{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:UYLP73A7DJBLISEIQM44M7IPNY","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":"9f1ba96e9a4ed9f007f65d3d173766ba2f096b97e0ce09683a0e6bb64d78694c","cross_cats_sorted":["math.QA","nlin.SI"],"license":"","primary_cat":"math.DG","submitted_at":"1998-12-25T16:37:37Z","title_canon_sha256":"524627b1947ecc2f01ed90489d3dd6f8d5a460ed71e95b306c520d6a70a7acf4"},"schema_version":"1.0","source":{"id":"math/9812146","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9812146","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9812146v2","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9812146","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"UYLP73A7DJBL","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"UYLP73A7DJBLISEI","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"UYLP73A7","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:3559338f748a2093cbd5f9fb88b116c2602b690ae87de7db790faa6af2a7f779","target":"graph","created_at":"2026-05-18T01:38:22Z","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":"In this paper we consider the Poisson algebraic structure associated with a classical $r$-matrix, i.e. with a solution of the modified classical Yang--Baxter equation. In Section 1 we recall the concept and basic facts of the $r$-matrix type Poisson orbits. Then we describe the $r$-matrix Poisson pencil (i.e the pair of compatible Poisson structures) of rank 1 or $CP^n$-type orbits of $SL(n,C)$. Here we calculate symplectic leaves and the integrable foliation associated with the pencil. We also describe the algebra of functions on $CP^n$-type orbits. In Section 2 we calculate the Poisson homol","authors_text":"Alexei Kotov","cross_cats":["math.QA","nlin.SI"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"1998-12-25T16:37:37Z","title":"Poisson homology of r-matrix type orbits I: example of computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9812146","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":"sha256:20aa9a4e19973f1c2b7ae2fcd8794173711c834aace8dd5e4700938024bbf74c","target":"record","created_at":"2026-05-18T01:38:22Z","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":"9f1ba96e9a4ed9f007f65d3d173766ba2f096b97e0ce09683a0e6bb64d78694c","cross_cats_sorted":["math.QA","nlin.SI"],"license":"","primary_cat":"math.DG","submitted_at":"1998-12-25T16:37:37Z","title_canon_sha256":"524627b1947ecc2f01ed90489d3dd6f8d5a460ed71e95b306c520d6a70a7acf4"},"schema_version":"1.0","source":{"id":"math/9812146","kind":"arxiv","version":2}},"canonical_sha256":"a616ffec1f1a42b448888339c67d0f6e32ea37dc1d01a9809cab8e9ac16ab887","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a616ffec1f1a42b448888339c67d0f6e32ea37dc1d01a9809cab8e9ac16ab887","first_computed_at":"2026-05-18T01:38:22.676138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:22.676138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ncJcDuTnDunNonVGFm3pQbHcN74u/Axiwb4/Ak1VHeJm41DAJdsCd9oJEpqD7c0Jhx55KIJq3liA6U1fTtR+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:22.676792Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9812146","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20aa9a4e19973f1c2b7ae2fcd8794173711c834aace8dd5e4700938024bbf74c","sha256:3559338f748a2093cbd5f9fb88b116c2602b690ae87de7db790faa6af2a7f779"],"state_sha256":"975f1f6c3f947e088a13eb1220818bd91a98e54fe67c74d728799425796853be"}