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d23d6f3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | # Potential integral density on curve character varieties
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
- [Integral points on character varieties of curves](../../preprints/Integral-points-on-character-varieties-of-curves-September-25-2026/paper.pdf)
## Scope
The integral-density question asks whether integral points become Zariski dense in every component of a curve character variety after one finite extension of the number field. The linked formalization proves a supporting compatibility result for its marked-surface construction. Given a proper diagram with finitely many vertices, a chosen seam with maximal adjacent facet rank and a positive-genus parent, puncture data, an existing solution over a field, and a chosen boundary occurrence, the produced marked values satisfy every seam equation.
This is conditional compatibility of the produced solution. Potential integral density, including the prescribed-boundary and all-component conclusions, remains outside the selected statement.
## Comparator links
| Result | Comparator statement |
| --- | --- |
| Compatibility of the produced marked solution with every seam equation | [CharacterVarietiesAllSeamsSupport.lean](../ComparatorChallenges/CharacterVarietiesAllSeamsSupport.lean) |
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