τ-Kilogram

The τ-kilogram is the natural unit of mass in the τ-framework: a structural mass scale rooted in the calibration anchor m_n. Unlike the other τ-natural units, mass is the single dimensionful quantity not predicted by ι_τ alone — it is fixed by the empirical neutron mass and propagated through the cascade.

Categorical invariant. Natural-unit mass kg_τ ≡ m_n; the unique dimensionful anchor of the τ-framework. All other masses are dimensionless ratios of m_n via ι_τ.

Primary registry anchor: V.R305

Supporting items: I.D34, IV.D255, 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.R305 — One-anchor remark: m_n sets the scale; ι_τ determines every ratio
5. V.D231 — The ι_τ-chain propagates m_n through all derived mass ratios (m_e, m_p, m_P)

Lean modules referenced: TauLib.BookIV.Calibration.CalibrationAnchor, TauLib.BookV.Coda.CalibrationChain

Numerical value: 1.674927498e-27 ± 9.5e-37 kg

Calibration anchor: PG-P01-neutron

Calibration chain:

1. m_n (anchor) = 1.674 927 498 × 10⁻²⁷ kg (CODATA 2018)
2. R = ι_τ⁻⁷ − (√3 + π³α²)ι_τ⁻² → m_e = m_n / R
3. m_P = m_n / ι_τ (Planck mass via Route 3)

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

Status: Formalized

Module: TauLib.BookIV.Calibration.CalibrationAnchor

Lean kind: structure

Lean symbol: CalibrationAnchor

Related glossary entries

• PG-P01-neutron τ-Neutron
• PG-U01-tau-second τ-Second
• PG-U02-tau-meter τ-Meter

Referenced by

• PG-U04-tau-joule τ-Joule