PRP0115canonicalv1ABC Gap Characterization
ABC gap = structural. Primorial tower is squarefree → avoids the hard case. Genuine difficulty in perfect-power parts. exponential_quantification (K4).
Payload
ABC Gap Characterization
ABC gap = structural. Primorial tower is squarefree → avoids the hard case. Genuine difficulty in perfect-power parts. exponential_quantification (K4).
ABC Gap Characterization
Summary
ABC gap = structural. Primorial tower is squarefree → avoids the hard case. Genuine difficulty in perfect-power parts. exponential_quantification (K4).
Statement
\label{prop:abc-gap}
The primorial tower is squarefree, so it avoids the hard case of ABC
entirely. The genuine difficulty lies in numbers with large perfect-power
factors (e.g., $2^n + 1$). The gap is \emph{structural}: the $\tau$
framework decomposes to the squarefree part, which is where ABC is easy.
\textbf{Registry:} III.P48.\quad
\textbf{Scope:} established (meta-theorem).
Proof / Justification
No immediate manuscript proof block was extracted in this pilot run.
Source Context
- Registry source:
book-03.jsonlline 282 - Manuscript source:
2nd-edition/book-iii-categorical-spectrum/02_mainmatter/part10/ch81-additive-conjectures-deep.texlines 382-390
Lean / Formalization Notes
- Formalization:
formalized - Module:
TauLib.BookIII.Bridge.ConjectureGaps - Name:
abc_gap_structural
Dependencies
- Canonical: III.P47, III.D69
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.P48abc-gap-characterizationprop:abc-gapRelease 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.