{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V7IZFMCGTSYMYBVFRBK7PBF7N3","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":"751dfbcda0afed3703117d9d1de13ba76795f9ae6d8ce7540af00dd9896f5578","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-06T20:34:00Z","title_canon_sha256":"cafe27e8e746e902c216295d0a63252462d1f0dbcd535fe60abbd3738f5107a0"},"schema_version":"1.0","source":{"id":"1501.01291","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01291","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01291v3","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01291","created_at":"2026-05-18T01:26:31Z"},{"alias_kind":"pith_short_12","alias_value":"V7IZFMCGTSYM","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V7IZFMCGTSYMYBVF","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V7IZFMCG","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:cc9cbf460ba2577a8fb4dfd87ebfd0de0e39fd780a6ab754ba6f187e9752dc2e","target":"graph","created_at":"2026-05-18T01:26:31Z","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"},"paper":{"abstract_excerpt":"In this paper we analyze Ricci flows on which the scalar curvature is globally or locally bounded from above by a uniform or time-dependent constant. On such Ricci flows we establish a new time-derivative bound for solutions to the heat equation. Based on this bound, we solve several open problems: 1. distance distortion estimates, 2. the existence of a cutoff function, 3. Gaussian bounds for heat kernels, and, 4. a backward pseudolocality theorem, which states that a curvature bound at a later time implies a curvature bound at a slightly earlier time.\n  Using the backward pseudolocality theor","authors_text":"Qi S. Zhang, Richard H. Bamler","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-06T20:34:00Z","title":"Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01291","kind":"arxiv","version":3},"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":"sha256:5b486c2fa54cdb028bdebcf7b75ed5c4a2bbce8045196aca705c3c16e4dcfae4","target":"record","created_at":"2026-05-18T01:26:31Z","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":"751dfbcda0afed3703117d9d1de13ba76795f9ae6d8ce7540af00dd9896f5578","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-06T20:34:00Z","title_canon_sha256":"cafe27e8e746e902c216295d0a63252462d1f0dbcd535fe60abbd3738f5107a0"},"schema_version":"1.0","source":{"id":"1501.01291","kind":"arxiv","version":3}},"canonical_sha256":"afd192b0469cb0cc06a58855f784bf6ec761b5eb8f79c71586a8618fd3d12474","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afd192b0469cb0cc06a58855f784bf6ec761b5eb8f79c71586a8618fd3d12474","first_computed_at":"2026-05-18T01:26:31.760789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:31.760789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I3zdDey5r/y0SFFqcNxy1m+dkhKoUIuCxDHlei27s1yW8qNWBYgESu2n9z38r+QCW6J32jd5AYz+PPrkwUyJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:31.761473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01291","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b486c2fa54cdb028bdebcf7b75ed5c4a2bbce8045196aca705c3c16e4dcfae4","sha256:cc9cbf460ba2577a8fb4dfd87ebfd0de0e39fd780a6ab754ba6f187e9752dc2e"],"state_sha256":"e68a9f712e516b87d7caea2eef4eb47198fed0c37a6a912236ba173354a672a7"}