{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V2ZBLPW3SOIWC44TENIHZALOYV","short_pith_number":"pith:V2ZBLPW3","canonical_record":{"source":{"id":"1102.1149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-06T13:31:49Z","cross_cats_sorted":["math.FA","math.RT"],"title_canon_sha256":"6201b58db181d5f8b4e3d4e6faa6e9bc8407d03398110df4e241efe8eee7418b","abstract_canon_sha256":"4254424e61e056e50fe439ccc440db51e5531cc5f624b91c4dbccc386603d3f8"},"schema_version":"1.0"},"canonical_sha256":"aeb215bedb939161739323507c816ec557b4a1d09f519c9c22fae5df164800c5","source":{"kind":"arxiv","id":"1102.1149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1149","created_at":"2026-05-18T02:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1149v1","created_at":"2026-05-18T02:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1149","created_at":"2026-05-18T02:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"V2ZBLPW3SOIW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V2ZBLPW3SOIWC44T","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V2ZBLPW3","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V2ZBLPW3SOIWC44TENIHZALOYV","target":"record","payload":{"canonical_record":{"source":{"id":"1102.1149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-06T13:31:49Z","cross_cats_sorted":["math.FA","math.RT"],"title_canon_sha256":"6201b58db181d5f8b4e3d4e6faa6e9bc8407d03398110df4e241efe8eee7418b","abstract_canon_sha256":"4254424e61e056e50fe439ccc440db51e5531cc5f624b91c4dbccc386603d3f8"},"schema_version":"1.0"},"canonical_sha256":"aeb215bedb939161739323507c816ec557b4a1d09f519c9c22fae5df164800c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:16.242604Z","signature_b64":"ezsWy/jeStmf5AODbHf0ZCZCebXDZmqLwOgQveipvkq+yeyk31S96Z1O9xiCNPgrVicyDjGNQguxSMXCNRs2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeb215bedb939161739323507c816ec557b4a1d09f519c9c22fae5df164800c5","last_reissued_at":"2026-05-18T02:03:16.242091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:16.242091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.1149","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":"2026-05-18T02:03:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AW+NBIU+Z8qf5FNlEICi0uG77WVBeRJVuNfILK3HinqRaXY0zJWXpNO9xitS/AyKUyHbwJzpk5F2AASROYZyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:38:18.644616Z"},"content_sha256":"e4b43fd95a81ba018dac197faf6f9b341fa117529862546382289e1f8b5af91f","schema_version":"1.0","event_id":"sha256:e4b43fd95a81ba018dac197faf6f9b341fa117529862546382289e1f8b5af91f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V2ZBLPW3SOIWC44TENIHZALOYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On structure of homogenenous Wick ideals in Wick $*$-algebras with braided coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.RT"],"primary_cat":"math.OA","authors_text":"Danil Proskurin, Lyudmila Turowska, Vasyl Ostrovskyi, Yurii Savchuk","submitted_at":"2011-02-06T13:31:49Z","abstract_excerpt":"We study the structure of Wick homogenenous ideals of higher degrees in quadratic algebras allowing Wick ordering. We present a method how to construct a homogeneous Wick ideal $\\mathcal{I}_{n+1}$ of degree $n+1$ out of a homogeneous Wick ideal $\\mathcal{I}_n$ of degree $n$ so that $\\mathcal{I}_{n+1}\\subset\\mathcal{I}_n$. We show that in some particular cases our procedure allows one to get a description of the largest homogeneous Wick ideals of higher degrees having generators of the largest quadratic Wick ideal only. Finally we study classes of $*$-representations of Wick version of CCR