predictedQubitDecoherence
plain-language theorem explainer
The declaration defines the predicted decoherence time for a typical superconducting qubit by direct application of the decoherenceTime constructor to the qubit's environmental mode count and a fixed coupling of 0.5. Quantum information theorists and experimentalists modeling first-principles decoherence would cite it for concrete Gap-45 predictions in Recognition Science. The definition is a one-line wrapper that supplies the mode structure and trivial norm_num bounds.
Claim. The predicted decoherence time for a typical superconducting qubit equals the value of the decoherence timescale function evaluated at the qubit's environmental mode count, coupling strength 0.5, and unit bounds: $τ_{decoherence} ≈ τ_0 φ^{-N}$ where $N$ is the mode count and $φ$ the golden ratio.
background
The QFT.Decoherence module derives decoherence timescales from the Gap-45 threshold, the boundary at roughly 10^45 operations separating the quantum regime (coherent superposition preserved) from the classical regime (entanglement with environment). Quantum coherence holds when a system remains below this threshold; crossing it produces decoherence via the formula $τ_{decoherence} ≈ τ_0 × φ^{-N}$, with $τ_0$ the fundamental tick and $N$ the number of coupled environmental modes. Upstream results supply the finite mode truncation via Galerkin2D.modes, the phi-power scaling via Cosmology.LargeScaleStructureFromRS.scale, and the J-cost structure via PhiForcingDerived.of together with PrimitiveDistinction.from.
proof idea
This is a one-line wrapper that applies the decoherenceTime function to the structure ⟨typicalSCQubit.env_modes, 0.5, by norm_num, by norm_num⟩, where the two norm_num tactics discharge the required bound proofs for the coupling interval.
why it matters
The definition supplies a concrete numerical anchor for the QF-009 decoherence derivation inside the Recognition Science framework, connecting the Gap-45 threshold directly to qubit parameters and supporting the patent proposals for threshold-based error correction. It rests on the phi-ladder and eight-tick octave from the T0-T8 forcing chain together with the Recognition Composition Law. No downstream theorems are recorded, leaving open the question of explicit numerical comparison against laboratory decoherence data.
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