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He-Schramm rigidity conjecture: circle domains with conformally removable boundary are rigid
Claims that every circle domain whose boundary is conformally removable is conformally rigid, with no bound on the number of complementary components and no boundary-extension hypothesis on the map. An intermediate theorem shows that a function continuous across a compact totally disconnected removable set with finite Dirichlet energy off it is globally Sobolev. Together with Rajala's counterexample this settles both directions of the He-Schramm equivalence: removable implies rigid, the converse fails. It does NOT characterize rigid circle domains.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: He-Schramm rigidity conjecture: circle domains with conformally removable boundary are rigid · He-Schramm rigidity (removable implies rigid)
Confidence: Not scored
Registry verification: lean checked · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Claims that every circle domain whose boundary is conformally removable is conformally rigid, with no bound on the number of complementary components and no boundary-extension hypothesis on the map. An intermediate theorem shows that a function continuous across a compact totally disconnected removable set with finite Dirichlet energy off it is globally Sobolev. Together with Rajala's counterexample this settles both directions of the He-Schramm equivalence: removable implies rigid, the converse fails. It does NOT characterize rigid circle domains. parent of this event
Lean: release scope note for this family evidence for this event
This event attributed to Unreleased internal OpenAI model
He and Schramm (1994), rigidity of circle domains with sigma-finite boundary evidence for this event
He-Schramm rigidity conjecture: circle domains with conformally removable boundary are rigid parent of this event
Lean comparator statement: circle-domain theorem and removable-boundary rigidity evidence for this event
Lean: solution module (koebe_circle_domain, removability_implies_rigidity) evidence for this event
Companion: Koebe's Circle-Domain Conjecture (supplies the transfer theorem used here) evidence for this event
He-Schramm rigidity conjecture: circle domains with conformally removable boundary are rigid evidence for this event
VibeMathed record: He-Schramm rigidity conjecture: circle domains with conformally removable boundary are rigid evidence for this event
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