anni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1149","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":"2026-05-18T02:03:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LVr6/l2LV7O1PgynnXO4GfLZhEk/6pIy75sZbZCKh2/f477LhHdbNro12esDAI6UkiZ1SudgFpHhgEEm8RXKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:38:18.645329Z"},"content_sha256":"6618d640f67bdaaee60afbb726fb33e40836262b45fdac8964a822b9fed07aa6","schema_version":"1.0","event_id":"sha256:6618d640f67bdaaee60afbb726fb33e40836262b45fdac8964a822b9fed07aa6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V2ZBLPW3SOIWC44TENIHZALOYV/bundle.json","state_url":"https://pith.science/pith/V2ZBLPW3SOIWC44TENIHZALOYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V2ZBLPW3SOIWC44TENIHZALOYV/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":"2026-05-27T17:38:18Z","links":{"resolver":"https://pith.science/pith/V2ZBLPW3SOIWC44TENIHZALOYV","bundle":"https://pith.science/pith/V2ZBLPW3SOIWC44TENIHZALOYV/bundle.json","state":"https://pith.science/pith/V2ZBLPW3SOIWC44TENIHZALOYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V2ZBLPW3SOIWC44TENIHZALOYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V2ZBLPW3SOIWC44TENIHZALOYV","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":"4254424e61e056e50fe439ccc440db51e5531cc5f624b91c4dbccc386603d3f8","cross_cats_sorted":["math.FA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-06T13:31:49Z","title_canon_sha256":"6201b58db181d5f8b4e3d4e6faa6e9bc8407d03398110df4e241efe8eee7418b"},"schema_version":"1.0","source":{"id":"1102.1149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1149","created_at":"2026-05-18T02:03:16Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1149v1","created_at":"2026-05-18T02:03:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1149","created_at":"2026-05-18T02:03:16Z"},{"alias_kind":"pith_short_12","alias_value":"V2ZBLPW3SOIW","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V2ZBLPW3SOIWC44T","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V2ZBLPW3","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6618d640f67bdaaee60afbb726fb33e40836262b45fdac8964a822b9fed07aa6","target":"graph","created_at":"2026-05-18T02:03:16Z","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 the structure of Wick homogenenous ideals of higher degrees in quadratic algebras allowing Wick ordering. We present a method how to construct a homogeneous Wick ideal $\\mathcal{I}_{n+1}$ of degree $n+1$ out of a homogeneous Wick ideal $\\mathcal{I}_n$ of degree $n$ so that $\\mathcal{I}_{n+1}\\subset\\mathcal{I}_n$. We show that in some particular cases our procedure allows one to get a description of the largest homogeneous Wick ideals of higher degrees having generators of the largest quadratic Wick ideal only. Finally we study classes of $*$-representations of Wick version of CCR anni","authors_text":"Danil Proskurin, Lyudmila Turowska, Vasyl Ostrovskyi, Yurii Savchuk","cross_cats":["math.FA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-06T13:31:49Z","title":"On structure of homogenenous Wick ideals in Wick $*$-algebras with braided coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1149","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:e4b43fd95a81ba018dac197faf6f9b341fa117529862546382289e1f8b5af91f","target":"record","created_at":"2026-05-18T02:03:16Z","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":"4254424e61e056e50fe439ccc440db51e5531cc5f624b91c4dbccc386603d3f8","cross_cats_sorted":["math.FA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-06T13:31:49Z","title_canon_sha256":"6201b58db181d5f8b4e3d4e6faa6e9bc8407d03398110df4e241efe8eee7418b"},"schema_version":"1.0","source":{"id":"1102.1149","kind":"arxiv","version":1}},"canonical_sha256":"aeb215bedb939161739323507c816ec557b4a1d09f519c9c22fae5df164800c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeb215bedb939161739323507c816ec557b4a1d09f519c9c22fae5df164800c5","first_computed_at":"2026-05-18T02:03:16.242091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:16.242091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ezsWy/jeStmf5AODbHf0ZCZCebXDZmqLwOgQveipvkq+yeyk31S96Z1O9xiCNPgrVicyDjGNQguxSMXCNRs2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:16.242604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4b43fd95a81ba018dac197faf6f9b341fa117529862546382289e1f8b5af91f","sha256:6618d640f67bdaaee60afbb726fb33e40836262b45fdac8964a822b9fed07aa6"],"state_sha256":"c810752bef9cb56038be60d948e4a2ebdb8b22a84c93199b2823ca02629380ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmF3tE1P6kFRiOhwE5cbv7B8lEYiLQ/E/0pv9W94/iE/ZBieaXXGkoAESnzm9OaOigW5vVUnDollkVBqxm85Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:38:18.648810Z","bundle_sha256":"acdf42476c69fa7211ee790174e7dc88a0b58589374cdd9915f53cb9ba276b8f"}}