The local rotor G = GφGr, fed by the rapidity fields, has its own canonical connection: the Maurer–Cartan form, projected on the flow, Ωτ = (DG/Dτ)G−1. Transported with the gravitational four-velocity Ug = G(cT̂)G† in the BQ triple product, its time channel is exactly the rate of the composed Lorentz factor:
Isorapidity, DΓ/Dτ = 0, is the statement that the connection has no boost rate along the flow. Step by step: a purely radial river cannot satisfy it, an azimuthal rapidity can, the Hubble river bounds the disk, and a virial closure at the bulge radius R fixes the constant and gives the rotation-curve law of the galaxy models. Choose the rapidities.
Units: c = 1, rs = 2GM/c² = 1. Paper chart: χr = ψN − ψH = √(rs/r) − Hr/c, so vr = c tanh χr ≈ √(2GM/r) − Hr in slow flow. The galaxy-scale preset takes M ≈ 10¹¹ M⊙, R ≈ 2 kpc and a local Hz chosen so that rc ≈ 20R.
BQ-Pauli level, following de Haas (2026), A Spin(1,3) Rapidity Theory for Galactic Rotation Curves, §2–3. Orthonormal spherical legs (Îr, Ĵθ, K̂φ) and (σ̂r, σ̂θ, σ̂φ) in the order (I, J, K). For a stationary, axisymmetric field D/Dτ = ur∂r with ur = c sinh χr.
Rotor, Maurer–Cartan connection, triple product and the rotation law (eqs. 42–53) from de Haas (2026), A Spin(1,3) Rapidity Theory for Galactic Rotation Curves, and de Haas (2025), the SPARC fits of the Constant-Lagrangian model. Part of the BQ algebra models.