Fiber T^2

The fiber of the tau^3 fibration: the two-dimensional space T^2 = {(B, C)} where B records the exponent (gamma-orbit) and C records the tetration height (eta-orbit). Carries the solenoidal coordinates.

Fiber T^2

Summary

The fiber of the tau^3 fibration: the two-dimensional space T^2 = {(B, C)} where B records the exponent (gamma-orbit) and C records the tetration height (eta-orbit). Carries the solenoidal coordinates.

Statement

%
\label{def:fiber-T2}
The \textbf{fiber} of the $\tau^3$ fibration is
the two-dimensional space
\[
    T^2
    \;:=\;
    \bigl\{\, (B, C) \;:\;
    B \in \mathbb{N}_{\geq 0},\;
    C \in \mathbb{N}_{\geq 0}
    \,\bigr\},
\]
where $B$ records the \textbf{exponent} (the $\gamma$-orbit:
how many times the leading prime $A$ appears)
and $C$ records the \textbf{tetration height}
(the $\eta$-orbit: the depth of iterated exponentiation).

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-02.jsonl line 12
• Manuscript source: 2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part01/ch06-tau3-fibration.tex lines 113-130

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookII.Interior.Tau3Fibration
• Name: Tau.BookII.Interior.FiberT2

Dependencies

• Canonical: I.D17

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.