{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OWI7K44Q64AIAQABVSYZJKDOKO","short_pith_number":"pith:OWI7K44Q","schema_version":"1.0","canonical_sha256":"7591f57390f700804001acb194a86e5395bf206d8ad1bb5c304bf18e0643e65a","source":{"kind":"arxiv","id":"1505.04422","version":1},"attestation_state":"computed","paper":{"title":"A twisted $\\bar{\\partial}_f$-Neumann problem and Toeplitz $n$-tuples from singularity theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hao Wen, Huijun Fan","submitted_at":"2015-05-17T17:33:46Z","abstract_excerpt":"A twisted $\\bar{\\partial}_f$-Neumann problem associated to a singularity $(\\mathscr{O}_n,f)$ is established. By constructing the connection to the Koszul complex for toeplitz $n$-tuples $(f_1,\\cdots,f_n)$ on Bergman spaces $B^0(D)$, we can solve this $\\bar{\\partial}_f$-Neumann problem. Moreover, we can compute the cohomology of the $L^2$ holomorphic Koszul complex $(B^*(D),\\partial f\\wedge)$ explicitly"},"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":"1505.04422","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-17T17:33:46Z","cross_cats_sorted":[],"title_canon_sha256":"6271e584fe8b00f7865282c0c6680baabbaaf0aa0b32eca638e74a38fb864428","abstract_canon_sha256":"9dba3c3e0a92da0affc2815941747e24239db48222d9d53acf8fe1b631e42f26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:25.464922Z","signature_b64":"lYu6hebubVLJ6KGhMbfvfX5sqTnkK4TLvDhmDzZXNy60KTGjhyh3jCcH42Uo/w7l3vclziaMQtL/ZsnW4sEMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7591f57390f700804001acb194a86e5395bf206d8ad1bb5c304bf18e0643e65a","last_reissued_at":"2026-05-18T02:07:25.464547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:25.464547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A twisted $\\bar{\\partial}_f$-Neumann problem and Toeplitz $n$-tuples from singularity theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hao Wen, Huijun Fan","submitted_at":"2015-05-17T17:33:46Z","abstract_excerpt":"A twisted $\\bar{\\partial}_f$-Neumann problem associated to a singularity $(\\mathscr{O}_n,f)$ is established. By constructing the connection to the Koszul complex for toeplitz $n$-tuples $(f_1,\\cdots,f_n)$ on Bergman spaces $B^0(D)$, we can solve this $\\bar{\\partial}_f$-Neumann problem. Moreover, we can compute the cohomology of the $L^2$ holomorphic Koszul complex $(B^*(D),\\partial f\\wedge)$ explicitly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04422","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":""},"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":"1505.04422","created_at":"2026-05-18T02:07:25.464609+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04422v1","created_at":"2026-05-18T02:07:25.464609+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04422","created_at":"2026-05-18T02:07:25.464609+00:00"},{"alias_kind":"pith_short_12","alias_value":"OWI7K44Q64AI","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OWI7K44Q64AIAQAB","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OWI7K44Q","created_at":"2026-05-18T12:29:34.919912+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/OWI7K44Q64AIAQABVSYZJKDOKO","json":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO.json","graph_json":"https://pith.science/api/pith-number/OWI7K44Q64AIAQABVSYZJKDOKO/graph.json","events_json":"https://pith.science/api/pith-number/OWI7K44Q64AIAQABVSYZJKDOKO/events.json","paper":"https://pith.science/paper/OWI7K44Q"},"agent_actions":{"view_html":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO","download_json":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO.json","view_paper":"https://pith.science/paper/OWI7K44Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04422&json=true","fetch_graph":"https://pith.science/api/pith-number/OWI7K44Q64AIAQABVSYZJKDOKO/graph.json","fetch_events":"https://pith.science/api/pith-number/OWI7K44Q64AIAQABVSYZJKDOKO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/action/storage_attestation","attest_author":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/action/author_attestation","sign_citation":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/action/citation_signature","submit_replication":"https://pith.science/pith/OWI7K44Q64AIAQABVSYZJKDOKO/action/replication_record"}},"created_at":"2026-05-18T02:07:25.464609+00:00","updated_at":"2026-05-18T02:07:25.464609+00:00"}