{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UX46WIJPNG7ARQTLUQAESEF4OQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0f1d3da0bb55018209127b8924ed590f4b67629a4d6f7ed0459992a3c55554ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T06:16:33Z","title_canon_sha256":"de589e3019cbcf0d7d3c4a48be21175eab8e761038fa25483f940f76fc3d602d"},"schema_version":"1.0","source":{"id":"1210.5689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5689","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5689v1","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5689","created_at":"2026-05-18T03:42:43Z"},{"alias_kind":"pith_short_12","alias_value":"UX46WIJPNG7A","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UX46WIJPNG7ARQTL","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UX46WIJP","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:1db184372465a28a6c9c3e8debb4424f4c3572b05a70eccfe0d7bd2a74faaff0","target":"graph","created_at":"2026-05-18T03:42:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We determine the Hausdorff limit-set of the Euclidean hypersurfaces with large $\\lambda_1$ or small extrinsic radius. The result depends on the $L^p$ norm of the curvature that is assumed to be bounded a priori, with a critical behaviour for $p$ equal to the dimension minus 1.","authors_text":"Erwann Aubry (JAD), Jean-Francois Grosjean (IECN)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T06:16:33Z","title":"Metric shape of hypersurfaces with small extrinsic radius or large $ \\lambda_1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5689","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:74de5ca5501af19b2c7914dabb360c848f6f041defa1aa0aac74b222179c8ccf","target":"record","created_at":"2026-05-18T03:42:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0f1d3da0bb55018209127b8924ed590f4b67629a4d6f7ed0459992a3c55554ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-10-21T06:16:33Z","title_canon_sha256":"de589e3019cbcf0d7d3c4a48be21175eab8e761038fa25483f940f76fc3d602d"},"schema_version":"1.0","source":{"id":"1210.5689","kind":"arxiv","version":1}},"canonical_sha256":"a5f9eb212f69be08c26ba4004910bc741f0ad60fdbad93a21039587840249bc4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5f9eb212f69be08c26ba4004910bc741f0ad60fdbad93a21039587840249bc4","first_computed_at":"2026-05-18T03:42:43.314670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:43.314670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mgTOm5ZRVKaci0bngPKCl0K9z98cUHJ4PRCUk9BooN3iADPk9VoMJKq9O4cNNVo2SGkKL2Q/dDkWeTthuvK7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:43.315428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74de5ca5501af19b2c7914dabb360c848f6f041defa1aa0aac74b222179c8ccf","sha256:1db184372465a28a6c9c3e8debb4424f4c3572b05a70eccfe0d7bd2a74faaff0"],"state_sha256":"088096bc9ddb6e7ebce6bc2c94ed54eacca53af08a99c65a9c2196d33913e806"}