circuitModes
plain-language theorem explainer
The definition fixes the count of resonance modes in superconducting circuits at eight, implementing the eight-tick octave for Josephson junction systems. Researchers mapping recognition phase variables to qubit circuits would cite this when certifying the five-element structure. It is supplied as a direct definition equating the mode count to two raised to the third power.
Claim. The number of Fourier modes for the superconducting circuit resonance is $2^3$.
background
The module treats superconducting qubits as Josephson junction circuits, identifying five canonical elements (Josephson junction, SQUID, transmon, fluxonium, CPB) with configuration dimension five. The Josephson junction phase acts as the recognition phase variable, with equilibrium at phase zero. Eight-tick DFT modes govern circuit resonance, drawing on the eight-tick octave (period $2^3$) from the unified forcing chain where spatial dimension three is forced.
proof idea
The declaration is introduced by direct definition as the exponential two raised to three, with no lemmas or tactics applied.
why it matters
It supplies the eight_modes component for the SCCircuitCert structure, which requires both five elements and eight modes. This realizes the T7 eight-tick octave landmark for the superconducting circuit application, linking recognition phase to resonance modes. Downstream results circuitModes_8 and circuitModes_2cubeD confirm the numerical value.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.