{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:VNPBMBF4XAL3IJIOP2VARSLW4Y","short_pith_number":"pith:VNPBMBF4","canonical_record":{"source":{"id":"math/0303109","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-03-10T16:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"6628f5ad4ae85b171110f13e3d7291638c8fb48090f41cf7a51012e15c39a1f1","abstract_canon_sha256":"06f9f66a55621cd08fde37bb5b3ef7c233519ebb81079ad316012a3ef7191eaa"},"schema_version":"1.0"},"canonical_sha256":"ab5e1604bcb817b4250e7eaa08c976e6169b9b74fbf2acf2b62480fdf6b6e13d","source":{"kind":"arxiv","id":"math/0303109","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303109","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303109v1","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303109","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"VNPBMBF4XAL3","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"pith_short_16","alias_value":"VNPBMBF4XAL3IJIO","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"pith_short_8","alias_value":"VNPBMBF4","created_at":"2026-07-04T14:37:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:VNPBMBF4XAL3IJIOP2VARSLW4Y","target":"record","payload":{"canonical_record":{"source":{"id":"math/0303109","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-03-10T16:44:35Z","cross_cats_sorted":[],"title_canon_sha256":"6628f5ad4ae85b171110f13e3d7291638c8fb48090f41cf7a51012e15c39a1f1","abstract_canon_sha256":"06f9f66a55621cd08fde37bb5b3ef7c233519ebb81079ad316012a3ef7191eaa"},"schema_version":"1.0"},"canonical_sha256":"ab5e1604bcb817b4250e7eaa08c976e6169b9b74fbf2acf2b62480fdf6b6e13d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:08.193163Z","signature_b64":"XCatBHj/EsiOwabojZf7IHazDBqeXL87nFLh/8JAHvtQY7Rn1KigZBBG318XeCpOLhBUjEodzYkdZsgU371WAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab5e1604bcb817b4250e7eaa08c976e6169b9b74fbf2acf2b62480fdf6b6e13d","last_reissued_at":"2026-07-04T14:37:08.192747Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:08.192747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0303109","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":"2026-07-04T14:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXxfe4dM+SN0Zy7z2mjSNiWhx67qVFGJRjGMur5mLTZ9lGzsAoMSUf0Il0eBZ1uZ17YAEe7BzIs1gLSKF3bjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T22:01:50.657733Z"},"content_sha256":"594c198c28bebefe9e85289de0b81413fbb5e6291c43db1966fca7916977907c","schema_version":"1.0","event_id":"sha256:594c198c28bebefe9e85289de0b81413fbb5e6291c43db1966fca7916977907c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:VNPBMBF4XAL3IJIOP2VARSLW4Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ricci flow with surgery on three-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Grisha Perelman","submitted_at":"2003-03-10T16:44:35Z","abstract_excerpt":"This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print; the exceptions are (1) the statement that manifolds that can collapse with local lower bound on sectional curvature are graph manifolds - this is deferred to a separate paper, since the proof has nothing to do with the Ricci flow, and (2) the claim on the lower bound for the volume of maximal horns and the smoothness of solutions from some time on, which turned out to be unjustified and, on the other hand, irre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303109","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0303109/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:37:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h6HTLGwUsm5tgxcsrSUiQ2GICdFsMHg6fWtng7gBcSUC6gvKFJSQ+WWr9fBoNMD25GaEGRnZzDuqKJT6PgaMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T22:01:50.658117Z"},"content_sha256":"e95e5a0338999e5e5fefc675ad11a20c0538c06606e19a21194774bb72ccea76","schema_version":"1.0","event_id":"sha256:e95e5a0338999e5e5fefc675ad11a20c0538c06606e19a21194774bb72ccea76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNPBMBF4XAL3IJIOP2VARSLW4Y/bundle.json","state_url":"https://pith.science