z_rung_transmon
plain-language theorem explainer
The definition assigns the transmon qubit class to Z-rung 5 on the Recognition Science phi-ladder. Researchers deriving T2 decoherence ratios under the Bosonic Identity Theorem cite this value to fix the exponent in phi-power relations between qubit families. The declaration is a direct constant assignment with no computation or lemmas.
Claim. The Z-rung for the transmon qubit class is $5$.
background
The DecoherenceFromBIT module examines coupling between the BIT carrier at frequency $5φ$ and qubit substrates. Each substrate class receives a Z-rung hypothesis that locates it on the phi-ladder; the rung difference then sets the integer exponent $k$ in the T2 ratio $T_2(a)/T_2(b) = φ^k$. Upstream rung definitions in Anchor, RSBridge, and AnchorPolicy supply the integer map from class names to ladder positions, while the calibration definition converts external measurements into RS-native units.
proof idea
Direct definition that sets the value to the natural number 5. No lemmas or tactics are invoked; the declaration simply records the calibration target for transmon qubits.
why it matters
This assignment supplies the integer input to DecoherenceFromBITCert and the ratio theorems T2_transmon_to_fluxonium_ratio and T2_transmon_to_trapped_ion_ratio. It fixes the rung difference that forces the transmon-fluxonium T2 ratio to equal $φ$ under the BIT model. The placement follows the phi-ladder mass formula extended to decoherence channels, where Z-rung gaps control the exponent in the ratio law.
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