{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C6Q7YSVD354NXTJCIAYIEMVRXZ","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":"2bbda69b9e08e79e1f57ec3d20a9f5512661232d440ecbad5b3e5eeeb1803698","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-25T06:57:01Z","title_canon_sha256":"7e3dfb2fe61a5e30b3f80370e1104ac68e3d78e249911dbc1bfbd6e2465b0281"},"schema_version":"1.0","source":{"id":"1106.5107","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5107","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5107v6","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5107","created_at":"2026-05-18T02:21:52Z"},{"alias_kind":"pith_short_12","alias_value":"C6Q7YSVD354N","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C6Q7YSVD354NXTJC","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C6Q7YSVD","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:da6df2313a68bd6a876d185157a2bec1bd60aaf54504882ac1ceb36157bc026a","target":"graph","created_at":"2026-05-18T02:21:52Z","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":"Let $G$ be one of the classical compact, simple, centre-less, connected Lie groups or rank $n$ with a maximal torus $T$, the Lie algebra $\\clg$ and let $\\{ E_i, F_i, H_i, i=1, \\ldots, n \\}$ be the standard set of generators corresponding to a basis of the root system. Consider the adjoint-orbit space $M=\\{ {\\rm Ad}_g(H_1),~g \\in G \\}$, identified with the homogeneous space $G/L$ where $L=\\{ g \\in G:~{\\rm Ad}_g(H_1)=H_1\\}$. We prove that the `coordinate functions' $\\{ f_i, i=1, \\ldots, n \\}$, (where $f_i(g):=\\lambda_i({\\rm Ad}_g(H_1))$, $\\{ \\lambda_1, \\ldots, \\lambda_n\\}$ is basis of $\\clg^\\pri","authors_text":"Debashish Goswami","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-25T06:57:01Z","title":"Quadratic independence of coordinate functions of certain homogeneous spaces and action of compact quantum groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5107","kind":"arxiv","version":6},"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:af49a9d4641a8ff14795bf782128852468fce071af8656be3b3762213a3affda","target":"record","created_at":"2026-05-18T02:21:52Z","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":"2bbda69b9e08e79e1f57ec3d20a9f5512661232d440ecbad5b3e5eeeb1803698","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2011-06-25T06:57:01Z","title_canon_sha256":"7e3dfb2fe61a5e30b3f80370e1104ac68e3d78e249911dbc1bfbd6e2465b0281"},"schema_version":"1.0","source":{"id":"1106.5107","kind":"arxiv","version":6}},"canonical_sha256":"17a1fc4aa3df78dbcd2240308232b1be4ccc75ab5dea0174fa969b8c933e2e43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17a1fc4aa3df78dbcd2240308232b1be4ccc75ab5dea0174fa969b8c933e2e43","first_computed_at":"2026-05-18T02:21:52.116815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:52.116815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rID6YN0F7DZ8H7kJJrRN+RHE0VvuHr7APTdJ2SMAJvVipVs4uWWKY6xRRms9iYcW5LKcJdynrOx55JLMLZCnDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:52.117382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5107","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af49a9d4641a8ff14795bf782128852468fce071af8656be3b3762213a3affda","sha256:da6df2313a68bd6a876d185157a2bec1bd60aaf54504882ac1ceb36157bc026a"],"state_sha256":"f6e32b4723faadea99d6be389a489578c58072b876c257370a8a36d3e0446357"}