{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:N7TL7KRIJQYBWTYRRLNKIURD4L","short_pith_number":"pith:N7TL7KRI","canonical_record":{"source":{"id":"1207.6036","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-25T16:00:29Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"be7fc31a754386191e75ba1264a8878aa135fdc36c14bee386293f7c46651147","abstract_canon_sha256":"afb6f62a00969230ac5d53bae8307397609ab2d47e599ddc381277ebad6f5a58"},"schema_version":"1.0"},"canonical_sha256":"6fe6bfaa284c301b4f118adaa45223e2fedd7a689486dd964e4e97703b1978f4","source":{"kind":"arxiv","id":"1207.6036","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6036","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6036v3","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6036","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"N7TL7KRIJQYB","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N7TL7KRIJQYBWTYR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N7TL7KRI","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:N7TL7KRIJQYBWTYRRLNKIURD4L","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6036","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-25T16:00:29Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"be7fc31a754386191e75ba1264a8878aa135fdc36c14bee386293f7c46651147","abstract_canon_sha256":"afb6f62a00969230ac5d53bae8307397609ab2d47e599ddc381277ebad6f5a58"},"schema_version":"1.0"},"canonical_sha256":"6fe6bfaa284c301b4f118adaa45223e2fedd7a689486dd964e4e97703b1978f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:43.024606Z","signature_b64":"atNoP4DYKE0U/IGXKi4SoKowJ/PXyeMxnUE2nZZftHt7cX1PqrPpSETx4sQB8tBkCM2z8sV5VZa9W4eUkQwQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fe6bfaa284c301b4f118adaa45223e2fedd7a689486dd964e4e97703b1978f4","last_reissued_at":"2026-05-18T02:41:43.023840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:43.023840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6036","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PdvriWoAZ1uLU0Q6K9zjxZ0avTqLxSEWZGSNSApG7qS/n/BtxxIqG6xahrPleqjkX1SExAwg/0bJsixwtu/SBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:29:03.153449Z"},"content_sha256":"76da6556bfb1107563e8ea8f11f62a6c07908ba8842274981102b8a28fed702e","schema_version":"1.0","event_id":"sha256:76da6556bfb1107563e8ea8f11f62a6c07908ba8842274981102b8a28fed702e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:N7TL7KRIJQYBWTYRRLNKIURD4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum symmetric Kac-Moody pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Stefan Kolb","submitted_at":"2012-07-25T16:00:29Z","abstract_excerpt":"The present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac-Moody algebras. The resulting quantum symmetric pairs are right coideal subalgebras of quantized enveloping algebras. They give rise to triangular decompositions, including a quantum analog of the Iwasawa decomposition, and they can be written explicitly in terms of generators and relations. Moreover, their centers and their specializations are determined. The constructions follow G. Letzter's theory of quantum symmetric pairs for semisimpl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6036","kind":"arxiv","version":3},"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":"2026-05-18T02:41:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/v+e8uPmDdULZdkSCR4A5YtTCsSDxNx5F7MCbrwggcg8TZp3bvFfeH9uPjyEH3ReBQ155QuvOED36FdNDzoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T12:29:03.153805Z"},"content_sha256":"e208eb1f7f839f36e9370b9ada4fcc508a6165c83effdde1cab7a9df5155e3f9","schema_version":"1.0","event_id":"sha256:e208eb1f7f839f36e9370b9ada4fcc508a6165c83effdde1cab7a9df5155e3f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7TL7KRIJQYBWTYRRLNKIURD4L/bundle.json","state_url":"https://pith.science/pith/N7TL7KRIJQYBWTYRRLNKIURD4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7TL7KRIJQYBWTYRRLNKIURD4L/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":"2026-05-21T12:29:03Z","links":{"resolver":"https://pith.science/pith/N7TL7KRIJQYBWTYRRLNKIURD4L","bundle":"https://pith.science/pith/N7TL7KRIJQYBWTYRRLNKIURD4L/bundle.json","state":"https://pith.science/pith/N7TL7KRIJQYBWTYRRLNKIURD4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7TL7KRIJQYBWTYRRLNKIURD4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N7TL7KRIJQYBWTYRRLNKIURD4L","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":"afb6f62a00969230ac5d53bae8307397609ab2d47e599ddc381277ebad6f5a58","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-25T16:00:29Z","title_canon_sha256":"be7fc31a754386191e75ba1264a8878aa135fdc36c14bee386293f7c46651147"},"schema_version":"1.0","source":{"id":"1207.6036","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6036","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6036v3","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6036","created_at":"2026-05-18T02:41:43Z"},{"alias_kind":"pith_short_12","alias_value":"N7TL7KRIJQYB","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N7TL7KRIJQYBWTYR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N7TL7KRI","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:e208eb1f7f839f36e9370b9ada4fcc508a6165c83effdde1cab7a9df5155e3f9","target":"graph","created_at":"2026-05-18T02:41:43Z","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 present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac-Moody algebras. The resulting quantum symmetric pairs are right coideal subalgebras of quantized enveloping algebras. They give rise to triangular decompositions, including a quantum analog of the Iwasawa decomposition, and they can be written explicitly in terms of generators and relations. Moreover, their centers and their specializations are determined. The constructions follow G. Letzter's theory of quantum symmetric pairs for semisimpl","authors_text":"Stefan Kolb","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-25T16:00:29Z","title":"Quantum symmetric Kac-Moody pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6036","kind":"arxiv","version":3},"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":"sha256:76da6556bfb1107563e8ea8f11f62a6c07908ba8842274981102b8a28fed702e","target":"record","created_at":"2026-05-18T02:41:43Z","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":"afb6f62a00969230ac5d53bae8307397609ab2d47e599ddc381277ebad6f5a58","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-07-25T16:00:29Z","title_canon_sha256":"be7fc31a754386191e75ba1264a8878aa135fdc36c14bee386293f7c46651147"},"schema_version":"1.0","source":{"id":"1207.6036","kind":"arxiv","version":3}},"canonical_sha256":"6fe6bfaa284c301b4f118adaa45223e2fedd7a689486dd964e4e97703b1978f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fe6bfaa284c301b4f118adaa45223e2fedd7a689486dd964e4e97703b1978f4","first_computed_at":"2026-05-18T02:41:43.023840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:43.023840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"atNoP4DYKE0U/IGXKi4SoKowJ/PXyeMxnUE2nZZftHt7cX1PqrPpSETx4sQB8tBkCM2z8sV5VZa9W4eUkQwQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:43.024606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6036","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76da6556bfb1107563e8ea8f11f62a6c07908ba8842274981102b8a28fed702e","sha256:e208eb1f7f839f36e9370b9ada4fcc508a6165c83effdde1cab7a9df5155e3f9"],"state_sha256":"a5567b125f2001d4c71e034a46e16f56ccc45b5dbc13fcb464cedfd66ad3861d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CTIjz3UQpRtljL7XS0ZVypgRBFpORgkezWYrKP7XA+0D4eqiOeaXz94SGSTxWxgWVaNIyMHfISm5CUxQb+DsCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T12:29:03.155976Z","bundle_sha256":"f19db7672a72993f0b1f7b064e5f5a276ea60682d2a655fa260b1e3316567797"}}