Master Constant iota_tau

iota_tau = 2/(pi+e) ~ 0.341304. The asymptotic B/C dominance mediator: parametrizes the split-complex decomposition and measures the asymmetry between the two lemniscate lobes. Earned from prime distribution, not imposed.

Master Constant iota_tau

Summary

iota_tau = 2/(pi+e) ~ 0.341304. The asymptotic B/C dominance mediator: parametrizes the split-complex decomposition and measures the asymmetry between the two lemniscate lobes. Earned from prime distribution, not imposed.

Statement

%
\label{def:iota-tau}
The \textbf{master constant} of Category $\tau$ is:
\[
    \boxed{\iota_\tau := \frac{2}{\pi + e}
    \approx 0.341304.}
\]
It parametrizes the asymptotic proportion of $B$-dominant primes:
$R_B = \iota_\tau$.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-01.jsonl line 84
• Manuscript source: 2nd-edition/book-i-categorical-foundations/02_mainmatter/part10/ch41-master-constant.tex lines 134-144

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookI.Boundary.Iota
• Name: Tau.Boundary.iota_tau_numer

Dependencies

• Canonical: I.D19, I.D20, I.T05

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.