{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:CNZ7K6NGRGQCOR7PCID3P6JLDY","short_pith_number":"pith:CNZ7K6NG","schema_version":"1.0","canonical_sha256":"1373f579a689a02747ef1207b7f92b1e31193cc8f58327c317a04f7173f49299","source":{"kind":"arxiv","id":"2108.13007","version":1},"attestation_state":"computed","paper":{"title":"Semilinear heat equations and parabolic variational inequalities on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong Lin, Yuanyuan Xie","submitted_at":"2021-08-30T06:34:12Z","abstract_excerpt":"Let $G=(V,E)$ be a locally finite connected weighted graph, and $\\Omega$ be an unbounded subset of $V$. Using Rothe's method, we study the existence of solutions for the semilinear heat equation $\\partial_tu+|u|^{p-1}\\cdot u=\\Delta u~(p\\ge1)$ and the parabolic variational inequality \\begin{eqnarray*} \\int_{\\Omega^\\circ} \\partial_tu\\cdot(v-u)\\,d\\mu\\ge \\int_{\\Omega^\\circ}(\\Delta u+f)\\cdot(v-u)\\,d\\mu \\qquad\\mbox{for any }v\\in \\mathcal{H}, \\end{eqnarray*} where $\\mathcal{H}=\\{u\\in W^{1,2}(V):u=0\\mbox{ on }V\\backslash\\Omega^\\circ\\}$."},"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":"2108.13007","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-08-30T06:34:12Z","cross_cats_sorted":[],"title_canon_sha256":"99965945ca3e7c9f90aa914b8e492a4085bb6b7c476f92358c3677f4bf011ccb","abstract_canon_sha256":"a5008c8cd0b2ba5b1243029226bd4d5653570b19a5305ba2d1bc4b9100bd7035"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:09:48.675928Z","signature_b64":"kjhAVPNOdWrPDesAJwRkdPAlmunyxL3k/MFMoN/XmZFbGdZqrCQBr0ioq96VcZ5YeCMHVLJZboPn3ys7ux0+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1373f579a689a02747ef1207b7f92b1e31193cc8f58327c317a04f7173f49299","last_reissued_at":"2026-07-05T03:09:48.675519Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:09:48.675519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semilinear heat equations and parabolic variational inequalities on graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yong Lin, Yuanyuan Xie","submitted_at":"2021-08-30T06:34:12Z","abstract_excerpt":"Let $G=(V,E)$ be a locally finite connected weighted graph, and $\\Omega$ be an unbounded subset of $V$. Using Rothe's method, we study the existence of solutions for the semilinear heat equation $\\partial_tu+|u|^{p-1}\\cdot u=\\Delta u~(p\\ge1)$ and the parabolic variational inequality \\begin{eqnarray*} \\int_{\\Omega^\\circ} \\partial_tu\\cdot(v-u)\\,d\\mu\\ge \\int_{\\Omega^\\circ}(\\Delta u+f)\\cdot(v-u)\\,d\\mu \\qquad\\mbox{for any }v\\in \\mathcal{H}, \\end{eqnarray*} where $\\mathcal{H}=\\{u\\in W^{1,2}(V):u=0\\mbox{ on }V\\backslash\\Omega^\\circ\\}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.13007","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/2108.13007/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":"2108.13007","created_at":"2026-07-05T03:09:48.675576+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.13007v1","created_at":"2026-07-05T03:09:48.675576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.13007","created_at":"2026-07-05T03:09:48.675576+00:00"},{"alias_kind":"pith_short_12","alias_value":"CNZ7K6NGRGQC","created_at":"2026-07-05T03:09:48.675576+00:00"},{"alias_kind":"pith_short_16","alias_value":"CNZ7K6NGRGQCOR7P","created_at":"2026-07-05T03:09:48.675576+00:00"},{"alias_kind":"pith_short_8","alias_value":"CNZ7K6NG","created_at":"2026-07-05T03:09:48.675576+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/CNZ7K6NGRGQCOR7PCID3P6JLDY","json":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY.json","graph_json":"https://pith.science/api/pith-number/CNZ7K6NGRGQCOR7PCID3P6JLDY/graph.json","events_json":"https://pith.science/api/pith-number/CNZ7K6NGRGQCOR7PCID3P6JLDY/events.json","paper":"https://pith.science/paper/CNZ7K6NG"},"agent_actions":{"view_html":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY","download_json":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY.json","view_paper":"https://pith.science/paper/CNZ7K6NG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.13007&json=true","fetch_graph":"https://pith.science/api/pith-number/CNZ7K6NGRGQCOR7PCID3P6JLDY/graph.json","fetch_events":"https://pith.science/api/pith-number/CNZ7K6NGRGQCOR7PCID3P6JLDY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY/action/storage_attestation","attest_author":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY/action/author_attestation","sign_citation":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY/action/citation_signature","submit_replication":"https://pith.science/pith/CNZ7K6NGRGQCOR7PCID3P6JLDY/action/replication_record"}},"created_at":"2026-07-05T03:09:48.675576+00:00","updated_at":"2026-07-05T03:09:48.675576+00:00"}