{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:63S5K2UXJ6A7MXYUR4N3CGLT37","short_pith_number":"pith:63S5K2UX","schema_version":"1.0","canonical_sha256":"f6e5d56a974f81f65f148f1bb11973dfc983f705bf6f3835522e961fb321e69f","source":{"kind":"arxiv","id":"2608.11931","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Alberto G. Setti, Bobo Hua, Davide Bianchi, Rados{\\l}aw K. Wojciechowski","submitted_at":"2026-08-12T11:17:24Z","abstract_excerpt":"We prove a nonlinear parabolic characterization of stochastic completeness at infinity for weighted graphs. For the filtration equation \\[\n  (\\partial_t + \\Delta \\Phi)u =0 \\] where $\\Delta$ is the non-negative formal graph Laplacian and $\\Phi u =\\phi \\circ u$ with $\\phi \\colon \\R\\to\\R$ nonconstant, continuous and increasing, stochastic completeness at infinity is equivalent to uniqueness of bounded pointwise solutions for every bounded initial datum. For \\(\\Phi=\\id\\), this recovers the classical heat equation characterization of stochastic completeness at infinity, and of stochastic completene"},"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":"2608.11931","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-08-12T11:17:24Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9742652fab25ac9161abb3f0cbfd2390718e2266b7cba6e1c229341ce1ad3ac3","abstract_canon_sha256":"d2f86b96f650097561d8827532cb9014fe9dd4e4b4c7b1e61b89c7a2c7a92859"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-13T01:28:59.253962Z","signature_b64":"vmSzhCPQvd+ffUhLyEQwF9FqnPWo9Sh3GlvzcsAeNX5SFrRo4ymmCfJHUCBFWIYZHooDPBhkFGSPY6ybrHFFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e5d56a974f81f65f148f1bb11973dfc983f705bf6f3835522e961fb321e69f","last_reissued_at":"2026-08-13T01:28:59.251555Z","signature_status":"signed_v1","first_computed_at":"2026-08-13T01:28:59.251555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear parabolic characterizations of stochastic completeness at infinity on weighted graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Alberto G. Setti, Bobo Hua, Davide Bianchi, Rados{\\l}aw K. Wojciechowski","submitted_at":"2026-08-12T11:17:24Z","abstract_excerpt":"We prove a nonlinear parabolic characterization of stochastic completeness at infinity for weighted graphs. For the filtration equation \\[\n  (\\partial_t + \\Delta \\Phi)u =0 \\] where $\\Delta$ is the non-negative formal graph Laplacian and $\\Phi u =\\phi \\circ u$ with $\\phi \\colon \\R\\to\\R$ nonconstant, continuous and increasing, stochastic completeness at infinity is equivalent to uniqueness of bounded pointwise solutions for every bounded initial datum. For \\(\\Phi=\\id\\), this recovers the classical heat equation characterization of stochastic completeness at infinity, and of stochastic completene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11931","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/2608.11931/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":"2608.11931","created_at":"2026-08-13T01:28:59.252775+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.11931v1","created_at":"2026-08-13T01:28:59.252775+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.11931","created_at":"2026-08-13T01:28:59.252775+00:00"},{"alias_kind":"pith_short_12","alias_value":"63S5K2UXJ6A7","created_at":"2026-08-13T01:28:59.252775+00:00"},{"alias_kind":"pith_short_16","alias_value":"63S5K2UXJ6A7MXYU","created_at":"2026-08-13T01:28:59.252775+00:00"},{"alias_kind":"pith_short_8","alias_value":"63S5K2UX","created_at":"2026-08-13T01:28:59.252775+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/63S5K2UXJ6A7MXYUR4N3CGLT37","json":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37.json","graph_json":"https://pith.science/api/pith-number/63S5K2UXJ6A7MXYUR4N3CGLT37/graph.json","events_json":"https://pith.science/api/pith-number/63S5K2UXJ6A7MXYUR4N3CGLT37/events.json","paper":"https://pith.science/paper/63S5K2UX"},"agent_actions":{"view_html":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37","download_json":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37.json","view_paper":"https://pith.science/paper/63S5K2UX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.11931&json=true","fetch_graph":"https://pith.science/api/pith-number/63S5K2UXJ6A7MXYUR4N3CGLT37/graph.json","fetch_events":"https://pith.science/api/pith-number/63S5K2UXJ6A7MXYUR4N3CGLT37/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37/action/timestamp_anchor","attest_storage":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37/action/storage_attestation","attest_author":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37/action/author_attestation","sign_citation":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37/action/citation_signature","submit_replication":"https://pith.science/pith/63S5K2UXJ6A7MXYUR4N3CGLT37/action/replication_record"}},"created_at":"2026-08-13T01:28:59.252775+00:00","updated_at":"2026-08-13T01:28:59.252775+00:00"}