Canonical Holomorphic Basis

Canonical Holomorphic Basis

Canonical Holomorphic Basis

Summary

Canonical Holomorphic Basis

Statement

%
\label{def:canonical-basis}
The \textbf{canonical holomorphic basis} of~$\tau^3$ is
\[
    \boxed{%
    \mathcal{B}_\tau
    \;:=\;
    \bigl\{\,
    E_{k,v}^{(\sigma)}
    \;\big|\;
    k \geq 1,\;
    p \mid P_k,\;
    v \in \mathbb{Z}/p\mathbb{Z},\;
    \sigma \in \{B, C\}
    \,\bigr\}.}
\]
The basis is \textbf{canonical}:
it is uniquely determined by the CRT decomposition
of the primorial tower (I.T18, Book~I),
the bipolar idempotent structure (I.D21, Book~I),
and the NF addressing of cylinders (II.D10).
No choices, conventions, or coordinates
are involved in its construction.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-02.jsonl line 101
• Manuscript source: 2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part06/ch35-canonical-basis.tex lines 298-322

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookII.Hartogs.CanonicalBasis
• Name: canonical_basis_check

Dependencies

• Canonical: II.D46, I.T18, I.D21

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.