PRP0114canonicalv1Squarefree Dominance Theorem
ABC trivially true for squarefree coprime triples: rad(abc)=abc≥c. Quality q<1 always. Zero high-quality among squarefree coprimes.
Payload
Squarefree Dominance Theorem
ABC trivially true for squarefree coprime triples: rad(abc)=abc≥c. Quality q<1 always. Zero high-quality among squarefree coprimes.
Squarefree Dominance Theorem
Summary
ABC trivially true for squarefree coprime triples: rad(abc)=abc≥c. Quality q<1 always. Zero high-quality among squarefree coprimes.
Statement
\label{prop:squarefree-dom-thm}
ABC is trivially true for squarefree coprime triples: if $\gcd(a,b) = 1$
and $a, b, c$ are squarefree, then $\mathrm{rad}(abc) = abc \ge c^2 > c$.
Quality $q < 1$ always.
\textbf{Registry:} III.P47.\quad
\textbf{Scope:} established.
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 281 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 373-380
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Arithmetic.ABCDeep - Name:
squarefree_dominance_thm
Dependencies
- Canonical: III.D110, III.T77
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.P47squarefree-dominance-theoremprop:squarefree-dom-thmRelease 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
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