DecoherenceFromBITCert
The structure DecoherenceFromBITCert bundles five properties for the BIT-coupled decoherence model: the carrier frequency lies in (7.5, 8.1), T2 times remain positive and strictly decrease with rung index k, and T2 ratios between any two classes equal phi to the integer rung difference. Quantum information researchers modeling substrate-dependent decoherence would cite it when calibrating phi-power scaling from a single T2_0 measurement. It is introduced as a structure definition that directly encodes the algebraic consequences of the closed T2
claimLet $T_2(k) := T_{2,0}/phi^k$ for rung index $k$. The certificate asserts $7.5 < omega_{BIT} < 8.1$, positivity $T_2(k) > 0$ whenever $T_{2,0} > 0$, strict decrease $T_2(k+1) < T_2(k)$, the ratio identity $T_2(k_a)/T_2(k_b) = phi^{k_b - k_a}$ for $k_a leq k_b$, and the transmon-to-fluxonium ratio equaling $phi$.
background
In the Decoherence from BIT module the Bosonic Identity Theorem supplies the carrier frequency omega_BIT = 5 phi in RS-native units. The substrate decoherence time is defined by T2_substrate T2_0 k = T2_0 / phi^k, where higher Z-rung produces stronger BIT coupling and faster decoherence. This structure packages the resulting positivity, monotonicity, and phi-power ratio properties that follow immediately from the definition.
proof idea
As a structure definition with empty proof body, DecoherenceFromBITCert simply assembles the five listed properties. The ratio and monotonicity claims follow directly from the closed-form expression of T2_substrate once positivity of phi is granted by the Constants structure.
why it matters in Recognition Science
This certificate serves as the master record for Track F1, feeding the inhabited instance decoherenceFromBITCert. It encodes the phi-power scaling forced by BIT coupling, consistent with the self-similar fixed point phi. The module notes that specific rung assignments remain hypotheses, with a falsifier given by cross-pair T2 ratios deviating more than 5% from any integer power of phi.
scope and limits
- Does not derive Z-rung assignments for specific qubit classes from first principles.
- Does not supply a dynamical model of the BIT-qubit interaction.
- Does not constrain the absolute scale of T2_0 beyond positivity.
- Does not address multi-qubit entanglement effects on decoherence.
formal statement (Lean)
162structure DecoherenceFromBITCert where
163 omega_BIT_band : (7.5 : ℝ) < omega_BIT ∧ omega_BIT < 8.1
164 T2_pos : ∀ T2_0 k, 0 < T2_0 → 0 < T2_substrate T2_0 k
165 T2_strictly_decreasing : ∀ T2_0 k, 0 < T2_0 →
166 T2_substrate T2_0 (k + 1) < T2_substrate T2_0 k
167 T2_ratio_phi_power : ∀ T2_0 k_a k_b, 0 < T2_0 → k_a ≤ k_b →
168 T2_substrate T2_0 k_a / T2_substrate T2_0 k_b = Constants.phi ^ (k_b - k_a)
169 transmon_fluxonium_ratio : ∀ T2_0, 0 < T2_0 →
170 T2_substrate T2_0 z_rung_transmon / T2_substrate T2_0 z_rung_fluxonium
171 = Constants.phi ^ 1
172
173/-- The master certificate is inhabited. -/