Master constant ι_τ

ι_τ = 2/(π + e) is the master algebraic constant of the τ-framework — the unique dimensionless number that governs every dimensionless ratio of physics. It is not measured; it is derived from the categorical kernel τ at Layer 0 of the SI calibration cascade. Every other physical constant is a sector readout of ι_τ calibrated by the neutron-mass anchor m_n.

Categorical invariant. ι_τ = 2/(π + e) ≈ 0.341 304 238 875… — the structural fixed point of the boundary holonomy algebra H_∂[ω].

Primary registry anchor: IV.D255

Supporting items: I.K0, V.D231, V.T142, V.T157

1. I.K0 — Universe Postulate — categorical kernel τ
2. IV.D255 — Master constant ι_τ defined as 2/(π+e)
3. V.D231 — The ι_τ chain — every constant cascades from ι_τ
4. V.T142 — E₁ Completeness — H_∂[ω] accounts for every known physical constant via ι_τ + m_n
5. V.T157 — Calibration Sufficiency — ι_τ + m_n determine every entry of the constants ledger with zero free parameters

Lean modules referenced: TauLib.BookV.Coda.CalibrationChain, TauLib.BookV.Coda.ConstantsLedger

Numerical value: 0.341304238875 ± 0 dimensionless

Calibration anchor: PG-P01-neutron

Calibration chain:

1. Layer 0 (algebraic): π, e (math constants) → ι_τ = 2/(π + e)
2. Layer 1 (dimensionless): ι_τ → κ(D), κ(A), κ(B), κ(C), α, R = m_n/m_e, α_G
3. Layer 2 (anchor): m_n (single experimental input) → m_e, m_P, G
4. Layer 3 (SI): m_e, m_P, G, α → c, ℏ, e, k_B, ε₀, μ₀, …
5. Layer 4 (verification): R_∞, a_0, λ_C, hydrogen spectrum

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-C01-newton-g Newton's gravitational constant G

Referenced by

• PG-C03-speed-of-light Speed of light c
• PG-C04-planck-hbar Planck's reduced constant ℏ
• PG-C05-fine-structure-alpha Fine-structure constant α
• PG-C06-elementary-charge Elementary charge e
• PG-C07-vacuum-permittivity Vacuum permittivity ε₀
• PG-C08-vacuum-permeability Vacuum permeability μ₀
• PG-C09-electron-mass Electron mass m_e
• PG-C10-proton-mass Proton mass m_p
• PG-C11-rydberg-constant Rydberg constant R_∞
• PG-C12-bohr-radius Bohr radius a_0
• PG-C13-planck-mass Planck mass m_P
• PG-C14-gravitational-fine-structure Gravitational fine-structure constant α_G
• PG-C15-boltzmann-constant Boltzmann constant k_B
• PG-C16-weinberg-angle Weak mixing angle sin²θ_W
• PG-C17-strong-coupling Strong coupling constant α_s
• PG-C18-kappa-tau Gravity-sector coupling κ_τ
• PG-C19-milgrom-acceleration Milgrom MOND acceleration a₀