{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:DVVL6FPOMWZZSLXXHGMID4ONSC","short_pith_number":"pith:DVVL6FPO","schema_version":"1.0","canonical_sha256":"1d6abf15ee65b3992ef7399881f1cd908ea690a92f0a56aea7d71300e1191a40","source":{"kind":"arxiv","id":"math/0307245","version":1},"attestation_state":"computed","paper":{"title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Grisha Perelman","submitted_at":"2003-07-17T15:26:38Z","abstract_excerpt":"Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci flow with surgery, defined in our previous paper math.DG/0303109, becomes extinct in finite time. The proof uses a version of the minimal disk argument from 1999 paper by Richard Hamilton, and a regularization of the curve shortening flow, worked out by Altschuler and Grayson."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0307245","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-07-17T15:26:38Z","cross_cats_sorted":[],"title_canon_sha256":"105070ba1d8296e692ef7749cfb5d62d950d6197129a0b49de8ed242352a5587","abstract_canon_sha256":"248eb45fc91f9d4b811418cc7b4b9209fdb56ba55b22c4c75ac853d265a65905"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:36.384685Z","signature_b64":"C0W3DG78ZWxZsQgB8dvrZWz8ok7BV12nRjcWQXAJ84G7AzEQkMvV1Bc2uYmQKs1nIJdZJsN3emDNj4dPgIvTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d6abf15ee65b3992ef7399881f1cd908ea690a92f0a56aea7d71300e1191a40","last_reissued_at":"2026-07-04T14:37:36.384240Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:36.384240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Grisha Perelman","submitted_at":"2003-07-17T15:26:38Z","abstract_excerpt":"Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci flow with surgery, defined in our previous paper math.DG/0303109, becomes extinct in finite time. The proof uses a version of the minimal disk argument from 1999 paper by Richard Hamilton, and a regularization of the curve shortening flow, worked out by Altschuler and Grayson."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307245","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/0307245/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0307245","created_at":"2026-07-04T14:37:36.384308+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0307245v1","created_at":"2026-07-04T14:37:36.384308+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307245","created_at":"2026-07-04T14:37:36.384308+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVVL6FPOMWZZ","created_at":"2026-07-04T14:37:36.384308+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVVL6FPOMWZZSLXX","created_at":"2026-07-04T14:37:36.384308+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVVL6FPO","created_at":"2026-07-04T14:37:36.384308+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":21,"internal_anchor_count":15,"sample":[{"citing_arxiv_id":"2606.13553","citing_title":"A Levi-type decomposition on two-step solvable Lie algebras with a complex structure","ref_index":33,"is_internal_anchor":true},{"citing_arxiv_id":"2606.13301","citing_title":"Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three","ref_index":10,"is_internal_anchor":true},{"citing_arxiv_id":"2606.09017","citing_title":"The Ollivier Ricci flow with prescribed curvature on infinite graphs","ref_index":30,"is_internal_anchor":true},{"citing_arxiv_id":"2606.06619","citing_title":"On the structure of complete $G_2$-solitons","ref_index":54,"is_internal_anchor":true},{"citing_arxiv_id":"2605.23679","citing_title":"Geometrisation of 3-manifolds","ref_index":4,"is_internal_anchor":true},{"citing_arxiv_id":"2302.04964","citing_title":"Ancient Ricci flows of bounded girth","ref_index":53,"is_internal_anchor":true},{"citing_arxiv_id":"2411.19400","citing_title":"Exotic aspherical 4-manifolds","ref_index":25,"is_internal_anchor":true},{"citing_arxiv_id":"2509.16553","citing_title":"Cosmological viability of anisotropic inflation in Thurston spacetimes","ref_index":18,"is_internal_anchor":true},{"citing_arxiv_id":"2511.20568","citing_title":"On the rigidity of special and exceptional geometries with torsion a closed $3$-form","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"2605.14572","citing_title":"Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes","ref_index":14,"is_internal_anchor":true},{"citing_arxiv_id":"2510.20320","citing_title":"Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow","ref_index":11,"is_internal_anchor":true},{"citing_arxiv_id":"2512.07708","citing_title":"Bianchi cosmologies in a Thurston-based theory of gravity","ref_index":46,"is_internal_anchor":true},{"citing_arxiv_id":"2603.10479","citing_title":"The Ricci flow with prescribed curvature on graphs","ref_index":28,"is_internal_anchor":true},{"citing_arxiv_id":"2605.14572","citing_title":"Modifications of CMB Temperature and Polarization Quadrupole Signals in Thurston Spacetimes","ref_index":14,"is_internal_anchor":true},{"citing_arxiv_id":"2604.02632","citing_title":"The Calabi flow with prescribed curvature on finite graphs","ref_index":27,"is_internal_anchor":true},{"citing_arxiv_id":"2605.05599","citing_title":"Notes on harmonic-Ricci flow on surface","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18678","citing_title":"The perturbative Ricci flow in gravity","ref_index":34,"is_internal_anchor":false},{"citing_arxiv_id":"2604.10007","citing_title":"On weak formulations of (super) Ricci flows","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06344","citing_title":"On the Chern-Ricci form of a twisted almost K\\\"{a}hler structure","ref_index":8,"is_internal_anchor":false},{"citing_arxiv_id":"2604.20761","citing_title":"Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02279","citing_title":"Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC","json":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC.json","graph_json":"https://pith.science/api/pith-number/DVVL6FPOMWZZSLXXHGMID4ONSC/graph.json","events_json":"https://pith.science/api/pith-number/DVVL6FPOMWZZSLXXHGMID4ONSC/events.json","paper":"https://pith.science/paper/DVVL6FPO"},"agent_actions":{"view_html":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC","download_json":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC.json","view_paper":"https://pith.science/paper/DVVL6FPO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0307245&json=true","fetch_graph":"https://pith.science/api/pith-number/DVVL6FPOMWZZSLXXHGMID4ONSC/graph.json","fetch_events":"https://pith.science/api/pith-number/DVVL6FPOMWZZSLXXHGMID4ONSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC/action/storage_attestation","attest_author":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC/action/author_attestation","sign_citation":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC/action/citation_signature","submit_replication":"https://pith.science/pith/DVVL6FPOMWZZSLXXHGMID4ONSC/action/replication_record"}},"created_at":"2026-07-04T14:37:36.384308+00:00","updated_at":"2026-07-04T14:37:36.384308+00:00"}