{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:X6PE2YDMW2KZHTJGVMQPJX3XMG","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":"84a4c31601d9bc0e1509c506e1134f0756d75f9873ec74f056c1429592590754","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-19T19:13:13Z","title_canon_sha256":"4a60f38380261ef076998a5496e5ca461f913849843471bbb4520a7fdc5c3d3d"},"schema_version":"1.0","source":{"id":"0812.3841","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3841","created_at":"2026-07-04T15:49:05Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3841v2","created_at":"2026-07-04T15:49:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3841","created_at":"2026-07-04T15:49:05Z"},{"alias_kind":"pith_short_12","alias_value":"X6PE2YDMW2KZ","created_at":"2026-07-04T15:49:05Z"},{"alias_kind":"pith_short_16","alias_value":"X6PE2YDMW2KZHTJG","created_at":"2026-07-04T15:49:05Z"},{"alias_kind":"pith_short_8","alias_value":"X6PE2YDM","created_at":"2026-07-04T15:49:05Z"}],"graph_snapshots":[{"event_id":"sha256:be4fd0f4eea41e81537a4c332fa6f6a247b2c3c6519e8617d36847290c339608","target":"graph","created_at":"2026-07-04T15:49:05Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0812.3841/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The author proves that there is an open non empty set of metrics on any 3-manifold such that there exists a family of stably embedded minimal 2-spheres whose area is unbounded. This generalizes the work of T. Colding and W. Minicozzi who have shown an analogous result for the torus and B. Dean who showed the positive genus case.","authors_text":"Joel I. Kramer","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-19T19:13:13Z","title":"Examples of stable embedded minimal spheres without area bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3841","kind":"arxiv","version":2},"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":"sha256:6bb10458e12bd8eaa159131182d59b13dd157ccb82a6af0bc778b0116aa150a5","target":"record","created_at":"2026-07-04T15:49:05Z","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":"84a4c31601d9bc0e1509c506e1134f0756d75f9873ec74f056c1429592590754","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-12-19T19:13:13Z","title_canon_sha256":"4a60f38380261ef076998a5496e5ca461f913849843471bbb4520a7fdc5c3d3d"},"schema_version":"1.0","source":{"id":"0812.3841","kind":"arxiv","version":2}},"canonical_sha256":"bf9e4d606cb69593cd26ab20f4df7761b2f4ac88624734516092fe0cb6130f51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf9e4d606cb69593cd26ab20f4df7761b2f4ac88624734516092fe0cb6130f51","first_computed_at":"2026-07-04T15:49:05.853402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:49:05.853402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQ2L3mQNkQGsrlpAVh5eH7X1oKJnmtmKapjqA8dwgHpNWJUB1uRIjR5pmE7OS3NvHd4PyvLEuxt2WWm0AI9+DA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:49:05.853787Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3841","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bb10458e12bd8eaa159131182d59b13dd157ccb82a6af0bc778b0116aa150a5","sha256:be4fd0f4eea41e81537a4c332fa6f6a247b2c3c6519e8617d36847290c339608"],"state_sha256":"63efe4fb4ab8c2c63a2f86649c897d16cb8589b824fa68ab86f0c03a59ad0f69"}