DEF0184canonicalv1Dimensional Rigidity
tau admits exactly one holomorphic structure with fibration index 3 (= 1 base + 2 fiber) and refinement dimension 4 (= ABCD rays). There is no family of tau-structures indexed by dimension; the 3 in tau^3 is an algebraic fibration index, not a metric dimension parameter.
Payload
Dimensional Rigidity
tau admits exactly one holomorphic structure with fibration index 3 (= 1 base + 2 fiber) and refinement dimension 4 (= ABCD rays). There is no family of tau-structures indexed by dimension; the 3 in tau^3 is an algebraic fibration index, not a metric dimension parameter.
Dimensional Rigidity
Summary
tau admits exactly one holomorphic structure with fibration index 3 (= 1 base + 2 fiber) and refinement dimension 4 (= ABCD rays). There is no family of tau-structures indexed by dimension; the 3 in tau^3 is an algebraic fibration index, not a metric dimension parameter.
Statement
%
\label{def:dimensional-rigidity}
A holomorphic framework exhibits
\textbf{dimensional rigidity}
if increasing the coordinate dimension
produces no qualitatively new phenomena---i.e.,
all features that appear at dimension $n > 1$
are already present at dimension~1
(or, equivalently, the framework does not
distinguish between ``complex dimension~1''
and ``complex dimension~$n$'' behaviors).
$\tau^3$ exhibits dimensional rigidity.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-02.jsonlline 190 - Manuscript source:
2nd-edition/book-ii-categorical-holomorphy/02_mainmatter/part11/ch63-refuses.texlines 276-289
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookII.Mirror.DimensionalLadder - Name:
DimensionalRigidity
Dependencies
- Canonical: II.D15, II.D02, II.T42
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.D76dimensional-rigiditydef:dimensional-rigidityRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (5)
Appears in (1)
Downstream uses (computed) (10)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
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Version & History
Status disclaimer
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