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Publication v7

Record details

Schiffer and Pompeiu conjectures →

Coverage & review

Coverage of this curation

Original question, distinct results, proof provenance, selected history and an explanatory schematic.

Formal proofs: Pinned formal statements and the computational archive are linked to their own targets. External build reports and independent mathematical assessment remain separate from OpenMath execution.

AI-assisted work: Colbrook and George Stepaniants own the analytic construction; Cao-Labora and Jaume de Dios Pont own the smooth family. Their AI disclosures describe different roles. The formal Pompeiu statement credits Himanshu Gupta and Moritz Firsching’s Google DeepMind Formal Conjectures statement; this is statement provenance, not discovery credit.

Search scope & review

Selected primary papers, exact formal declarations, project provenance and official descriptions checked on 13 October 2026.

Checked Oct 13, 2026 · independent review pending.

  • Independent mathematical assessment of the cited constructions remains pending.
  • No OpenMath execution of the certificate or either Lean project is recorded.

General status observations

Source identities & rights

A computer-assisted counterexample to the planar Pompeiu and Schiffer conjectures ↗

Matthew J. Colbrook, George Stepaniants · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
schiffer-pompeiu:source:computer:v1
Revision
2026-08-03
Content SHA-256
0a228277208a58f7a4a918a57c0db911c2b4354cee05587f47a4cfa11345b1b7
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

Counterexamples to Schiffer’s Conjecture ↗

Gonzalo Cao-Labora, Jaume de Dios Pont · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
schiffer-pompeiu:source:bifurcation:v1
Revision
2026-08-05
Content SHA-256
857b2f4975bfc4b2ccc113020bf6e9fc9e1ef36c4caa09c09ff73e08f7840026
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

Lean proof of the star-shaped Schiffer/Pompeiu construction ↗

Jaume de Dios Pont, Gonzalo Cao-Labora · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
schiffer-pompeiu:source:lean:v1
Revision
2938e277969c329caf154e48a3d8823f3635c7f1
Content SHA-256
02cdbc8f521968df2c2da3c6caad9fc1e93245230efff82ae4509615dc390e96
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

Numerical certificate and reproduction report ↗

Matthew J. Colbrook, George Stepaniants · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
schiffer-pompeiu:source:certificate:v1
Revision
2fb3f2ecafd3233dbca390d73e764fe6e04a9c7d
Content SHA-256
66b8c4fcf6bf61f9a529ad70af05de7cdfc8970d3d92bfbf2bfa911033f5f0be
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

Lean proof of the analytic tenfold construction ↗

Matthew J. Colbrook, George Stepaniants · metadata-link · Original source license and document rights apply.

OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms

1 cited entry · exact source identity
Version
schiffer-pompeiu:source:computer-lean:v1
Revision
2fb3f2ecafd3233dbca390d73e764fe6e04a9c7d
Content SHA-256
f14c1f0df5e92636dfe42cd78674f23cf0fa2f1ab221fcfaba6bc1ce38ed611a
Source update
Unavailable
Observed
2026-10-13
Check cadence
90 days

Publication history

Problem ID
problem-schiffer-pompeiu
Publication checksum
f315cdce71af678d5630bba696c72d741588ae401f692a7a2efd5ff73664ae99
Published
2026-10-20T21:33:54.953478+00:00
Publication reason
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
  1. Version 1 · Oct 13, 2026

    Source-linked pilot import; independent mathematical review remains pending.

  2. Version 2 · Oct 13, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  3. Version 3 · Oct 13, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  4. Version 4 · Oct 13, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  5. Version 5 · Oct 14, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  6. Version 6 · Oct 15, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

  7. Version 7 · Oct 20, 2026

    Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.

Download version-reference manifest →