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def definition def or abbrev high

decoherenceCert

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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

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

depends on (3)

Lean names referenced from this declaration's body.