Corpus definition canonical 2026-05-27T20:53:50+00:00
Corpus v3 · Definition cid001252DEF0125canonicalv1

Two-Readout Principle

Two-Readout Principle: topology (fine-grain) and geometry (coarse-grain) are parallel readouts of the coherence kernel

Payload

Two-Readout Principle

Two-Readout Principle: topology (fine-grain) and geometry (coarse-grain) are parallel readouts of the coherence kernel

Two-Readout Principle

Summary

Two-Readout Principle: topology (fine-grain) and geometry (coarse-grain) are parallel readouts of the coherence kernel

Statement

%
\label{def:two-readout-principle}
The \textbf{two-readout principle} states
that the coherence kernel $\tau_0$
provides two parallel readouts
on the point set~$\tau^3$:
\begin{enumerate}
    \item[\textbf{(F)}] \textbf{Fine-grain readout (topology).}
          Ultrametric cylinder domains
          $\{C_k(x)\}$ (II.D10),
          clopen basis (II.T04),
          totally disconnected Stone space (II.D14).
          The fine-grain probe is
          \emph{CRT tower depth refinement}:
          increasing stage~$k$ resolves finer
          cylinder partitions.

    \item[\textbf{(C)}] \textbf{Coarse-grain readout (geometry).}
          Betweenness, congruence, orthogonality---a
          relational structure that does \textbf{not}
          generate the cylinder topology.
          The coarse-grain probe is
          \emph{incidence and distance comparison}:
          relational data visible at any
          fixed finite stage.
\end{enumerate}
These readouts are \textbf{parallel},
not layered:
the fine-grain readout does not
produce the coarse-grain readout
by any continuous-path construction.
Both are earned from holomorphy
(the inverted dependency of II.T06),
which itself is earned from
the coherence kernel.

Proof / Justification

This item is definitional. No manuscript proof is required.

Source Context

  • Registry source: book-02.jsonl line 45
  • Manuscript source: 2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part03/ch18-connectivity-via-coherence.tex lines 122-158

Lean / Formalization Notes

  • Formalization: formalized
  • Module: TauLib.BookII.Topology.CoherenceConnectivity
  • Name: two_readout_check

Dependencies

  • Canonical: I.D17, I.T04, I.T05, II.D10, II.D13, II.D14, II.T04, II.T06

Generated by later projection phases.

Generated by later projection phases.

Revision Notes

  • 2026-04-24: Initial pilot migration.

Identifiers

  • Corpus ID cid001252
  • Primary alias DEF0125
  • Type Definition
  • Status canonical
  • Visibility public
  • Version v1

Aliases & legacy IDs

II.D18atwo-readout-principledef:two-readout-principle

Release lines

corpus_v3_workingcorpus_v2

Relations

Appears in (1)

Sources

  • Monograph cid000001Book II, Part 3, Chapter 18 (Part III)

Version & History

  • v1 · 2026-05-10 imported from v2 registry

Status disclaimer

A Corpus Item page reports the program's current internal record for this item. It does not imply external verification, scientific consensus, or final proof unless explicitly stated. Read it together with its dependencies, formalization status, and the program's overall stance.

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