{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AQ2DHHR5T6LL7SP75NYHCNRTMY","short_pith_number":"pith:AQ2DHHR5","canonical_record":{"source":{"id":"1812.11970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-27T08:21:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"28fb1eca061b1270afab47ec8fe416469a89fca2315430df640893e380210274","abstract_canon_sha256":"4d03285250d43f67007adcae8e4332a7d65c3028a6e86fbeabf125ecdc4affad"},"schema_version":"1.0"},"canonical_sha256":"0434339e3d9f96bfc9ffeb70713633662aa9098004f2b07ccb5a78a39d287aa1","source":{"kind":"arxiv","id":"1812.11970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11970","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11970v1","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11970","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"AQ2DHHR5T6LL","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AQ2DHHR5T6LL7SP7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AQ2DHHR5","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AQ2DHHR5T6LL7SP75NYHCNRTMY","target":"record","payload":{"canonical_record":{"source":{"id":"1812.11970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-27T08:21:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"28fb1eca061b1270afab47ec8fe416469a89fca2315430df640893e380210274","abstract_canon_sha256":"4d03285250d43f67007adcae8e4332a7d65c3028a6e86fbeabf125ecdc4affad"},"schema_version":"1.0"},"canonical_sha256":"0434339e3d9f96bfc9ffeb70713633662aa9098004f2b07ccb5a78a39d287aa1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:42.710694Z","signature_b64":"d591pLRJShcuZVp5IN9tuOjexEl5H80gD9DSrSvaoHp+7Y5ffjs3Sb/oJf5hb2AmuFO2uvnrqeqovOOZKys5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0434339e3d9f96bfc9ffeb70713633662aa9098004f2b07ccb5a78a39d287aa1","last_reissued_at":"2026-05-17T23:44:42.710070Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:42.710070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.11970","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":"2026-05-17T23:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c7T3oaT8sPzoqge18zy2nRxwnzj2Bncqt3LwTSLvsUxjpvlULJboczkF2OIuCiOIjWvFgT+j+soV479J6DreBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:02:01.839998Z"},"content_sha256":"df42739e2e911b9cfdcde3c89ead6c5a217c834a9d530f110e73e8a3c45c3056","schema_version":"1.0","event_id":"sha256:df42739e2e911b9cfdcde3c89ead6c5a217c834a9d530f110e73e8a3c45c3056"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AQ2DHHR5T6LL7SP75NYHCNRTMY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Adel Rezaei-Aghdam, Ghorbanali Haghighatdoost, Zohreh Ravanpak","submitted_at":"2018-12-27T08:21:50Z","abstract_excerpt":"We study {\\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called {\\em r-qn structures} on the corresponding Lie algebra $\\mathfrak g$. We investigate the procedure of the classification of such structures on the Lie algebras and then for clarity of our results we classify, up to a natural equivalence, all $r$-$qn$ structures on two types of four-dimensional real Lie algebras. We mention some remarks on the relation between $r$-$qn$ structures and the generalized complex structures on the Li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11970","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":"2026-05-17T23:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iWb6TMoGpF8plorFKHL1ubzZvYectrA7mXU5ArwdpBP8z4rTuKCvx2mPTAqP2KpXMDqMFHurXz9cMgYKiHecDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:02:01.840393Z"},"content_sha256":"e80d33c2a535424b6e7318ee2a15eb79cc03206f00dcf308b762c9820b49ba37","schema_version":"1.0","event_id":"sha256:e80d33c2a535424b6e7318ee2a15eb79cc03206f00dcf308b762c9820b49ba37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQ2DHHR5T6LL7SP75NYHCNRTMY/bundle.json","state_url":"https://pith.science/pith/AQ2DHHR5T6LL7SP75NYHCNRTMY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQ2DHHR5T6LL7SP75NYHCNRTMY/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":"2026-06-03T13:02:01Z","links":{"resolver":"https://pith.science/pith/AQ2DHHR5T6LL7SP75NYHCNRTMY","bundle":"https://pith.science/pith/AQ2DHHR5T6LL7SP75NYHCNRTMY/bundle.json","state":"https://pith.science/pith/AQ2DHHR5T6LL7SP75NYHCNRTMY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQ2DHHR5T6LL7SP75NYHCNRTMY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AQ2DHHR5T6LL7SP75NYHCNRTMY","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":"4d03285250d43f67007adcae8e4332a7d65c3028a6e86fbeabf125ecdc4affad","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-27T08:21:50Z","title_canon_sha256":"28fb1eca061b1270afab47ec8fe416469a89fca2315430df640893e380210274"},"schema_version":"1.0","source":{"id":"1812.11970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.11970","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1812.11970v1","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.11970","created_at":"2026-05-17T23:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"AQ2DHHR5T6LL","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AQ2DHHR5T6LL7SP7","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AQ2DHHR5","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:e80d33c2a535424b6e7318ee2a15eb79cc03206f00dcf308b762c9820b49ba37","target":"graph","created_at":"2026-05-17T23:44:42Z","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 {\\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called {\\em r-qn structures} on the corresponding Lie algebra $\\mathfrak g$. We investigate the procedure of the classification of such structures on the Lie algebras and then for clarity of our results we classify, up to a natural equivalence, all $r$-$qn$ structures on two types of four-dimensional real Lie algebras. We mention some remarks on the relation between $r$-$qn$ structures and the generalized complex structures on the Li","authors_text":"Adel Rezaei-Aghdam, Ghorbanali Haghighatdoost, Zohreh Ravanpak","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-27T08:21:50Z","title":"Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11970","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:df42739e2e911b9cfdcde3c89ead6c5a217c834a9d530f110e73e8a3c45c3056","target":"record","created_at":"2026-05-17T23:44:42Z","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":"4d03285250d43f67007adcae8e4332a7d65c3028a6e86fbeabf125ecdc4affad","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-12-27T08:21:50Z","title_canon_sha256":"28fb1eca061b1270afab47ec8fe416469a89fca2315430df640893e380210274"},"schema_version":"1.0","source":{"id":"1812.11970","kind":"arxiv","version":1}},"canonical_sha256":"0434339e3d9f96bfc9ffeb70713633662aa9098004f2b07ccb5a78a39d287aa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0434339e3d9f96bfc9ffeb70713633662aa9098004f2b07ccb5a78a39d287aa1","first_computed_at":"2026-05-17T23:44:42.710070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:42.710070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d591pLRJShcuZVp5IN9tuOjexEl5H80gD9DSrSvaoHp+7Y5ffjs3Sb/oJf5hb2AmuFO2uvnrqeqovOOZKys5Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:42.710694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.11970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df42739e2e911b9cfdcde3c89ead6c5a217c834a9d530f110e73e8a3c45c3056","sha256:e80d33c2a535424b6e7318ee2a15eb79cc03206f00dcf308b762c9820b49ba37"],"state_sha256":"6c5870579237352d8976b7a5d428ca6fd03052f86a75992040408d164f24ed80"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KfLKx0pGEsVdoasvVnqBcxqHxbYN14eKH2OelndYqnTieqcySZFE4lLj8SwgOEJbkJlXjxD9u6tvAUm/U/+uDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:02:01.842534Z","bundle_sha256":"d31f68822d843d44d1b3ba9d471c414f9939d4fdfc02c9fd380717acdba4ca8b"}}