PRP0071canonicalv1Balanced Sector Uniqueness
The A-sector (weak) is the unique primitive sector with balanced spectral polarity: pol(S_g) = 1 iff g = π. Proved by orbit exhaustion over ABCD coordinates.
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Balanced Sector Uniqueness
The A-sector (weak) is the unique primitive sector with balanced spectral polarity: pol(S_g) = 1 iff g = π. Proved by orbit exhaustion over ABCD coordinates.
Balanced Sector Uniqueness
Summary
The A-sector (weak) is the unique primitive sector with balanced spectral polarity: pol(S_g) = 1 iff g = π. Proved by orbit exhaustion over ABCD coordinates.
Statement
%
\label{prop:balanced-sector-uniqueness}
Among the four primitive sectors
$\Sector{\eta}, \Sector{\alpha}, \Sector{\gamma}, \Sector{\pi}$,
the A-sector $\Sector{\pi}$ is the unique sector
with balanced spectral polarity:
\begin{equation}\label{eq:ch12-unique-balanced}
\mathrm{pol}(\Sector{g}) = 1
\quad\iff\quad
g = \pi.
\end{equation}
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 33 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part02/ch12-the-parity-bridge-theorem.texlines 211-223
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Sectors.LanglandsReflection - Name:
balanced_uniqueness_5
Dependencies
- Canonical: III.D17
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
III.P04balanced-sector-uniquenessprop:balanced-sector-uniquenessRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (2)
Appears in (1)
Downstream uses (computed) (4)
Items in the corpus that reference this one via load-bearing relations. Computed from the full corpus-v3 graph at build time.
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.