
background
In the Recognition Science treatment of quantum decoherence the coherence ratio at rung k follows the phi-decay law obtained from the J-cost functional equation. The structure DecoherenceCert requires two fields: five_mechanisms asserting that the cardinality of the set of decoherence mechanisms equals 5, and phi_decay asserting the ratio equality to the inverse of phi for every rung k. The module states that five canonical channels (phonon scattering, photon emission, spin-environment coupling, charge noise, flux noise) correspond to configDim D=5, with each channel reducing coherence by the factor 1/phi per characteristic time scaled by phi to the rung power.
proof idea
The definition is a direct record constructor that supplies the five_mechanisms field from the theorem decoherenceMechanismCount and the phi_decay field from the theorem coherenceDecay.
why it matters in Recognition Science
This certificate closes the B-tier quantum physics module by confirming the five-mechanism count and phi-decay law predicted from the J-cost. It aligns with the Recognition Science forcing chain in which configDim extends the spatial dimension D=3 to five decoherence channels and the phi-ladder governs all decay rates. The result supplies the concrete instance of the required structure for any RS analysis of coherence loss.
scope and limits
- Does not derive the five mechanisms from the J-cost equation.
- Does not compute explicit numerical decoherence times.
- Does not address coupling strengths between channels.
- Does not extend the certificate to higher-dimensional or non-canonical mechanisms.
formal statement (Lean)
48noncomputable def decoherenceCert : DecoherenceCert where
49 five_mechanisms := decoherenceMechanismCount
proof body
Definition body.
50 phi_decay := coherenceDecay
51
52end IndisputableMonolith.Physics.QuantumDecoherenceFromJCost