vortex_quantum
plain-language theorem explainer
Vortex quantum supplies the base circulation unit κ = 2π/m in natural units for RS superfluid models. Researchers deriving quantized vortex lines in eight-tick Bose condensates cite it to anchor the U(1) phase winding. The declaration is a direct one-line assignment with no lemmas or reductions required.
Claim. The vortex circulation quantum is defined by $κ(m) = 2π/m$ for real mass parameter $m$.
background
The module treats superfluid He-4 as a BEC of integer-spin (8-tick) bosons and He-3 via Cooper pairing of half-integer-spin (4-tick) fermions, with quantized vortices arising from U(1) gauge invariance. Upstream results supply structural guarantees: OptionAEmpiricalProgram.is ensures collision-free ledger properties, SimplicialLedger.EdgeLengthFromPsi.is provides algebraic tautologies for edge lengths, MechanismDesignFromSigma.is gives clean combinatorial structure, and MockThetaPhantom.is verifies explicit construction of mock theta shadows. These establish the coherence background for the eight-tick octave before the vortex unit is introduced.
proof idea
This is a direct definition that assigns the expression 2 * Real.pi / m with no tactic steps or lemma applications. It functions as a one-line wrapper supplying the natural-unit form of h/m for all downstream uses.
why it matters
The definition supplies the elementary circulation quantum that vortex_quantized invokes to prove ∮ v_s dl = n × (2π/m) and that vortex_quantum_positive invokes for positivity. It closes the link from T7 eight-tick coherence and U(1) invariance in the module doc to observable vortex quanta, feeding the two-fluid model and critical-exponent statements that follow in the same file.
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