Corpus v3 · Definition
cid001450
DEF0220canonicalv1Sieve-Accelerated ABC
ABC quality check pushed to bound 100. Weak ABC (c < rad(abc)²) for all coprime pairs.
Payload
Sieve-Accelerated ABC
ABC quality check pushed to bound 100. Weak ABC (c < rad(abc)²) for all coprime pairs.
Sieve-Accelerated ABC
Summary
ABC quality check pushed to bound 100. Weak ABC (c < rad(abc)²) for all coprime pairs.
Statement
\label{def:abc-sieve}
For coprime pairs $(a, b)$ with $c = a + b$: verify
$c < \mathrm{rad}(abc)^2$ (weak ABC, $\varepsilon = 1$).
Pushed from bound~15 to~100.
\textbf{Lean:} \texttt{abc\_sieve\_check}.\quad
\textbf{Registry:} III.D108.
Proof / Justification
This item is definitional. No manuscript proof is required.
Source Context
- Registry source:
book-03.jsonlline 275 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 319-326
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Arithmetic.ABCDeep - Name:
abc_sieve_check
Dependencies
- Canonical: III.D97, III.D98
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.D108sieve-accelerated-abcdef:abc-sieveRelease 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.