{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:COIAIMNQNPRJKRNXSZYZVITOMB","short_pith_number":"pith:COIAIMNQ","canonical_record":{"source":{"id":"math/0505570","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2005-05-26T13:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"ca9ada1248a1877203e5757a6c9ce143f2004abbdc727b4754148946cba4cd32","abstract_canon_sha256":"c2edf8ba80c770e29121cb69040de5932268150076cd82511bd180ea88abe9b4"},"schema_version":"1.0"},"canonical_sha256":"13900431b06be29545b796719aa26e60782f02734db83f1caadf7b0588d00c2a","source":{"kind":"arxiv","id":"math/0505570","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505570","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505570v2","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505570","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"COIAIMNQNPRJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"COIAIMNQNPRJKRNX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"COIAIMNQ","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:COIAIMNQNPRJKRNXSZYZVITOMB","target":"record","payload":{"canonical_record":{"source":{"id":"math/0505570","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2005-05-26T13:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"ca9ada1248a1877203e5757a6c9ce143f2004abbdc727b4754148946cba4cd32","abstract_canon_sha256":"c2edf8ba80c770e29121cb69040de5932268150076cd82511bd180ea88abe9b4"},"schema_version":"1.0"},"canonical_sha256":"13900431b06be29545b796719aa26e60782f02734db83f1caadf7b0588d00c2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:21.457155Z","signature_b64":"1jL9EDfuFQ6lNv8ycTbmi5suSWUCSf2auNSTgXlGbKrejVJR9QwfgONjXLRJO3SGGHz5ZjCTsP512xmvaXpyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13900431b06be29545b796719aa26e60782f02734db83f1caadf7b0588d00c2a","last_reissued_at":"2026-05-18T04:06:21.456378Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:21.456378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0505570","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oaYSk0aNQPdeAJNB40tPh51/GnENssnYEA3sluIf1LLCgrUljqzhxOesnS+42uxntCVOy+qp8oRY0aUDtvi+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:20:44.639353Z"},"content_sha256":"1a9cc328d3703e8f7d91323b7d35f51afa6a8e6e2ab587f041b0479848c6a384","schema_version":"1.0","event_id":"sha256:1a9cc328d3703e8f7d91323b7d35f51afa6a8e6e2ab587f041b0479848c6a384"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:COIAIMNQNPRJKRNXSZYZVITOMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PBW-deformations of N-Koszul algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gunnar Fl{\\o}ystad, Jon Eivind Vatne","submitted_at":"2005-05-26T13:50:50Z","abstract_excerpt":"For a quotient algebra $U$ of the tensor algebra we give explicit conditions on its relations for $U$ being a PBW-deformation of an $N$-Koszul algebra $A$. We show there is a one-one correspondence between such deformations and a class of $A_\\infty$-structures on the Yoneda algebra $Ext_A^*(k,k)$ of $A$. We compute the PBW-deformations of the algebra whose relations are the anti-symmetrizers of degree $N$ and also of cubic Artin-Schelter algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505570","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:06:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5DM/6VfEWw1vwHbq91zsdeeR66VfdgEwyoeceqEP+R8PMmGFfhxugzTeZVW+eIYzkd5AnuAh3kkYhCFQdK92Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T10:20:44.639957Z"},"content_sha256":"9df6b044d09d571638c10a220095062c76f28201776dca0dda81f007447bd651","schema_version":"1.0","event_id":"sha256:9df6b044d09d571638c10a220095062c76f28201776dca0dda81f007447bd651"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COIAIMNQNPRJKRNXSZYZVITOMB/bundle.json","state_url":"https://pith.science/pith/COIAIMNQNPRJKRNXSZYZVITOMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COIAIMNQNPRJKRNXSZYZVITOMB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T10:20:44Z","links":{"resolver":"https://pith.science/pith/COIAIMNQNPRJKRNXSZYZVITOMB","bundle":"https://pith.science/pith/COIAIMNQNPRJKRNXSZYZVITOMB/bundle.json","state":"https://pith.science/pith/COIAIMNQNPRJKRNXSZYZVITOMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COIAIMNQNPRJKRNXSZYZVITOMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:COIAIMNQNPRJKRNXSZYZVITOMB","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":"c2edf8ba80c770e29121cb69040de5932268150076cd82511bd180ea88abe9b4","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2005-05-26T13:50:50Z","title_canon_sha256":"ca9ada1248a1877203e5757a6c9ce143f2004abbdc727b4754148946cba4cd32"},"schema_version":"1.0","source":{"id":"math/0505570","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505570","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505570v2","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505570","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"COIAIMNQNPRJ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"COIAIMNQNPRJKRNX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"COIAIMNQ","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:9df6b044d09d571638c10a220095062c76f28201776dca0dda81f007447bd651","target":"graph","created_at":"2026-05-18T04:06:21Z","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":"For a quotient algebra $U$ of the tensor algebra we give explicit conditions on its relations for $U$ being a PBW-deformation of an $N$-Koszul algebra $A$. We show there is a one-one correspondence between such deformations and a class of $A_\\infty$-structures on the Yoneda algebra $Ext_A^*(k,k)$ of $A$. We compute the PBW-deformations of the algebra whose relations are the anti-symmetrizers of degree $N$ and also of cubic Artin-Schelter algebras.","authors_text":"Gunnar Fl{\\o}ystad, Jon Eivind Vatne","cross_cats":[],"headline":"","license":"","primary_cat":"math.RA","submitted_at":"2005-05-26T13:50:50Z","title":"PBW-deformations of N-Koszul algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505570","kind":"arxiv","version":2},"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":"sha256:1a9cc328d3703e8f7d91323b7d35f51afa6a8e6e2ab587f041b0479848c6a384","target":"record","created_at":"2026-05-18T04:06:21Z","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":"c2edf8ba80c770e29121cb69040de5932268150076cd82511bd180ea88abe9b4","cross_cats_sorted":[],"license":"","primary_cat":"math.RA","submitted_at":"2005-05-26T13:50:50Z","title_canon_sha256":"ca9ada1248a1877203e5757a6c9ce143f2004abbdc727b4754148946cba4cd32"},"schema_version":"1.0","source":{"id":"math/0505570","kind":"arxiv","version":2}},"canonical_sha256":"13900431b06be29545b796719aa26e60782f02734db83f1caadf7b0588d00c2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13900431b06be29545b796719aa26e60782f02734db83f1caadf7b0588d00c2a","first_computed_at":"2026-05-18T04:06:21.456378Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:21.456378Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1jL9EDfuFQ6lNv8ycTbmi5suSWUCSf2auNSTgXlGbKrejVJR9QwfgONjXLRJO3SGGHz5ZjCTsP512xmvaXpyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:21.457155Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0505570","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a9cc328d3703e8f7d91323b7d35f51afa6a8e6e2ab587f041b0479848c6a384","sha256:9df6b044d09d571638c10a220095062c76f28201776dca0dda81f007447bd651"],"state_sha256":"d2e2a92729438a0fefed69bf720b989afdfe1f510f574827d03d3611da322cf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZaH4bgyebHrC3wjwMkx8PI7MgNjWhThgi4YBzPBelfBtRcfuXrqeGi0qKFboM/EzfVXAQZmybFVIFhoPOnFMCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T10:20:44.643638Z","bundle_sha256":"5d0030900acb358b1f84cd136cfec9dc835637520c8161212c3ca5595a80d032"}}