{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:G3G5JJL6K62YBHHKXT37IAA4BP","short_pith_number":"pith:G3G5JJL6","schema_version":"1.0","canonical_sha256":"36cdd4a57e57b5809ceabcf7f4001c0be1d01e4f2e0f6132ea7b8146252c61e7","source":{"kind":"arxiv","id":"1510.04332","version":3},"attestation_state":"computed","paper":{"title":"Pseudo-locality for a coupled Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bin Guo, Duong H. Phong, Zhijie Huang","submitted_at":"2015-10-14T22:18:58Z","abstract_excerpt":"Let $(M,g,\\phi)$ be a solution to the Ricci flow coupled with the heat equation for a scalar field $\\phi$. We show that a complete, $\\kappa$-noncollapsed solution $(M,g,\\phi)$ to this coupled Ricci flow with a Type I singularity at time $T<\\infty$ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base point is Type I singular. A key ingredient is a version of Perelman pseudo-locality for the coupled Ricci flow."},"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":"1510.04332","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-14T22:18:58Z","cross_cats_sorted":[],"title_canon_sha256":"ebd432ca8e1a56584ed49e89addac40e0d3495b78ba623945ecd8fe1ac9bdc11","abstract_canon_sha256":"7c041ee076261582393fd59ddfcdfdb4c92bf34bbbee13852de455f5fdad2ee9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:56.369546Z","signature_b64":"MnwXZluAFgoBt3YD7BMOZaY944aKjhPrxZ5FWeoJm/y1jO5b3Npphcy9pvcQEDOR90a0t9jwS4BsAL2+UAu+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36cdd4a57e57b5809ceabcf7f4001c0be1d01e4f2e0f6132ea7b8146252c61e7","last_reissued_at":"2026-05-18T01:25:56.368966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:56.368966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pseudo-locality for a coupled Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Bin Guo, Duong H. Phong, Zhijie Huang","submitted_at":"2015-10-14T22:18:58Z","abstract_excerpt":"Let $(M,g,\\phi)$ be a solution to the Ricci flow coupled with the heat equation for a scalar field $\\phi$. We show that a complete, $\\kappa$-noncollapsed solution $(M,g,\\phi)$ to this coupled Ricci flow with a Type I singularity at time $T<\\infty$ will converge to a non-trivial Ricci soliton after parabolic rescaling, if the base point is Type I singular. A key ingredient is a version of Perelman pseudo-locality for the coupled Ricci flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04332","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":""},"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":"1510.04332","created_at":"2026-05-18T01:25:56.369060+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.04332v3","created_at":"2026-05-18T01:25:56.369060+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04332","created_at":"2026-05-18T01:25:56.369060+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3G5JJL6K62Y","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3G5JJL6K62YBHHK","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3G5JJL6","created_at":"2026-05-18T12:29:22.688609+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/G3G5JJL6K62YBHHKXT37IAA4BP","json":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP.json","graph_json":"https://pith.science/api/pith-number/G3G5JJL6K62YBHHKXT37IAA4BP/graph.json","events_json":"https://pith.science/api/pith-number/G3G5JJL6K62YBHHKXT37IAA4BP/events.json","paper":"https://pith.science/paper/G3G5JJL6"},"agent_actions":{"view_html":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP","download_json":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP.json","view_paper":"https://pith.science/paper/G3G5JJL6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.04332&json=true","fetch_graph":"https://pith.science/api/pith-number/G3G5JJL6K62YBHHKXT37IAA4BP/graph.json","fetch_events":"https://pith.science/api/pith-number/G3G5JJL6K62YBHHKXT37IAA4BP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP/action/storage_attestation","attest_author":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP/action/author_attestation","sign_citation":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP/action/citation_signature","submit_replication":"https://pith.science/pith/G3G5JJL6K62YBHHKXT37IAA4BP/action/replication_record"}},"created_at":"2026-05-18T01:25:56.369060+00:00","updated_at":"2026-05-18T01:25:56.369060+00:00"}