{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:23M4H7TB3WXWD45Z5QACNQWSMD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c8ea727bb5c8cc659ac92d42c72531d25deacab6b9d107c8bf39674779de9c82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-01-16T10:43:41Z","title_canon_sha256":"ee6e7ed4f5f0a85818e8f685d49ff02d81ee903263395da31f7251b4995edf81"},"schema_version":"1.0","source":{"id":"1401.3981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.3981","created_at":"2026-05-18T03:01:57Z"},{"alias_kind":"arxiv_version","alias_value":"1401.3981v1","created_at":"2026-05-18T03:01:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3981","created_at":"2026-05-18T03:01:57Z"},{"alias_kind":"pith_short_12","alias_value":"23M4H7TB3WXW","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"23M4H7TB3WXWD45Z","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"23M4H7TB","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:40edd28d53cc4d126a0f9995a2796a113c989dbcf367842fe1a5d6f4d45d4cb8","target":"graph","created_at":"2026-05-18T03:01:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study $\\phi_\\epsilon$-coordinated modules for vertex algebras, where $\\phi_\\epsilon$ with $\\epsilon$ an integer parameter is a family of associates of the one-dimensional additive formal group. As the main results, we obtain a Jacobi type identity and a commutator formula for $\\phi_\\epsilon$-coordinated modules. We then use these results to study $\\phi_\\epsilon$-coordinated modules for vertex algebras associated to Novikov algebras by Primc.","authors_text":"Chengming Bai, Haisheng Li, Yufeng Pei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-01-16T10:43:41Z","title":"$\\phi_\\epsilon$-coordinated modules for vertex algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3981","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3fb9c9a1c1f36362e1eb8f4367a37a740cabc8024027822debeae939698a9021","target":"record","created_at":"2026-05-18T03:01:57Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c8ea727bb5c8cc659ac92d42c72531d25deacab6b9d107c8bf39674779de9c82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2014-01-16T10:43:41Z","title_canon_sha256":"ee6e7ed4f5f0a85818e8f685d49ff02d81ee903263395da31f7251b4995edf81"},"schema_version":"1.0","source":{"id":"1401.3981","kind":"arxiv","version":1}},"canonical_sha256":"d6d9c3fe61ddaf61f3b9ec0026c2d260f26372428e6a9269c1cb5d12ab6fdd55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6d9c3fe61ddaf61f3b9ec0026c2d260f26372428e6a9269c1cb5d12ab6fdd55","first_computed_at":"2026-05-18T03:01:57.528748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:57.528748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8fHbC94UfzRWxuKASl7E9GNY6PDi0JOFcGXzIU8/KahA7H+qKe+F16TcKy4BnCjQ6o6sFl/rkCBtIGgMA76Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:57.529652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.3981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fb9c9a1c1f36362e1eb8f4367a37a740cabc8024027822debeae939698a9021","sha256:40edd28d53cc4d126a0f9995a2796a113c989dbcf367842fe1a5d6f4d45d4cb8"],"state_sha256":"9a345c85423079a1d54859ab94e23c32680e70c5c459a03f2b6d9d8e304d6f64"}