Velocity

Velocity in the τ-framework (V.D262) is the Linearized Velocity Scale: the rate of change of operational distance with respect to proper time on a defect bundle's worldline, evaluated in the linearized regime where the τ-metric reduces to a flat tangent. It is bounded above by c (IV.D293) by τ-categorical structure.

Categorical invariant. Velocity(γ) := d(OperationalDistance)/d(ProperTime) on worldline γ; an E1 invariant in the linearized regime, |v| ≤ c.

Primary registry anchor: V.D262

Supporting items: V.D17, V.D28, IV.D293

1. I.K0 — Universe Postulate establishes τ
2. V.D17 — Proper Time as τ-arc-length
3. V.D28 — Operational Distance as spatial τ-arc-length
4. V.D262 — Linearized Velocity Scale := dx/dτ in linearized τ-metric
5. IV.D293 — Speed of light in relational units fixes |v| ≤ c bound

Lean modules referenced: TauLib.BookV.Temporal.BaseCircle, TauLib.BookV.GravityField.LorentzNoMinkowski

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. m via c (IV.D293) → length scale
3. s via Cs hyperfine → time scale
4. v = dx/dt composed from these

Manuscript reference: manuscript-sources/book-05/part04-kinematics/ch-velocity.tex

Status: Formalized

Module: TauLib.BookV.GravityField.LorentzNoMinkowski

Lean kind: def

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q10-proper-time Proper Time
• PG-Q11-operational-distance Operational Distance