{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2Q6WBINKWL67V6GWEM2DZVMCU4","short_pith_number":"pith:2Q6WBINK","schema_version":"1.0","canonical_sha256":"d43d60a1aab2fdfaf8d623343cd582a70c725577f46324852ee52303449e437b","source":{"kind":"arxiv","id":"2502.13150","version":1},"attestation_state":"computed","paper":{"title":"On a semilinear parabolic equation with time-dependent source term on infinite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Sacco, Fabio Punzo","submitted_at":"2025-02-12T12:51:03Z","abstract_excerpt":"We are concerned with semilinear parabolic equations, with a time-dependent source term of the form $h(t)u^q$ with $q>1$, posed on an infinite graph. We assume that the bottom of the $L^2$-spectrum of the Laplacian on the graph, denoted by $\\lambda_1(G)$, is positive. In dependence of $q, h(t)$ and $\\lambda_1(G)$, we show global in time existence or finite time blow-up of solutions."},"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":"2502.13150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-02-12T12:51:03Z","cross_cats_sorted":[],"title_canon_sha256":"8c252a1508c8f26b4ace13495cca7629f11da87dde0e3de49f097fc14c43d77a","abstract_canon_sha256":"a7f1836e69982871c398ce6fd898b56190f3cd4cedc57edc2624c7e4ece8d30b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:16:43.062149Z","signature_b64":"UlYEGVXQFFdY3bEmB+RaN5dEQiOQ0VP5nY/+mcSzYAqf4R600bPIIBEHoihB0nXEPl7w5qUSndcPXJomSX/VAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d43d60a1aab2fdfaf8d623343cd582a70c725577f46324852ee52303449e437b","last_reissued_at":"2026-07-05T10:16:43.061695Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:16:43.061695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a semilinear parabolic equation with time-dependent source term on infinite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Sacco, Fabio Punzo","submitted_at":"2025-02-12T12:51:03Z","abstract_excerpt":"We are concerned with semilinear parabolic equations, with a time-dependent source term of the form $h(t)u^q$ with $q>1$, posed on an infinite graph. We assume that the bottom of the $L^2$-spectrum of the Laplacian on the graph, denoted by $\\lambda_1(G)$, is positive. In dependence of $q, h(t)$ and $\\lambda_1(G)$, we show global in time existence or finite time blow-up of solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13150","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/2502.13150/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":"2502.13150","created_at":"2026-07-05T10:16:43.061750+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.13150v1","created_at":"2026-07-05T10:16:43.061750+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13150","created_at":"2026-07-05T10:16:43.061750+00:00"},{"alias_kind":"pith_short_12","alias_value":"2Q6WBINKWL67","created_at":"2026-07-05T10:16:43.061750+00:00"},{"alias_kind":"pith_short_16","alias_value":"2Q6WBINKWL67V6GW","created_at":"2026-07-05T10:16:43.061750+00:00"},{"alias_kind":"pith_short_8","alias_value":"2Q6WBINK","created_at":"2026-07-05T10:16:43.061750+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2601.18549","citing_title":"Semilinear Diffusion Equations on Infinite Graphs: The Dissipative and Lipschitz Cases","ref_index":33,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4","json":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4.json","graph_json":"https://pith.science/api/pith-number/2Q6WBINKWL67V6GWEM2DZVMCU4/graph.json","events_json":"https://pith.science/api/pith-number/2Q6WBINKWL67V6GWEM2DZVMCU4/events.json","paper":"https://pith.science/paper/2Q6WBINK"},"agent_actions":{"view_html":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4","download_json":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4.json","view_paper":"https://pith.science/paper/2Q6WBINK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.13150&json=true","fetch_graph":"https://pith.science/api/pith-number/2Q6WBINKWL67V6GWEM2DZVMCU4/graph.json","fetch_events":"https://pith.science/api/pith-number/2Q6WBINKWL67V6GWEM2DZVMCU4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4/action/storage_attestation","attest_author":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4/action/author_attestation","sign_citation":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4/action/citation_signature","submit_replication":"https://pith.science/pith/2Q6WBINKWL67V6GWEM2DZVMCU4/action/replication_record"}},"created_at":"2026-07-05T10:16:43.061750+00:00","updated_at":"2026-07-05T10:16:43.061750+00:00"}