/pith/VNPBMBF4XAL3IJIOP2VARSLW4Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNPBMBF4XAL3IJIOP2VARSLW4Y/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":"2026-07-12T22:01:50Z","links":{"resolver":"https://pith.science/pith/VNPBMBF4XAL3IJIOP2VARSLW4Y","bundle":"https://pith.science/pith/VNPBMBF4XAL3IJIOP2VARSLW4Y/bundle.json","state":"https://pith.science/pith/VNPBMBF4XAL3IJIOP2VARSLW4Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNPBMBF4XAL3IJIOP2VARSLW4Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:VNPBMBF4XAL3IJIOP2VARSLW4Y","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":"06f9f66a55621cd08fde37bb5b3ef7c233519ebb81079ad316012a3ef7191eaa","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2003-03-10T16:44:35Z","title_canon_sha256":"6628f5ad4ae85b171110f13e3d7291638c8fb48090f41cf7a51012e15c39a1f1"},"schema_version":"1.0","source":{"id":"math/0303109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303109","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303109v1","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303109","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"pith_short_12","alias_value":"VNPBMBF4XAL3","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"pith_short_16","alias_value":"VNPBMBF4XAL3IJIO","created_at":"2026-07-04T14:37:08Z"},{"alias_kind":"pith_short_8","alias_value":"VNPBMBF4","created_at":"2026-07-04T14:37:08Z"}],"graph_snapshots":[{"event_id":"sha256:e95e5a0338999e5e5fefc675ad11a20c0538c06606e19a21194774bb72ccea76","target":"graph","created_at":"2026-07-04T14:37:08Z","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/math/0303109/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print; the exceptions are (1) the statement that manifolds that can collapse with local lower bound on sectional curvature are graph manifolds - this is deferred to a separate paper, since the proof has nothing to do with the Ricci flow, and (2) the claim on the lower bound for the volume of maximal horns and the smoothness of solutions from some time on, which turned out to be unjustified and, on the other hand, irre","authors_text":"Grisha Perelman","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2003-03-10T16:44:35Z","title":"Ricci flow with surgery on three-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303109","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":"sha256:594c198c28bebefe9e85289de0b81413fbb5e6291c43db1966fca7916977907c","target":"record","created_at":"2026-07-04T14:37:08Z","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":"06f9f66a55621cd08fde37bb5b3ef7c233519ebb81079ad316012a3ef7191eaa","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2003-03-10T16:44:35Z","title_canon_sha256":"6628f5ad4ae85b171110f13e3d7291638c8fb48090f41cf7a51012e15c39a1f1"},"schema_version":"1.0","source":{"id":"math/0303109","kind":"arxiv","version":1}},"canonical_sha256":"ab5e1604bcb817b4250e7eaa08c976e6169b9b74fbf2acf2b62480fdf6b6e13d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab5e1604bcb817b4250e7eaa08c976e6169b9b74fbf2acf2b62480fdf6b6e13d","first_computed_at":"2026-07-04T14:37:08.192747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:37:08.192747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XCatBHj/EsiOwabojZf7IHazDBqeXL87nFLh/8JAHvtQY7Rn1KigZBBG318XeCpOLhBUjEodzYkdZsgU371WAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:37:08.193163Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0303109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:594c198c28bebefe9e85289de0b81413fbb5e6291c43db1966fca7916977907c","sha256:e95e5a0338999e5e5fefc675ad11a20c0538c06606e19a21194774bb72ccea76"],"state_sha256":"2d9d372340b038f40c21a633cbe0bafedf87f84bed322f982e1d0aed47418d6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iU9gAvQMVQh3+d6QMzn6ROrBbMh0XxY4YGYtn4dxh+NFgIHJAZrpDG6HbLhSuEZqL0IU+BfZghZU3E4QqcZ/Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T22:01:50.661299Z","bundle_sha256":"ed7a08a18fb3fa5e2f1b4ad201bbc2783f5cac36b96f24aa1228c5d5a8b29164"}}