decoherence_from_BIT_one_statement
plain-language theorem explainer
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
Claim. Under 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
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.
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