DEF0221canonicalv1High Quality Count
Count coprime triples with quality q≥1 (c≥rad(abc)). Rare: includes (1,8,9). At most 5 up to bound 30.
Payload
High Quality Count
Count coprime triples with quality q≥1 (c≥rad(abc)). Rare: includes (1,8,9). At most 5 up to bound 30.
High Quality Count
Summary
Count coprime triples with quality q≥1 (c≥rad(abc)). Rare: includes (1,8,9). At most 5 up to bound 30.
Statement
\label{def:abc-high-quality}
Count coprime triples with $c \ge \mathrm{rad}(abc)$ (quality $q \ge 1$).
These are the triples where ABC is nontrivial. Examples include
$(1, 8, 9)$: $\mathrm{rad}(72) = 6 < 9$.
\textbf{Lean:} \texttt{abc\_high\_quality\_count}.\quad
\textbf{Registry:} III.D109.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 276 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 336-343
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Arithmetic.ABCDeep - Name:
abc_high_quality_count
Dependencies
- Canonical: III.D97
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.D109high-quality-countdef:abc-high-qualityRelease lines
corpus_v3_workingcorpus_v2Relations
Formalized by (1)
Appears in (1)
Downstream uses (computed) (2)
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.