Planck's reduced constant ℏ
Planck's reduced constant ℏ is, in the τ-framework, the dimensional unit-conversion factor M · L² · H that closes the (M, L, ℏ) triple at E₁. It is a Tier-I (Established) entry of the constants ledger — exact by 2019 SI definition (h is fixed) and identically exact in the τ-cascade.
τ-Definition
Planck's reduced constant ℏ is, in the τ-framework, the dimensional unit-conversion factor M · L² · H that closes the (M, L, ℏ) triple at E₁. It is a Tier-I (Established) entry of the constants ledger — exact by 2019 SI definition (h is fixed) and identically exact in the τ-cascade.
Categorical invariant. ℏ = M · L² · H — the action quantum that closes the τ³ → (M, L, ℏ) projection at enrichment layer E₁.
Primary registry anchor:
IV.D34
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
V.D231— The ι_τ chain -
IV.D34— Planck Constant — the M · L² · H closure of the dimensional triple at E₁ -
V.T142— E₁ Completeness — ℏ is one of six Tier-I unit conversions
Lean modules referenced:
TauLib.BookIV.Calibration.SIReference,
TauLib.BookV.Coda.ConstantsLedger
SI Translation
Numerical value: 1.054571817e-34 ± 0 J s
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e)
- Layer 2: m_n sets the kg scale; ℏ = h/(2π) with h exact by 2019 SI definition
- Layer 3: ℏ closes (M, L, ℏ) — every action-quantised quantity (Bohr radius, Rydberg, Compton wavelength) is built from ℏ
- Layer 4: ℏ appears in G = (c³/ℏ) ι_τ² (Route 1) and in R_∞ = α² m_e c / (2ℏ)
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex