{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:NXVMJTYKIEPPIPBSRGH2SUR7IC","short_pith_number":"pith:NXVMJTYK","schema_version":"1.0","canonical_sha256":"6deac4cf0a411ef43c32898fa9523f409ef975b1417cf4374c1dc6e214855522","source":{"kind":"arxiv","id":"2008.07093","version":3},"attestation_state":"computed","paper":{"title":"Entropy and heat kernel bounds on a Ricci flow background","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Richard H Bamler","submitted_at":"2020-08-17T05:27:42Z","abstract_excerpt":"In this paper we establish new geometric and analytic bounds for Ricci flows, which will form the basis of a compactness, partial regularity and structure theory for Ricci flows in [Bam20a, Bam20b].\n  The bounds are optimal up to a constant that only depends on the dimension and possibly a lower scalar curvature bound. In the special case in which the flow consists of Einstein metrics, these bounds agree with the optimal bounds for spaces with Ricci curvature bounded from below. Moreover, our bounds are local in the sense that if a bound depends on the collapsedness of the underlying flow, the"},"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":"2008.07093","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-08-17T05:27:42Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f7e74373c50a13f7996d98501554dc99e8e8546ade34107757bca1bf6a8876f6","abstract_canon_sha256":"93d01ee51da01e4ceb6d7ba5e39df7d230ca54b9a502b47ec53c0092bc7dfcfe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:16:29.983873Z","signature_b64":"H2aXvVZTzmaZ/tl3Q+X1HZfC1QrHifIYrHDWxC+9Thx6JNftao0vJIajY9xUNRn1kJAvzECMEvVeF4ztjKguCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6deac4cf0a411ef43c32898fa9523f409ef975b1417cf4374c1dc6e214855522","last_reissued_at":"2026-07-05T03:16:29.983402Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:16:29.983402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy and heat kernel bounds on a Ricci flow background","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Richard H Bamler","submitted_at":"2020-08-17T05:27:42Z","abstract_excerpt":"In this paper we establish new geometric and analytic bounds for Ricci flows, which will form the basis of a compactness, partial regularity and structure theory for Ricci flows in [Bam20a, Bam20b].\n  The bounds are optimal up to a constant that only depends on the dimension and possibly a lower scalar curvature bound. In the special case in which the flow consists of Einstein metrics, these bounds agree with the optimal bounds for spaces with Ricci curvature bounded from below. Moreover, our bounds are local in the sense that if a bound depends on the collapsedness of the underlying flow, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.07093","kind":"arxiv","version":3},"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/2008.07093/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":"2008.07093","created_at":"2026-07-05T03:16:29.983458+00:00"},{"alias_kind":"arxiv_version","alias_value":"2008.07093v3","created_at":"2026-07-05T03:16:29.983458+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.07093","created_at":"2026-07-05T03:16:29.983458+00:00"},{"alias_kind":"pith_short_12","alias_value":"NXVMJTYKIEPP","created_at":"2026-07-05T03:16:29.983458+00:00"},{"alias_kind":"pith_short_16","alias_value":"NXVMJTYKIEPPIPBS","created_at":"2026-07-05T03:16:29.983458+00:00"},{"alias_kind":"pith_short_8","alias_value":"NXVMJTYK","created_at":"2026-07-05T03:16:29.983458+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.17402","citing_title":"Convergence of Scalar Curvature of Long Time K\\\"ahler-Ricci Flow on K\\\"ahler Manifold","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2606.13301","citing_title":"Gromov-Hausdorff convergence of time-slices of singular Ricci flows in dimension three","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2606.12379","citing_title":"A Local Singularity Analysis for the Ricci Flow and its Applications to Ricci Flows with Bounded Scalar Curvature -- Part II","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21193","citing_title":"Sharp Gaussian Isoperimetry along a Ricci Flow","ref_index":2,"is_internal_anchor":false},{"citing_arxiv_id":"2510.20320","citing_title":"Strong uniqueness of tangent flows at cylindrical singularities in Ricci flow","ref_index":1,"is_internal_anchor":false},{"citing_arxiv_id":"2604.04710","citing_title":"Gromov-Hausdorff limits of the Chern-Ricci flow on smooth Hermitian minimal models of general type","ref_index":2,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC","json":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC.json","graph_json":"https://pith.science/api/pith-number/NXVMJTYKIEPPIPBSRGH2SUR7IC/graph.json","events_json":"https://pith.science/api/pith-number/NXVMJTYKIEPPIPBSRGH2SUR7IC/events.json","paper":"https://pith.science/paper/NXVMJTYK"},"agent_actions":{"view_html":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC","download_json":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC.json","view_paper":"https://pith.science/paper/NXVMJTYK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2008.07093&json=true","fetch_graph":"https://pith.science/api/pith-number/NXVMJTYKIEPPIPBSRGH2SUR7IC/graph.json","fetch_events":"https://pith.science/api/pith-number/NXVMJTYKIEPPIPBSRGH2SUR7IC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC/action/storage_attestation","attest_author":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC/action/author_attestation","sign_citation":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC/action/citation_signature","submit_replication":"https://pith.science/pith/NXVMJTYKIEPPIPBSRGH2SUR7IC/action/replication_record"}},"created_at":"2026-07-05T03:16:29.983458+00:00","updated_at":"2026-07-05T03:16:29.983458+00:00"}