τ-Meter

The τ-meter is the natural unit of length in the τ-framework: a structural extent derived from the master constant ι_τ and the dimensional bookkeeping of the calibration cascade. SI meters are recovered by multiplying the τ-meter by a dimensionless ι_τ-chain factor and the m_n-anchored length scale.

Categorical invariant. Natural-unit length m_τ defined by the master-constant chain rooted in ι_τ ≈ 0.341304 and the calibration cascade.

Primary registry anchor: IV.D255

Supporting items: I.D34, V.D231

1. I.K0 — Universe Postulate establishes τ
2. I.D34 — Master constant ι_τ ≈ 0.341304 emerges from the categorical kernel
3. IV.D255 — ι_τ at the E₁ physics layer governs the dimensional cascade
4. V.D231 — The ι_τ-chain organizes the natural-unit derivations across all dimensions
5. V.T157 — Calibration Sufficiency: ι_τ + m_n determine every constant, including the SI length scale

Lean modules referenced: TauLib.BookV.Coda.CalibrationChain

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor)
2. ℏ_τ via ι_τ chain
3. natural length scale ℓ_τ = ℏ_τ / (m_n c_τ)

Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex

Status: Formalized

Module: TauLib.BookV.Coda.CalibrationChain

Lean kind: def

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-U01-tau-second τ-Second

Referenced by

• PG-U03-tau-kilogram τ-Kilogram
• PG-U04-tau-joule τ-Joule
• PG-U08-tau-newton τ-Newton
• PG-U09-tau-pascal τ-Pascal