{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:FIWXHHQK2YGALYUJB5TDRF5FZ4","short_pith_number":"pith:FIWXHHQK","schema_version":"1.0","canonical_sha256":"2a2d739e0ad60c05e2890f663897a5cf140830b018235bf7c303e3b0c34c2e4b","source":{"kind":"arxiv","id":"math/0306129","version":1},"attestation_state":"computed","paper":{"title":"Critical behavior in Ricci flow","license":"","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"David Garfinkle, James Isenberg","submitted_at":"2003-06-07T03:14:20Z","abstract_excerpt":"We use numerical techniques to study the formation of singularities in Ricci flow. Comparing the Ricci flows corresponding to a one parameter family of initial geometries on S^3 with varying amounts of S^2 neck pinching, we find critical behavior at the threshold of singularity formation."},"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/0306129","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2003-06-07T03:14:20Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"1d5412d591ed2280c00ee0563a9acf1086ce3603f1b2094fd70de41836c0d156","abstract_canon_sha256":"5396544608a8e034fcf1af2df12a2ef85d2191e238b26d1a8f384c43a7d4d463"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:37:23.259409Z","signature_b64":"WgVluF3hu6ZnWW/LeW7JZvOP/ARU+/k1AgR1tXQGNuOff2XZUi7iaYqhX1UAeLeFsNWQq/rlVZiY3RUoR1QjAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a2d739e0ad60c05e2890f663897a5cf140830b018235bf7c303e3b0c34c2e4b","last_reissued_at":"2026-07-04T14:37:23.259007Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:37:23.259007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical behavior in Ricci flow","license":"","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"David Garfinkle, James Isenberg","submitted_at":"2003-06-07T03:14:20Z","abstract_excerpt":"We use numerical techniques to study the formation of singularities in Ricci flow. Comparing the Ricci flows corresponding to a one parameter family of initial geometries on S^3 with varying amounts of S^2 neck pinching, we find critical behavior at the threshold of singularity formation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306129","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/0306129/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/0306129","created_at":"2026-07-04T14:37:23.259065+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0306129v1","created_at":"2026-07-04T14:37:23.259065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0306129","created_at":"2026-07-04T14:37:23.259065+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIWXHHQK2YGA","created_at":"2026-07-04T14:37:23.259065+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIWXHHQK2YGALYUJ","created_at":"2026-07-04T14:37:23.259065+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIWXHHQK","created_at":"2026-07-04T14:37:23.259065+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1202.5809","citing_title":"Dynamical Boson Stars","ref_index":206,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4","json":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4.json","graph_json":"https://pith.science/api/pith-number/FIWXHHQK2YGALYUJB5TDRF5FZ4/graph.json","events_json":"https://pith.science/api/pith-number/FIWXHHQK2YGALYUJB5TDRF5FZ4/events.json","paper":"https://pith.science/paper/FIWXHHQK"},"agent_actions":{"view_html":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4","download_json":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4.json","view_paper":"https://pith.science/paper/FIWXHHQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0306129&json=true","fetch_graph":"https://pith.science/api/pith-number/FIWXHHQK2YGALYUJB5TDRF5FZ4/graph.json","fetch_events":"https://pith.science/api/pith-number/FIWXHHQK2YGALYUJB5TDRF5FZ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4/action/storage_attestation","attest_author":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4/action/author_attestation","sign_citation":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4/action/citation_signature","submit_replication":"https://pith.science/pith/FIWXHHQK2YGALYUJB5TDRF5FZ4/action/replication_record"}},"created_at":"2026-07-04T14:37:23.259065+00:00","updated_at":"2026-07-04T14:37:23.259065+00:00"}