{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DOU767N6JIBKDO44R54KRXNIV7","short_pith_number":"pith:DOU767N6","canonical_record":{"source":{"id":"1206.5511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-24T15:47:48Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"bd71e2d48525c6c434955717676c290818654bfa2ac125217092b9e7a71cc239","abstract_canon_sha256":"d690a9b7d9406b5cdeecaed1459a7821fd356cf13dfb33efd90fcf0e5d35ea11"},"schema_version":"1.0"},"canonical_sha256":"1ba9ff7dbe4a02a1bb9c8f78a8dda8aff55a9a951bee516fd71338e8a2593828","source":{"kind":"arxiv","id":"1206.5511","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5511","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5511v1","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5511","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"DOU767N6JIBK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DOU767N6JIBKDO44","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DOU767N6","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DOU767N6JIBKDO44R54KRXNIV7","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-24T15:47:48Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"bd71e2d48525c6c434955717676c290818654bfa2ac125217092b9e7a71cc239","abstract_canon_sha256":"d690a9b7d9406b5cdeecaed1459a7821fd356cf13dfb33efd90fcf0e5d35ea11"},"schema_version":"1.0"},"canonical_sha256":"1ba9ff7dbe4a02a1bb9c8f78a8dda8aff55a9a951bee516fd71338e8a2593828","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:39.885428Z","signature_b64":"Og3aIizaw0DgN+SpZQ8nZ7z72Nj2XxW40+c+W+Hc14IVaUCWbiVLNnV4eTDxMwqL0XtnwXtESBI+lv8s2qySBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ba9ff7dbe4a02a1bb9c8f78a8dda8aff55a9a951bee516fd71338e8a2593828","last_reissued_at":"2026-05-18T03:52:39.884699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:39.884699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5511","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A7QfPDHs2PVaxgILKvTPhFCUXTHEEOv7OB/0oGeJV5tGdGME5xVptr5XuypRvPLGoCs+8bZ8Wi0HItYP1RlMCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:50:26.210529Z"},"content_sha256":"cf3ee1229a158afe3ff42a3e3ccdd9fb255be9157550cf10b00b7b8b9f7f264f","schema_version":"1.0","event_id":"sha256:cf3ee1229a158afe3ff42a3e3ccdd9fb255be9157550cf10b00b7b8b9f7f264f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DOU767N6JIBKDO44R54KRXNIV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hawking mass and local rigidity of minimal two-spheres in three-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Davi M\\'aximo, Ivaldo Nunes","submitted_at":"2012-06-24T15:47:48Z","abstract_excerpt":"We study rigidity of minimal two-spheres $\\Sigma$ that locally maximize the Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature. After assuming strict stability of $\\Sigma$, we prove that a neighborhood of it in $M$ is isometric to one of the deSitter-Schwarzschild metrics on $(- \\epsilon,\\epsilon)\\times \\Sigma$. We also show that if $\\Sigma$ is a critical point for the Hawking mass on the deSitter-Schwarzschild manifold $\\mathbb{R}\\times\\Sph^2$ and can be written as a graph over a slice $\\Sigma_r=\\{r\\}\\times\\mathbb{S}^2$, then $\\Sigma$ itself must b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5511","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:52:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Syj2NTAFpwPNA3o0Ek9iDozYfgcoD1lG+Bhz7gMaLrERJKx+rt2/iLny9kVx4skbuC/69ou1C51gxE8RT+/JDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:50:26.210875Z"},"content_sha256":"c6f7982c30842e93d87ca1eef2f7bb1f61b52227a7d71c2b06dc7345d9c240e9","schema_version":"1.0","event_id":"sha256:c6f7982c30842e93d87ca1eef2f7bb1f61b52227a7d71c2b06dc7345d9c240e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOU767N6JIBKDO44R54KRXNIV7/bundle.json","state_url":"https://pith.science/pith/DOU767N6JIBKDO44R54KRXNIV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOU767N6JIBKDO44R54KRXNIV7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T05:50:26Z","links":{"resolver":"https://pith.science/pith/DOU767N6JIBKDO44R54KRXNIV7","bundle":"https://pith.science/pith/DOU767N6JIBKDO44R54KRXNIV7/bundle.json","state":"https://pith.science/pith/DOU767N6JIBKDO44R54KRXNIV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOU767N6JIBKDO44R54KRXNIV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DOU767N6JIBKDO44R54KRXNIV7","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":"d690a9b7d9406b5cdeecaed1459a7821fd356cf13dfb33efd90fcf0e5d35ea11","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-24T15:47:48Z","title_canon_sha256":"bd71e2d48525c6c434955717676c290818654bfa2ac125217092b9e7a71cc239"},"schema_version":"1.0","source":{"id":"1206.5511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5511","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5511v1","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5511","created_at":"2026-05-18T03:52:39Z"},{"alias_kind":"pith_short_12","alias_value":"DOU767N6JIBK","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DOU767N6JIBKDO44","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DOU767N6","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:c6f7982c30842e93d87ca1eef2f7bb1f61b52227a7d71c2b06dc7345d9c240e9","target":"graph","created_at":"2026-05-18T03:52:39Z","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 study rigidity of minimal two-spheres $\\Sigma$ that locally maximize the Hawking mass on a Riemannian three-manifold with a positive lower bound on its scalar curvature. After assuming strict stability of $\\Sigma$, we prove that a neighborhood of it in $M$ is isometric to one of the deSitter-Schwarzschild metrics on $(- \\epsilon,\\epsilon)\\times \\Sigma$. We also show that if $\\Sigma$ is a critical point for the Hawking mass on the deSitter-Schwarzschild manifold $\\mathbb{R}\\times\\Sph^2$ and can be written as a graph over a slice $\\Sigma_r=\\{r\\}\\times\\mathbb{S}^2$, then $\\Sigma$ itself must b","authors_text":"Davi M\\'aximo, Ivaldo Nunes","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-24T15:47:48Z","title":"Hawking mass and local rigidity of minimal two-spheres in three-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5511","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:cf3ee1229a158afe3ff42a3e3ccdd9fb255be9157550cf10b00b7b8b9f7f264f","target":"record","created_at":"2026-05-18T03:52:39Z","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":"d690a9b7d9406b5cdeecaed1459a7821fd356cf13dfb33efd90fcf0e5d35ea11","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-06-24T15:47:48Z","title_canon_sha256":"bd71e2d48525c6c434955717676c290818654bfa2ac125217092b9e7a71cc239"},"schema_version":"1.0","source":{"id":"1206.5511","kind":"arxiv","version":1}},"canonical_sha256":"1ba9ff7dbe4a02a1bb9c8f78a8dda8aff55a9a951bee516fd71338e8a2593828","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ba9ff7dbe4a02a1bb9c8f78a8dda8aff55a9a951bee516fd71338e8a2593828","first_computed_at":"2026-05-18T03:52:39.884699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:39.884699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Og3aIizaw0DgN+SpZQ8nZ7z72Nj2XxW40+c+W+Hc14IVaUCWbiVLNnV4eTDxMwqL0XtnwXtESBI+lv8s2qySBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:39.885428Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf3ee1229a158afe3ff42a3e3ccdd9fb255be9157550cf10b00b7b8b9f7f264f","sha256:c6f7982c30842e93d87ca1eef2f7bb1f61b52227a7d71c2b06dc7345d9c240e9"],"state_sha256":"de6b9d5d0b3478202d3dcfa4bf9c8050e3b08e9d032557e71fa3f651b9d59349"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MqURgMfwxwtY/cIGakYOavKOjDGp/0BaTYWSoU2Fy2KX4N9cgn12IWffXEpwyAEbrHdGxtSwN212AvlhI5kRBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T05:50:26.212926Z","bundle_sha256":"4d3bb2dd3c086b690695dc3a68d5ac17d5cff2008dad0c132e8c6af8462752db"}}