decoherence_from_BIT_one_statement
Quantum engineers modeling decoherence in superconducting qubits cite this result for its prediction that T2 ratios between substrate classes are exact powers of the golden ratio phi. The statement asserts three properties under the BIT-coupling model: the carrier frequency omega_BIT lies between 7.5 and 8.1, T2 decreases strictly with increasing Z-rung, and cross-class T2 ratios equal phi to the power of the rung difference. Its proof is a direct term that packages the three component lemmas omega_BIT_band, T2_substrate_strictly_decreasing and
claimUnder the BIT-coupling decoherence model, the canonical carrier frequency satisfies $7.5 < omega_{BIT} < 8.1$, the substrate decoherence time $T_2(k)$ is strictly decreasing in the Z-rung $k$ for any positive base value $T_{2,0}$, and the ratio between any two classes satisfies $T_2(k_a)/T_2(k_b) = phi^{k_b - k_a}$ for $k_a leq k_b$.
background
The module treats decoherence induced by coupling a qubit substrate to the Bosonic Identity Theorem carrier at frequency omega_BIT = 5 phi in RS-native units. The central definition is T2_substrate(T2_0, k) := T2_0 / phi^k, which encodes stronger BIT coupling at higher Z-rung and therefore faster decoherence. Upstream results supply the rung function from multiple engineering and foundation modules together with the band predicate that places the carrier inside the stated interval.
proof idea
The proof is a term-mode one-liner that constructs the required conjunction directly from the three sibling lemmas omega_BIT_band, T2_substrate_strictly_decreasing and T2_ratio_is_phi_power.
why it matters in Recognition Science
This declaration packages the algebraic core of the BIT-coupling decoherence model, realizing the structural phi-power ratio law required by the Bosonic Identity Theorem in the Recognition framework. It connects to the phi fixed point (T6) and supplies the scaling relation that downstream quantum-computing applications would use once Z-rung assignments are fixed empirically. The module documentation leaves those assignments as open hypotheses.
scope and limits
- Does not assign specific Z-rungs to qubit families such as transmon or fluxonium.
- Does not derive the BIT carrier frequency from first principles.
- Does not supply numerical values for T2_0 in physical units.
- Does not address decoherence mechanisms beyond the BIT-coupling channel.
formal statement (Lean)
189theorem decoherence_from_BIT_one_statement :
190 -- (1) Carrier in band.
191 ((7.5 : ℝ) < omega_BIT ∧ omega_BIT < 8.1) ∧
192 -- (2) `T₂` strictly decreasing in Z-rung.
193 (∀ T2_0 k, 0 < T2_0 →
194 T2_substrate T2_0 (k + 1) < T2_substrate T2_0 k) ∧
195 -- (3) Cross-class ratio is a φ-power.
196 (∀ T2_0 k_a k_b, 0 < T2_0 → k_a ≤ k_b →
197 T2_substrate T2_0 k_a / T2_substrate T2_0 k_b = Constants.phi ^ (k_b - k_a)) :=
proof body
Term-mode proof.
198 ⟨omega_BIT_band, T2_substrate_strictly_decreasing, T2_ratio_is_phi_power⟩
199
200end
201
202end DecoherenceFromBIT
203end QuantumComputing
204end IndisputableMonolith