{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LCE4GI5SHIDI6HTMSEUS2OZP7K","short_pith_number":"pith:LCE4GI5S","canonical_record":{"source":{"id":"0902.2719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-02-16T16:02:26Z","cross_cats_sorted":[],"title_canon_sha256":"fb7eb490e747ff256dd22f3f33ad452e5e89d03f62d5b70cd2e626760c181557","abstract_canon_sha256":"bd389fdc75a9cfc62e4e0949c216b418d31955a938e17588db7914a1dc607df1"},"schema_version":"1.0"},"canonical_sha256":"5889c323b23a068f1e6c91292d3b2ffab8b808340d2d77a63649a8b86a9315e2","source":{"kind":"arxiv","id":"0902.2719","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2719","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2719v2","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2719","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"LCE4GI5SHIDI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LCE4GI5SHIDI6HTM","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LCE4GI5S","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LCE4GI5SHIDI6HTMSEUS2OZP7K","target":"record","payload":{"canonical_record":{"source":{"id":"0902.2719","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-02-16T16:02:26Z","cross_cats_sorted":[],"title_canon_sha256":"fb7eb490e747ff256dd22f3f33ad452e5e89d03f62d5b70cd2e626760c181557","abstract_canon_sha256":"bd389fdc75a9cfc62e4e0949c216b418d31955a938e17588db7914a1dc607df1"},"schema_version":"1.0"},"canonical_sha256":"5889c323b23a068f1e6c91292d3b2ffab8b808340d2d77a63649a8b86a9315e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:04.724944Z","signature_b64":"3synpL+m/3xoWE/mQIKKOVJP0DSsRDbTkiOwmQzdWxCx9fG2OKs2u2egiuEj0W4G6U1Vc92jLseC6dWo/MRDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5889c323b23a068f1e6c91292d3b2ffab8b808340d2d77a63649a8b86a9315e2","last_reissued_at":"2026-05-18T04:30:04.724537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:04.724537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.2719","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4sO1W41kOylso/vcyqQMzFwzyVQfs7O3FuvcOmXn9z8lKwcoEuZ8SLK33udVnn2Vq/apRQ2fuyq8DD1mbP5Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:42:18.083113Z"},"content_sha256":"1c2d38727265e41d88f519e182b3335c194b39df38e59228fc3b8c582855521e","schema_version":"1.0","event_id":"sha256:1c2d38727265e41d88f519e182b3335c194b39df38e59228fc3b8c582855521e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LCE4GI5SHIDI6HTMSEUS2OZP7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants of the half-liberated orthogonal group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Roland Vergnioux, Teodor Banica","submitted_at":"2009-02-16T16:02:26Z","abstract_excerpt":"The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum group between the orthogonal group $O_n$, and its free version $O_n^+$. We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between $O_n^*$ and $U_n$, a non abelian discrete group playing the role of weight lattice for $O_n^*$, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that the discrete quantum group dual to $O_n^*$ has polynomial g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2719","kind":"arxiv","version":2},"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":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SK04wqOlPnErdq7fZtVfJvPE0Akn2lwzh/g7HpTuwa7VLlKUhTG65gFrzXfOhoWMn4P8WeVQSaLGkobbaerbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:42:18.083904Z"},"content_sha256":"1947647d1ea9dfd48627e0bb1aa2d34ae7de59e82a46b1a5e9afe33a220fb3c5","schema_version":"1.0","event_id":"sha256:1947647d1ea9dfd48627e0bb1aa2d34ae7de59e82a46b1a5e9afe33a220fb3c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LCE4GI5SHIDI6HTMSEUS2OZP7K/bundle.json","state_url":"https://pith.science/pith/LCE4GI5SHIDI6HTMSEUS2OZP7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LCE4GI5SHIDI6HTMSEUS2OZP7K/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":"2026-05-31T14:42:18Z","links":{"resolver":"https://pith.science/pith/LCE4GI5SHIDI6HTMSEUS2OZP7K","bundle":"https://pith.science/pith/LCE4GI5SHIDI6HTMSEUS2OZP7K/bundle.json","state":"https://pith.science/pith/LCE4GI5SHIDI6HTMSEUS2OZP7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LCE4GI5SHIDI6HTMSEUS2OZP7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LCE4GI5SHIDI6HTMSEUS2OZP7K","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":"bd389fdc75a9cfc62e4e0949c216b418d31955a938e17588db7914a1dc607df1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-02-16T16:02:26Z","title_canon_sha256":"fb7eb490e747ff256dd22f3f33ad452e5e89d03f62d5b70cd2e626760c181557"},"schema_version":"1.0","source":{"id":"0902.2719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.2719","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"0902.2719v2","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2719","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"LCE4GI5SHIDI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LCE4GI5SHIDI6HTM","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LCE4GI5S","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:1947647d1ea9dfd48627e0bb1aa2d34ae7de59e82a46b1a5e9afe33a220fb3c5","target":"graph","created_at":"2026-05-18T04:30:04Z","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":"The half-liberated orthogonal group $O_n^*$ appears as intermediate quantum group between the orthogonal group $O_n$, and its free version $O_n^+$. We discuss here its basic algebraic properties, and we classify its irreducible representations. The classification of representations is done by using a certain twisting-type relation between $O_n^*$ and $U_n$, a non abelian discrete group playing the role of weight lattice for $O_n^*$, and a number of methods inspired from the theory of Lie algebras. We use these results for showing that the discrete quantum group dual to $O_n^*$ has polynomial g","authors_text":"Roland Vergnioux, Teodor Banica","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-02-16T16:02:26Z","title":"Invariants of the half-liberated orthogonal group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2719","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":"sha256:1c2d38727265e41d88f519e182b3335c194b39df38e59228fc3b8c582855521e","target":"record","created_at":"2026-05-18T04:30:04Z","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":"bd389fdc75a9cfc62e4e0949c216b418d31955a938e17588db7914a1dc607df1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-02-16T16:02:26Z","title_canon_sha256":"fb7eb490e747ff256dd22f3f33ad452e5e89d03f62d5b70cd2e626760c181557"},"schema_version":"1.0","source":{"id":"0902.2719","kind":"arxiv","version":2}},"canonical_sha256":"5889c323b23a068f1e6c91292d3b2ffab8b808340d2d77a63649a8b86a9315e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5889c323b23a068f1e6c91292d3b2ffab8b808340d2d77a63649a8b86a9315e2","first_computed_at":"2026-05-18T04:30:04.724537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:04.724537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3synpL+m/3xoWE/mQIKKOVJP0DSsRDbTkiOwmQzdWxCx9fG2OKs2u2egiuEj0W4G6U1Vc92jLseC6dWo/MRDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:04.724944Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.2719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c2d38727265e41d88f519e182b3335c194b39df38e59228fc3b8c582855521e","sha256:1947647d1ea9dfd48627e0bb1aa2d34ae7de59e82a46b1a5e9afe33a220fb3c5"],"state_sha256":"45561ec084c1b7a039005f068013910f023e04067b53866d1deaca60249f043d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nkpf5UAbQ2A8VIN7o/GqC/DSIPXQjqGlNRb2LQJhOtcbGReylGnyw/8xJ12jzRGEvY7TUKZQ1chC3EnyaOA/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:42:18.088116Z","bundle_sha256":"983b9df46cefa3d98ee55f93503fb10265436fd5c191b9d0d89d24470c4bfd9e"}}