Proper Time

Proper Time (V.D17) is the τ-categorical arc-length of a defect bundle's worldline on the τ-base. It is not a coordinate but an intrinsic invariant — the cumulative phase carried by the bundle along its trajectory — and is the quantity made manifest by the Time Derivation Theorem (V.T08).

Categorical invariant. ProperTime(γ) := arc length of trajectory γ on the τ-base; an E1 invariant equal to the integrated base-circulation phase.

Primary registry anchor: V.D17

Supporting items: V.T08, IV.D79

1. I.K0 — Universe Postulate establishes τ
2. V.T08 — Time Derivation Theorem recovers proper time from τ-internal arc-length
3. V.D17 — Proper Time = arc length of bundle's worldline on τ-base
4. IV.D79 — Frequency as base-circulation rate is the conjugate quantity to proper time

Lean modules referenced: TauLib.BookV.Temporal.BaseCircle, TauLib.BookV.Temporal.BoundaryData

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. Caesium hyperfine ν via IV.D300
3. second := 9 192 631 770 cycles of the Cs hyperfine transition (SI definition)

Manuscript reference: manuscript-sources/book-05/part01-base/ch-proto-chronos.tex

Status: Formalized

Module: TauLib.BookV.Temporal.BaseCircle

Lean kind: def

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-Q09-frequency Frequency

Referenced by

• PG-Q11-operational-distance Operational Distance
• PG-Q19-action-space Action (Crossing-Point Action Space)
• PG-Q24-velocity Velocity