{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:YMKOVWEZJVGUIJ57IJVZNFSZN2","short_pith_number":"pith:YMKOVWEZ","schema_version":"1.0","canonical_sha256":"c314ead8994d4d4427bf426b9696596eac47cae30d595ae1ef2f95ff9211a2ab","source":{"kind":"arxiv","id":"0709.0188","version":1},"attestation_state":"computed","paper":{"title":"Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kenichiro Tanabe","submitted_at":"2007-09-03T11:04:05Z","abstract_excerpt":"A commutative associative algebra $A$ over ${\\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an associative algebra are not well understood.\n  In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one variable over ${\\mathbb C}$ as a vertex algebra."},"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":"0709.0188","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2007-09-03T11:04:05Z","cross_cats_sorted":[],"title_canon_sha256":"7803f97e35648f21cf86388315e6456db2a18520b70a22e45a2274d8fbcc29fd","abstract_canon_sha256":"aa3927edd71093ee1959074894d390a7d317de48d2f6ae160aab74e456dcbc47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:24.508390Z","signature_b64":"c3uXiVcvxJuvb9NSq5LLLq/CLgEPnYK6ozCH/uqnzYTk4+73f/wtnzTlMwLCM8Hw9W7gSvcxZZfnkPGo9qLMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c314ead8994d4d4427bf426b9696596eac47cae30d595ae1ef2f95ff9211a2ab","last_reissued_at":"2026-05-18T03:04:24.507762Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:24.507762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite-dimensional modules for the polynomial ring in one variable as a vertex algebra","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kenichiro Tanabe","submitted_at":"2007-09-03T11:04:05Z","abstract_excerpt":"A commutative associative algebra $A$ over ${\\mathbb C}$ with a derivation is one of the simplest examples of a vertex algebra. However, the differences between the modules for $A$ as a vertex algebra and the modules for $A$ as an associative algebra are not well understood.\n  In this paper, I give the classification of finite-dimensional indecomposable untwisted or twisted modules for the polynomial ring in one variable over ${\\mathbb C}$ as a vertex algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.0188","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":"0709.0188","created_at":"2026-05-18T03:04:24.507854+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.0188v1","created_at":"2026-05-18T03:04:24.507854+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.0188","created_at":"2026-05-18T03:04:24.507854+00:00"},{"alias_kind":"pith_short_12","alias_value":"YMKOVWEZJVGU","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"YMKOVWEZJVGUIJ57","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"YMKOVWEZ","created_at":"2026-05-18T12:25:56.245647+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/YMKOVWEZJVGUIJ57IJVZNFSZN2","json":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2.json","graph_json":"https://pith.science/api/pith-number/YMKOVWEZJVGUIJ57IJVZNFSZN2/graph.json","events_json":"https://pith.science/api/pith-number/YMKOVWEZJVGUIJ57IJVZNFSZN2/events.json","paper":"https://pith.science/paper/YMKOVWEZ"},"agent_actions":{"view_html":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2","download_json":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2.json","view_paper":"https://pith.science/paper/YMKOVWEZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.0188&json=true","fetch_graph":"https://pith.science/api/pith-number/YMKOVWEZJVGUIJ57IJVZNFSZN2/graph.json","fetch_events":"https://pith.science/api/pith-number/YMKOVWEZJVGUIJ57IJVZNFSZN2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2/action/storage_attestation","attest_author":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2/action/author_attestation","sign_citation":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2/action/citation_signature","submit_replication":"https://pith.science/pith/YMKOVWEZJVGUIJ57IJVZNFSZN2/action/replication_record"}},"created_at":"2026-05-18T03:04:24.507854+00:00","updated_at":"2026-05-18T03:04:24.507854+00:00"}