Diagonal Discipline

Structural principle preventing free contraction/reuse; forces exactly four orbit channels via three successive diagonal rewirings.

Diagonal Discipline

Summary

Structural principle preventing free contraction/reuse; forces exactly four orbit channels via three successive diagonal rewirings.

Statement

%
\label{def:diagonal-discipline}
The \textbf{diagonal discipline} is the structural principle
that governs how iterated operations overflow
between orbit channels.
It asserts:
\begin{enumerate}
    \item \textbf{No unearned diagonals.}
          The self-product of an operation at level~$k$
          cannot be absorbed within the same orbit channel.
          It must overflow into a distinct channel at level~$k{+}1$.
    \item \textbf{Each overflow consumes one channel.}
          The new operation at level~$k{+}1$
          is canonically associated with a dedicated orbit channel.
    \item \textbf{Saturation.}
          When no further orbit channel is available,
          the overflow is blocked.
          The ladder of iterated operations terminates.
\end{enumerate}

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

• Registry source: book-01.jsonl line 4
• Manuscript source: 2nd-edition/book-i-categorical-foundations/02_mainmatter/part01/ch05-diagonal-discipline.tex lines 64-84

Lean / Formalization Notes

• Formalization: formalized
• Module: TauLib.BookI.Kernel.Diagonal
• Name: Tau.Kernel.diagonal_discipline

Dependencies

• Canonical: I.D01

Related Results

Generated by later projection phases.

Related Publications

Generated by later projection phases.

Revision Notes

• 2026-04-24: Initial pilot migration.