{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:HMPURCBRT7CPQEQWAKOBTTIEGN","short_pith_number":"pith:HMPURCBR","canonical_record":{"source":{"id":"math/0512581","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2005-12-27T00:52:57Z","cross_cats_sorted":[],"title_canon_sha256":"4dd1287095a2674a713dbae07b290268e69010ee4fdf87bd27a7bde50833eb19","abstract_canon_sha256":"ef7a8797c82ac560cd72c7c9e3f6f4d951a9269f97bc7341f16975e5175328f8"},"schema_version":"1.0"},"canonical_sha256":"3b1f4888319fc4f81216029c19cd04336ad5b4515da53682d41c6fb8d5abe6fb","source":{"kind":"arxiv","id":"math/0512581","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512581","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512581v2","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512581","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"pith_short_12","alias_value":"HMPURCBRT7CP","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"pith_short_16","alias_value":"HMPURCBRT7CPQEQW","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"pith_short_8","alias_value":"HMPURCBR","created_at":"2026-07-04T14:52:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:HMPURCBRT7CPQEQWAKOBTTIEGN","target":"record","payload":{"canonical_record":{"source":{"id":"math/0512581","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2005-12-27T00:52:57Z","cross_cats_sorted":[],"title_canon_sha256":"4dd1287095a2674a713dbae07b290268e69010ee4fdf87bd27a7bde50833eb19","abstract_canon_sha256":"ef7a8797c82ac560cd72c7c9e3f6f4d951a9269f97bc7341f16975e5175328f8"},"schema_version":"1.0"},"canonical_sha256":"3b1f4888319fc4f81216029c19cd04336ad5b4515da53682d41c6fb8d5abe6fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:52:17.672494Z","signature_b64":"vTT2S5w4eXZoyWm23oEgaj0sk2z6eXBAvFOJg3sst1mgei0tK2T6cEYOPnyiJfgUWwsDqcNBgHp/a7nZDLYJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b1f4888319fc4f81216029c19cd04336ad5b4515da53682d41c6fb8d5abe6fb","last_reissued_at":"2026-07-04T14:52:17.672069Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:52:17.672069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0512581","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":"2026-07-04T14:52:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9Oub8svkma3/DDyQWIi1ZEZ70ECe+UAw9VfRUvz7HSjra8CFOYr8m9h1fIj3ROy2ySV4XUOvUy6iD/liRH5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T15:40:51.709814Z"},"content_sha256":"ea0d50e8db9fae97562cba5e2026e69fbb225245405946c410f76fb64fb10b24","schema_version":"1.0","event_id":"sha256:ea0d50e8db9fae97562cba5e2026e69fbb225245405946c410f76fb64fb10b24"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:HMPURCBRT7CPQEQWAKOBTTIEGN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Symmetric Pairs and the Reflection Equation","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Stefan Kolb","submitted_at":"2005-12-27T00:52:57Z","abstract_excerpt":"It is shown that central elements in G. Letzter's quantum group analogs of symmetric pairs lead to solutions of the reflection equation. This clarifies the relation between Letzter's approach to quantum symmetric pairs and the approach taken by M. Noumi, T. Sugitani, and M. Dijkhuizen.\n  We develop general tools to show that a Noumi-Sugitani-Dijkhuizen type construction of quantum symmetric pairs can be performed preserving spherical representations from the classical situation. These tools apply to the symmetric pair FII and to all symmetric pairs which correspond to an automorphism of the un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512581","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0512581/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:52:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ctA6izYo9vREbWsEDzkAXFBgLLsPsvw9nLKzwq6EyoLuSrdclphQwRcFH6fpugrCCqYfe/+5t3IZgVBC7SzNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T15:40:51.710724Z"},"content_sha256":"f8d2034b9dd187b0b6cbaa4d7e1555839e50d57267258298017afc1a3ca569bf","schema_version":"1.0","event_id":"sha256:f8d2034b9dd187b0b6cbaa4d7e1555839e50d57267258298017afc1a3ca569bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMPURCBRT7CPQEQWAKOBTTIEGN/bundle.json","state_url":"https://pith.science/pith/HMPURCBRT7CPQEQWAKOBTTIEGