{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GDFM2MWHSGJHGPUO4FIPBCIVMG","short_pith_number":"pith:GDFM2MWH","canonical_record":{"source":{"id":"1212.4063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-17T16:47:52Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5e58b2369459411ab9713ba4dea011c9125cb4fb93bef5ef5943de512576f39c","abstract_canon_sha256":"06ab211074aed86bea344050951bde34131b4d37e819787bf70f01957eea818d"},"schema_version":"1.0"},"canonical_sha256":"30cacd32c79192733e8ee150f0891561afdbc020b0fe446f1611564d5d5257b5","source":{"kind":"arxiv","id":"1212.4063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4063","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4063v1","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4063","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"GDFM2MWHSGJH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GDFM2MWHSGJHGPUO","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GDFM2MWH","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GDFM2MWHSGJHGPUO4FIPBCIVMG","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-17T16:47:52Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5e58b2369459411ab9713ba4dea011c9125cb4fb93bef5ef5943de512576f39c","abstract_canon_sha256":"06ab211074aed86bea344050951bde34131b4d37e819787bf70f01957eea818d"},"schema_version":"1.0"},"canonical_sha256":"30cacd32c79192733e8ee150f0891561afdbc020b0fe446f1611564d5d5257b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:21.605804Z","signature_b64":"50Z79Xzx6ojf+7Z7eGhs8O1pKTbnZMt5slE7gmBeQojGv4XQkmHHT4rOpOVVQD0+UUz4kH4MXAExUJZ/qRpCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30cacd32c79192733e8ee150f0891561afdbc020b0fe446f1611564d5d5257b5","last_reissued_at":"2026-05-18T03:38:21.604845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:21.604845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4063","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JDVv+JFmcfhaZRU+S8DpTzsGrRukLOsbGD0EkZWsaI8PXe5qObKgRmZEFNn9UnB6OHhzWdqRl1Mos2XPVCFjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:02:02.724408Z"},"content_sha256":"13e7197f431bb212a00c6fd5ec888c4f72b2a3b8ad5e45f86f41c258b375e914","schema_version":"1.0","event_id":"sha256:13e7197f431bb212a00c6fd5ec888c4f72b2a3b8ad5e45f86f41c258b375e914"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GDFM2MWHSGJHGPUO4FIPBCIVMG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ore extensions and Poisson algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"David A. Jordan","submitted_at":"2012-12-17T16:47:52Z","abstract_excerpt":"For a derivation d of a commutative Noetherian complex algebra A, a homeomorphism is established between the prime spectrum of the Ore extension A[z;d] and the Poisson prime spectrum of the polynomial algebra A[z] endowed with the Poisson bracket such that {A,A}=0 and {z,a}=d(a) for all a in A. Several illustrative examples are discussed including some where A is known to be d-simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4063","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:38:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gqMDl3qIwBGA4sUWVWtGuFitcULK0lQIAGwaoCWL7YEC4Rg7T7Cg4M/AaiaD0hGmsiDW5VBJJuEB18RxRIPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:02:02.724772Z"},"content_sha256":"e2c7d353fcc5fb7b186425229ece7fef105230d4f5298fdf929cdf934df919c0","schema_version":"1.0","event_id":"sha256:e2c7d353fcc5fb7b186425229ece7fef105230d4f5298fdf929cdf934df919c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GDFM2MWHSGJHGPUO4FIPBCIVMG/bundle.json","state_url":"https://pith.science/pith/GDFM2MWHSGJHGPUO4FIPBCIVMG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GDFM2MWHSGJHGPUO4FIPBCIVMG/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":"2026-06-23T15:02:02Z","links":{"resolver":"https://pith.science/pith/GDFM2MWHSGJHGPUO4FIPBCIVMG","bundle":"https://pith.science/pith/GDFM2MWHSGJHGPUO4FIPBCIVMG/bundle.json","state":"https://pith.science/pith/GDFM2MWHSGJHGPUO4FIPBCIVMG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GDFM2MWHSGJHGPUO4FIPBCIVMG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GDFM2MWHSGJHGPUO4FIPBCIVMG","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":"06ab211074aed86bea344050951bde34131b4d37e819787bf70f01957eea818d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-17T16:47:52Z","title_canon_sha256":"5e58b2369459411ab9713ba4dea011c9125cb4fb93bef5ef5943de512576f39c"},"schema_version":"1.0","source":{"id":"1212.4063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4063","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4063v1","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4063","created_at":"2026-05-18T03:38:21Z"},{"alias_kind":"pith_short_12","alias_value":"GDFM2MWHSGJH","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GDFM2MWHSGJHGPUO","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GDFM2MWH","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:e2c7d353fcc5fb7b186425229ece7fef105230d4f5298fdf929cdf934df919c0","target":"graph","created_at":"2026-05-18T03:38:21Z","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 derivation d of a commutative Noetherian complex algebra A, a homeomorphism is established between the prime spectrum of the Ore extension A[z;d] and the Poisson prime spectrum of the polynomial algebra A[z] endowed with the Poisson bracket such that {A,A}=0 and {z,a}=d(a) for all a in A. Several illustrative examples are discussed including some where A is known to be d-simple.","authors_text":"David A. Jordan","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-17T16:47:52Z","title":"Ore extensions and Poisson algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4063","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":"sha256:13e7197f431bb212a00c6fd5ec888c4f72b2a3b8ad5e45f86f41c258b375e914","target":"record","created_at":"2026-05-18T03:38:21Z","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":"06ab211074aed86bea344050951bde34131b4d37e819787bf70f01957eea818d","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-12-17T16:47:52Z","title_canon_sha256":"5e58b2369459411ab9713ba4dea011c9125cb4fb93bef5ef5943de512576f39c"},"schema_version":"1.0","source":{"id":"1212.4063","kind":"arxiv","version":1}},"canonical_sha256":"30cacd32c79192733e8ee150f0891561afdbc020b0fe446f1611564d5d5257b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30cacd32c79192733e8ee150f0891561afdbc020b0fe446f1611564d5d5257b5","first_computed_at":"2026-05-18T03:38:21.604845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:21.604845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"50Z79Xzx6ojf+7Z7eGhs8O1pKTbnZMt5slE7gmBeQojGv4XQkmHHT4rOpOVVQD0+UUz4kH4MXAExUJZ/qRpCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:21.605804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13e7197f431bb212a00c6fd5ec888c4f72b2a3b8ad5e45f86f41c258b375e914","sha256:e2c7d353fcc5fb7b186425229ece7fef105230d4f5298fdf929cdf934df919c0"],"state_sha256":"fbe12468cecdc02f23f9595a5c7acc3d6aef4c8e76a9df9e67e817496ca50030"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4N5dxmLKHx/FOmTNVga68PnpCP+qvtr+M6HVGAt2ZK+2aoNGYDPHw/E+nEjggUuwKZBJiSg2DgKSm+FKBbucBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:02:02.726749Z","bundle_sha256":"39b9eeda3572f38b2a2eaeb384d6ad584b53323e4b416953962f7b0153ebfe5c"}}