DEF0125canonicalv1Two-Readout Principle
Two-Readout Principle: topology (fine-grain) and geometry (coarse-grain) are parallel readouts of the coherence kernel
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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.jsonlline 45 - Manuscript source:
2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part03/ch18-connectivity-via-coherence.texlines 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
Related Results
Generated by later projection phases.
Related Publications
Generated by later projection phases.
Revision Notes
- 2026-04-24: Initial pilot migration.
Identifiers
Aliases & legacy IDs
II.D18atwo-readout-principledef:two-readout-principleRelease lines
corpus_v3_workingcorpus_v2Relations
Appears in (1)
Sources
Version & History
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.