z_rung_trapped_ion
plain-language theorem explainer
The declaration assigns the trapped-ion qubit class to Z-rung 8 on the phi-ladder inside the BIT decoherence model. Researchers computing T2 ratios across qubit families cite this fixed rung to obtain exact phi-power predictions. It is a bare numerical definition with no derivation or proof obligations.
Claim. The trapped-ion qubit substrate is assigned rung $8$ on the phi-ladder.
background
In the Decoherence from BIT module each qubit class receives an integer Z-rung that locates it on the phi-ladder. The difference between two rungs supplies the integer exponent k such that the substrate T2 ratio equals phi to the power k. Trapped-ion qubits are placed at rung 8, one of several empirical assignments that also include transmon at rung 5, fluxonium at rung 6 and NV centers at rung 7. The module treats these rung values as hypothesis-grade calibration targets while the structural claim that ratios are phi-powers is proved algebraically. The local setting is the Bosonic Identity Theorem carrier at frequency 5 phi coupling to qubit substrates and producing a substrate-dependent decoherence channel.
proof idea
The declaration is a direct numerical definition that binds the natural number 8 to the identifier z_rung_trapped_ion.
why it matters
This rung value is consumed by the downstream theorem T2_transmon_to_trapped_ion_ratio, which concludes that the transmon-to-trapped-ion T2 ratio equals exactly phi cubed. It participates in the module's claim that all inter-class T2 ratios are phi-powers under BIT coupling, consistent with the phi-ladder and eight-tick octave of Recognition Science. The assignment itself remains an open calibration target subject to empirical refinement.
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