{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RHLHF2DFBKPZBPE2NYTLZ7T7QX","short_pith_number":"pith:RHLHF2DF","schema_version":"1.0","canonical_sha256":"89d672e8650a9f90bc9a6e26bcfe7f85ce5860a671a8c5545f6402904e93be9d","source":{"kind":"arxiv","id":"1611.06137","version":2},"attestation_state":"computed","paper":{"title":"Local control on the geometry in 3D Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Miles Simon, Peter M. Topping","submitted_at":"2016-11-18T16:02:26Z","abstract_excerpt":"The geometry of a ball within a Riemannian manifold is coarsely controlled if it has a lower bound on its Ricci curvature and a positive lower bound on its volume. We prove that such coarse local geometric control must persist for a definite amount of time under three-dimensional Ricci flow, and leads to local C/t decay of the full curvature tensor, irrespective of what is happening beyond the local region.\n  As a by-product, our results generalise the Pseudolocality theorem of Perelman and Tian-Wang in this dimension by not requiring the Ricci curvature to be almost-positive, and not asking t"},"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":"1611.06137","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-18T16:02:26Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"e02ff85e72433e8d9eb8b909477195f7c718c76fd371db4aeacfaaa7a93a605e","abstract_canon_sha256":"0cc04176e963bdf2fee564d170abcf7f5b7032621277ae604c7c07b1eb13cda9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:12.731102Z","signature_b64":"kgkoA7E7E+0Zh/xPOMu/bDCFOHUcheMrrS3KGhyor+F4lGRODJZnR3dv1ZrZaO5+dgiWosXdynXvHfhNfP+GCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89d672e8650a9f90bc9a6e26bcfe7f85ce5860a671a8c5545f6402904e93be9d","last_reissued_at":"2026-05-18T00:41:12.730251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:12.730251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local control on the geometry in 3D Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Miles Simon, Peter M. Topping","submitted_at":"2016-11-18T16:02:26Z","abstract_excerpt":"The geometry of a ball within a Riemannian manifold is coarsely controlled if it has a lower bound on its Ricci curvature and a positive lower bound on its volume. We prove that such coarse local geometric control must persist for a definite amount of time under three-dimensional Ricci flow, and leads to local C/t decay of the full curvature tensor, irrespective of what is happening beyond the local region.\n  As a by-product, our results generalise the Pseudolocality theorem of Perelman and Tian-Wang in this dimension by not requiring the Ricci curvature to be almost-positive, and not asking t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06137","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.06137","created_at":"2026-05-18T00:41:12.730388+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.06137v2","created_at":"2026-05-18T00:41:12.730388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06137","created_at":"2026-05-18T00:41:12.730388+00:00"},{"alias_kind":"pith_short_12","alias_value":"RHLHF2DFBKPZ","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"RHLHF2DFBKPZBPE2","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"RHLHF2DF","created_at":"2026-05-18T12:30:41.710351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX","json":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX.json","graph_json":"https://pith.science/api/pith-number/RHLHF2DFBKPZBPE2NYTLZ7T7QX/graph.json","events_json":"https://pith.science/api/pith-number/RHLHF2DFBKPZBPE2NYTLZ7T7QX/events.json","paper":"https://pith.science/paper/RHLHF2DF"},"agent_actions":{"view_html":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX","download_json":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX.json","view_paper":"https://pith.science/paper/RHLHF2DF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.06137&json=true","fetch_graph":"https://pith.science/api/pith-number/RHLHF2DFBKPZBPE2NYTLZ7T7QX/graph.json","fetch_events":"https://pith.science/api/pith-number/RHLHF2DFBKPZBPE2NYTLZ7T7QX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX/action/storage_attestation","attest_author":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX/action/author_attestation","sign_citation":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX/action/citation_signature","submit_replication":"https://pith.science/pith/RHLHF2DFBKPZBPE2NYTLZ7T7QX/action/replication_record"}},"created_at":"2026-05-18T00:41:12.730388+00:00","updated_at":"2026-05-18T00:41:12.730388+00:00"}