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMPURCBRT7CPQEQWAKOBTTIEGN/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":"2026-08-10T15:40:51Z","links":{"resolver":"https://pith.science/pith/HMPURCBRT7CPQEQWAKOBTTIEGN","bundle":"https://pith.science/pith/HMPURCBRT7CPQEQWAKOBTTIEGN/bundle.json","state":"https://pith.science/pith/HMPURCBRT7CPQEQWAKOBTTIEGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMPURCBRT7CPQEQWAKOBTTIEGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:HMPURCBRT7CPQEQWAKOBTTIEGN","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":"ef7a8797c82ac560cd72c7c9e3f6f4d951a9269f97bc7341f16975e5175328f8","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2005-12-27T00:52:57Z","title_canon_sha256":"4dd1287095a2674a713dbae07b290268e69010ee4fdf87bd27a7bde50833eb19"},"schema_version":"1.0","source":{"id":"math/0512581","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0512581","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"arxiv_version","alias_value":"math/0512581v2","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512581","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"pith_short_12","alias_value":"HMPURCBRT7CP","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"pith_short_16","alias_value":"HMPURCBRT7CPQEQW","created_at":"2026-07-04T14:52:17Z"},{"alias_kind":"pith_short_8","alias_value":"HMPURCBR","created_at":"2026-07-04T14:52:17Z"}],"graph_snapshots":[{"event_id":"sha256:f8d2034b9dd187b0b6cbaa4d7e1555839e50d57267258298017afc1a3ca569bf","target":"graph","created_at":"2026-07-04T14:52:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0512581/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is shown that central elements in G. Letzter's quantum group analogs of symmetric pairs lead to solutions of the reflection equation. This clarifies the relation between Letzter's approach to quantum symmetric pairs and the approach taken by M. Noumi, T. Sugitani, and M. Dijkhuizen.\n  We develop general tools to show that a Noumi-Sugitani-Dijkhuizen type construction of quantum symmetric pairs can be performed preserving spherical representations from the classical situation. These tools apply to the symmetric pair FII and to all symmetric pairs which correspond to an automorphism of the un","authors_text":"Stefan Kolb","cross_cats":[],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2005-12-27T00:52:57Z","title":"Quantum Symmetric Pairs and the Reflection Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512581","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:ea0d50e8db9fae97562cba5e2026e69fbb225245405946c410f76fb64fb10b24","target":"record","created_at":"2026-07-04T14:52:17Z","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":"ef7a8797c82ac560cd72c7c9e3f6f4d951a9269f97bc7341f16975e5175328f8","cross_cats_sorted":[],"license":"","primary_cat":"math.QA","submitted_at":"2005-12-27T00:52:57Z","title_canon_sha256":"4dd1287095a2674a713dbae07b290268e69010ee4fdf87bd27a7bde50833eb19"},"schema_version":"1.0","source":{"id":"math/0512581","kind":"arxiv","version":2}},"canonical_sha256":"3b1f4888319fc4f81216029c19cd04336ad5b4515da53682d41c6fb8d5abe6fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b1f4888319fc4f81216029c19cd04336ad5b4515da53682d41c6fb8d5abe6fb","first_computed_at":"2026-07-04T14:52:17.672069Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:52:17.672069Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vTT2S5w4eXZoyWm23oEgaj0sk2z6eXBAvFOJg3sst1mgei0tK2T6cEYOPnyiJfgUWwsDqcNBgHp/a7nZDLYJCA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:52:17.672494Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0512581","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea0d50e8db9fae97562cba5e2026e69fbb225245405946c410f76fb64fb10b24","sha256:f8d2034b9dd187b0b6cbaa4d7e1555839e50d57267258298017afc1a3ca569bf"],"state_sha256":"50fa41be520d4089cefa9ae2a75ffb6728c389ef9840fd0279723ad82b802c1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bu6K7m1z0/pYB3MuhnnbDMNgOdGwDUFkPGLf5MgcH9pLnDjULoMBgLvTT8/JGFDNV5/Q/vjYCW9N505jQJq2AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T15:40:51.716336Z","bundle_sha256":"30c5f7f15a6606787d9b708cd761e4599342ec8669d3b6018e07f94eeb7582ca"}}