Gravity-sector coupling κ_τ

κ_τ = 1 − ι_τ is the τ-effective dimensionless coupling of the dual (D) sector — the gravitational complement of the master constant ι_τ at depth 1. It is one of the two complementary couplings (κ_A + κ_D = 1) that organise the temporal structure of the boundary holonomy.

Categorical invariant. κ_τ = κ(D; 1) = 1 − ι_τ — the dual-sector coupling at depth 1; complement of κ(A; 1) = ι_τ.

Primary registry anchor: V.T23

Supporting items: IV.D255, V.D231, V.T142

1. I.K0 — Universe Postulate
2. IV.D255 — Master constant ι_τ
3. V.D231 — The ι_τ chain — κ couplings cascade from ι_τ
4. V.T23 — σ-equivariance of κ_τ — κ_τ = 1 − ι_τ as the structural complement
5. V.T142 — E₁ Completeness — κ(A) + κ(D) = 1 (temporal complement, ledger entry #28, exact)

Lean modules referenced: TauLib.BookIV.Calibration.DimensionlessCouplings, TauLib.BookV.Coda.ConstantsLedger

Numerical value: 0.658695761125 ± 0 dimensionless

Calibration anchor: PG-P01-neutron

Calibration chain:

1. Layer 0: ι_τ = 2/(π + e_math) ≈ 0.341 304
2. Layer 1: κ_τ = 1 − ι_τ ≈ 0.658 696
3. Temporal complement: κ(A) + κ(D) = ι_τ + (1 − ι_τ) = 1 (ledger entry #28, scope E)
4. κ_τ enters the Milgrom acceleration a_0 = c²/(2ℓ_τ) and the Cabibbo angle ι_τ · κ_D

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

Status: Formalized

Module: TauLib.BookIV.Calibration.DimensionlessCouplings

Lean kind: theorem

Related glossary entries

• PG-C02-iota-tau Master constant ι_τ
• PG-C16-weinberg-angle Weak mixing angle sin²θ_W
• PG-C01-newton-g Newton's gravitational constant G

Referenced by

• PG-C19-milgrom-acceleration Milgrom MOND acceleration a₀