{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:PGPKKYCDZMP4ATHWMBCTGAGCC3","short_pith_number":"pith:PGPKKYCD","schema_version":"1.0","canonical_sha256":"799ea56043cb1fc04cf660453300c216c0d0e5e407efb0ab3ff97c23ccae9637","source":{"kind":"arxiv","id":"2303.08186","version":1},"attestation_state":"computed","paper":{"title":"A sharp Harnack bound for a nonlocal heat equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mateusz Dembny, Miko{\\l}aj Sier\\.z\\k{e}ga","submitted_at":"2023-03-14T19:13:28Z","abstract_excerpt":"A sharp double-sided Harnack bound is derived for positive solutions of a fractional order heat equation."},"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":"2303.08186","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-03-14T19:13:28Z","cross_cats_sorted":[],"title_canon_sha256":"d043cd1083e169bfb298c316c718ced58d1dd8d3b79e56305c4b06b30eff436d","abstract_canon_sha256":"b744a464a2165d583192ba26f7767f55b5d2e88e2957460aed7fd184ccd7749b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:51:16.931423Z","signature_b64":"iUI+frclEOpj91NEMRpx1jDixRjVB3uoB8PtD2DTj126FkW/Od2D1hJq9z2lJLxnBwGDyy9eUV3jsff/8U+JAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"799ea56043cb1fc04cf660453300c216c0d0e5e407efb0ab3ff97c23ccae9637","last_reissued_at":"2026-07-05T05:51:16.930968Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:51:16.930968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A sharp Harnack bound for a nonlocal heat equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mateusz Dembny, Miko{\\l}aj Sier\\.z\\k{e}ga","submitted_at":"2023-03-14T19:13:28Z","abstract_excerpt":"A sharp double-sided Harnack bound is derived for positive solutions of a fractional order heat equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.08186","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/2303.08186/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":"2303.08186","created_at":"2026-07-05T05:51:16.931027+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.08186v1","created_at":"2026-07-05T05:51:16.931027+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.08186","created_at":"2026-07-05T05:51:16.931027+00:00"},{"alias_kind":"pith_short_12","alias_value":"PGPKKYCDZMP4","created_at":"2026-07-05T05:51:16.931027+00:00"},{"alias_kind":"pith_short_16","alias_value":"PGPKKYCDZMP4ATHW","created_at":"2026-07-05T05:51:16.931027+00:00"},{"alias_kind":"pith_short_8","alias_value":"PGPKKYCD","created_at":"2026-07-05T05:51:16.931027+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.08187","citing_title":"Geometric aspects of the Harnack Inequality for a nonlocal heat equation","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3","json":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3.json","graph_json":"https://pith.science/api/pith-number/PGPKKYCDZMP4ATHWMBCTGAGCC3/graph.json","events_json":"https://pith.science/api/pith-number/PGPKKYCDZMP4ATHWMBCTGAGCC3/events.json","paper":"https://pith.science/paper/PGPKKYCD"},"agent_actions":{"view_html":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3","download_json":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3.json","view_paper":"https://pith.science/paper/PGPKKYCD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.08186&json=true","fetch_graph":"https://pith.science/api/pith-number/PGPKKYCDZMP4ATHWMBCTGAGCC3/graph.json","fetch_events":"https://pith.science/api/pith-number/PGPKKYCDZMP4ATHWMBCTGAGCC3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3/action/storage_attestation","attest_author":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3/action/author_attestation","sign_citation":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3/action/citation_signature","submit_replication":"https://pith.science/pith/PGPKKYCDZMP4ATHWMBCTGAGCC3/action/replication_record"}},"created_at":"2026-07-05T05:51:16.931027+00:00","updated_at":"2026-07-05T05:51:16.931027+00:00"}