coherenceAtRung
plain-language theorem explainer
Coherence at rung k on the phi-ladder is defined as phi to the power k. Researchers deriving RS predictions for superconducting qubit T2 scaling would cite this when establishing ratio properties across the ladder. The declaration is introduced as a direct noncomputable definition with no lemmas or reduction steps.
Claim. For each natural number $k$, the coherence at rung $k$ equals $phi^k$.
background
The phi-ladder supplies discrete scaling by successive powers of the golden ratio phi, the self-similar fixed point obtained from the J-uniqueness condition in the forcing chain. This module adapts the coherenceAtRung concept, which appears upstream with negative exponent for decay factors, to positive exponent for coherence times. The local setting from RS_PAT_043 states that transmon qubit T1 and T2 times follow phi^k scaling with optimal anharmonicity at ladder positions, and five canonical qubit types equal configDim D = 5.
proof idea
This is a direct definition that assigns phi^k to coherenceAtRung(k). No lemmas are invoked and no tactics are used; the body is the assignment itself.
why it matters
The definition supplies the positive scaling used to prove the phi_ratio property inside SCQubitCert and the coherenceRatio theorem. It implements the RS qubit ladder statement T2(k+1) = T2(k) * phi from RS_PAT_043 and connects to the phi fixed point at T6 of the forcing chain. It closes the mathematical side of the five-type qubit certificate without addressing experimental calibration.
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