{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:T5I4PYP33MTON2NMAHSIJTJJ22","short_pith_number":"pith:T5I4PYP3","schema_version":"1.0","canonical_sha256":"9f51c7e1fbdb26e6e9ac01e484cd29d6a3f66528bed10e2170c569bb2b20b4cc","source":{"kind":"arxiv","id":"2202.02525","version":3},"attestation_state":"computed","paper":{"title":"Existence of solutions to a generalized self-dual Chern-Simons equation on finite graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuanyang Hu","submitted_at":"2022-02-05T10:08:07Z","abstract_excerpt":"Let $G=(V,E)$ be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on $G$ \\begin{equation*}\n  \\Delta u=\\lambda \\mathrm{e}^{u}\\left(\\mathrm{e}^{u}-1\\right)^{5}+4 \\pi \\sum_{s=1}^{N} \\delta_{p_{s}} \\quad , \\end{equation*} where $\\lambda>0$, $\\delta_{p_{s}}$ is the Dirac mass at the vetex $p_s$, and $p_1, p_2,\\dots, p_N$ are arbitrarily chosen distinct vertices on the graph. We show that there exists a critial value $\\hat{\\lambda}$ such that when $\\lambda > \\hat{\\lambda}$, the generalized Chern-Simons equation has at least two solutio"},"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":"2202.02525","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-02-05T10:08:07Z","cross_cats_sorted":[],"title_canon_sha256":"b86ef811ced42663c4f61ca5b49636559b7cf27f19670a5155ddb0dcd7a8708a","abstract_canon_sha256":"c288edcd2fdb9e012783b6f984520ecd39038d8c272bc3892c97b7a28351b3b2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:19:05.598322Z","signature_b64":"sG6BiFQp5ejuYyuZaxNbNNriypMiYjG6q/l8Mcp229ErD/7GOkSuknL8914KkN5tpONsGbWlsYOur8YHOWJKAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f51c7e1fbdb26e6e9ac01e484cd29d6a3f66528bed10e2170c569bb2b20b4cc","last_reissued_at":"2026-07-05T04:19:05.597801Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:19:05.597801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of solutions to a generalized self-dual Chern-Simons equation on finite graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuanyang Hu","submitted_at":"2022-02-05T10:08:07Z","abstract_excerpt":"Let $G=(V,E)$ be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on $G$ \\begin{equation*}\n  \\Delta u=\\lambda \\mathrm{e}^{u}\\left(\\mathrm{e}^{u}-1\\right)^{5}+4 \\pi \\sum_{s=1}^{N} \\delta_{p_{s}} \\quad , \\end{equation*} where $\\lambda>0$, $\\delta_{p_{s}}$ is the Dirac mass at the vetex $p_s$, and $p_1, p_2,\\dots, p_N$ are arbitrarily chosen distinct vertices on the graph. We show that there exists a critial value $\\hat{\\lambda}$ such that when $\\lambda > \\hat{\\lambda}$, the generalized Chern-Simons equation has at least two solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.02525","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.02525/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":"2202.02525","created_at":"2026-07-05T04:19:05.597862+00:00"},{"alias_kind":"arxiv_version","alias_value":"2202.02525v3","created_at":"2026-07-05T04:19:05.597862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.02525","created_at":"2026-07-05T04:19:05.597862+00:00"},{"alias_kind":"pith_short_12","alias_value":"T5I4PYP33MTO","created_at":"2026-07-05T04:19:05.597862+00:00"},{"alias_kind":"pith_short_16","alias_value":"T5I4PYP33MTON2NM","created_at":"2026-07-05T04:19:05.597862+00:00"},{"alias_kind":"pith_short_8","alias_value":"T5I4PYP3","created_at":"2026-07-05T04:19:05.597862+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.14799","citing_title":"Existence theory for elliptic equations of general exponential nonlinearity on finite graphs","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22","json":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22.json","graph_json":"https://pith.science/api/pith-number/T5I4PYP33MTON2NMAHSIJTJJ22/graph.json","events_json":"https://pith.science/api/pith-number/T5I4PYP33MTON2NMAHSIJTJJ22/events.json","paper":"https://pith.science/paper/T5I4PYP3"},"agent_actions":{"view_html":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22","download_json":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22.json","view_paper":"https://pith.science/paper/T5I4PYP3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2202.02525&json=true","fetch_graph":"https://pith.science/api/pith-number/T5I4PYP33MTON2NMAHSIJTJJ22/graph.json","fetch_events":"https://pith.science/api/pith-number/T5I4PYP33MTON2NMAHSIJTJJ22/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22/action/storage_attestation","attest_author":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22/action/author_attestation","sign_citation":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22/action/citation_signature","submit_replication":"https://pith.science/pith/T5I4PYP33MTON2NMAHSIJTJJ22/action/replication_record"}},"created_at":"2026-07-05T04:19:05.597862+00:00","updated_at":"2026-07-05T04:19:05.597862+00:00"}