{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1999:UWTRT6NQT4S6OSLJ442E37WUTP","short_pith_number":"pith:UWTRT6NQ","canonical_record":{"source":{"id":"math/9911194","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"1999-11-24T19:48:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"79a2e5550ce2e765a513166c84680d27c02a4c5ee1f670e9e72159477c43c9ba","abstract_canon_sha256":"bce33630c8e8dd09aa4e5de8f8e209250bccac2a5a1071f268b00a21f0f46b38"},"schema_version":"1.0"},"canonical_sha256":"a5a719f9b09f25e74969e7344dfed49be30094472b2ebc2ff55cee06ca83a1b7","source":{"kind":"arxiv","id":"math/9911194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9911194","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9911194v1","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9911194","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"UWTRT6NQT4S6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"UWTRT6NQT4S6OSLJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"UWTRT6NQ","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1999:UWTRT6NQT4S6OSLJ442E37WUTP","target":"record","payload":{"canonical_record":{"source":{"id":"math/9911194","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"1999-11-24T19:48:32Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"79a2e5550ce2e765a513166c84680d27c02a4c5ee1f670e9e72159477c43c9ba","abstract_canon_sha256":"bce33630c8e8dd09aa4e5de8f8e209250bccac2a5a1071f268b00a21f0f46b38"},"schema_version":"1.0"},"canonical_sha256":"a5a719f9b09f25e74969e7344dfed49be30094472b2ebc2ff55cee06ca83a1b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:22.298197Z","signature_b64":"stEdvGB+gTvkzQ+KaB8WeMwiqheghczGiHxmmgT6Q9mYaLxsKxkaI7qh+TuVuLcFpa18uVOfYxfWDoe1CUNzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5a719f9b09f25e74969e7344dfed49be30094472b2ebc2ff55cee06ca83a1b7","last_reissued_at":"2026-05-18T01:38:22.297550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:22.297550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9911194","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJNK7ggG0n5tT1u8hjf4sovq4+v2QwUHPx92G4vcnOmFVh/dl5exBQlGU2pVIjfZXxj4B3NJ/QwHikyEWtVhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:52:59.200679Z"},"content_sha256":"348d42ae125a761580b60bef0f6b06802c5021611fd7ca75183e38caae27dd71","schema_version":"1.0","event_id":"sha256:348d42ae125a761580b60bef0f6b06802c5021611fd7ca75183e38caae27dd71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1999:UWTRT6NQT4S6OSLJ442E37WUTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Deepak Parashar, Roger J. McDermott","submitted_at":"1999-11-24T19:48:32Z","abstract_excerpt":"The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contraction method. We apply the contraction procedure to G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then extended to the coloured quantum group GL_r{\\lambda,\\mu}(2) to yield a new Jordanian quantum group GL_m{\\lambda,\\mu}(2). Both G_r,s and G_m,k are then generalised to their coloured versions which inturn provide si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911194","kind":"arxiv","version":1},"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":"2026-05-18T01:38:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FTowN5NpMAiMhMQ5O49er05hpcTgdHQSMdorqO0obBXGDms5gDrBnseFI40bFtyyvAQAVhH5Ss4IWiWevuf9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:52:59.201265Z"},"content_sha256":"52ee2bf2b8d82c5106bd50b30f1b4023f6c67ecac0ba4253721ad0a15bd5fbe3","schema_version":"1.0","event_id":"sha256:52ee2bf2b8d82c5106bd50b30f1b4023f6c67ecac0ba4253721ad0a15bd5fbe3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UWTRT6NQT4S6OSLJ442E37WUTP/bundle.json","state_url":"https://pith.science/pith/UWTRT6NQT4S6OSLJ442E37WUTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UWTRT6NQT4S6OSLJ442E37WUTP/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":"2026-06-07T09:52:59Z","links":{"resolver":"https://pith.science/pith/UWTRT6NQT4S6OSLJ442E37WUTP","bundle":"https://pith.science/pith/UWTRT6NQT4S6OSLJ442E37WUTP/bundle.json","state":"https://pith.science/pith/UWTRT6NQT4S6OSLJ442E37WUTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UWTRT6NQT4S6OSLJ442E37WUTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:UWTRT6NQT4S6OSLJ442E37WUTP","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":"bce33630c8e8dd09aa4e5de8f8e209250bccac2a5a1071f268b00a21f0f46b38","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"1999-11-24T19:48:32Z","title_canon_sha256":"79a2e5550ce2e765a513166c84680d27c02a4c5ee1f670e9e72159477c43c9ba"},"schema_version":"1.0","source":{"id":"math/9911194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9911194","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/9911194v1","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9911194","created_at":"2026-05-18T01:38:22Z"},{"alias_kind":"pith_short_12","alias_value":"UWTRT6NQT4S6","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"UWTRT6NQT4S6OSLJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"UWTRT6NQ","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:52ee2bf2b8d82c5106bd50b30f1b4023f6c67ecac0ba4253721ad0a15bd5fbe3","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":"The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contraction method. We apply the contraction procedure to G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then extended to the coloured quantum group GL_r{\\lambda,\\mu}(2) to yield a new Jordanian quantum group GL_m{\\lambda,\\mu}(2). Both G_r,s and G_m,k are then generalised to their coloured versions which inturn provide si","authors_text":"Deepak Parashar, Roger J. McDermott","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"1999-11-24T19:48:32Z","title":"Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9911194","kind":"arxiv","version":1},"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":"sha256:348d42ae125a761580b60bef0f6b06802c5021611fd7ca75183e38caae27dd71","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":"bce33630c8e8dd09aa4e5de8f8e209250bccac2a5a1071f268b00a21f0f46b38","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"1999-11-24T19:48:32Z","title_canon_sha256":"79a2e5550ce2e765a513166c84680d27c02a4c5ee1f670e9e72159477c43c9ba"},"schema_version":"1.0","source":{"id":"math/9911194","kind":"arxiv","version":1}},"canonical_sha256":"a5a719f9b09f25e74969e7344dfed49be30094472b2ebc2ff55cee06ca83a1b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5a719f9b09f25e74969e7344dfed49be30094472b2ebc2ff55cee06ca83a1b7","first_computed_at":"2026-05-18T01:38:22.297550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:22.297550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"stEdvGB+gTvkzQ+KaB8WeMwiqheghczGiHxmmgT6Q9mYaLxsKxkaI7qh+TuVuLcFpa18uVOfYxfWDoe1CUNzAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:22.298197Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9911194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:348d42ae125a761580b60bef0f6b06802c5021611fd7ca75183e38caae27dd71","sha256:52ee2bf2b8d82c5106bd50b30f1b4023f6c67ecac0ba4253721ad0a15bd5fbe3"],"state_sha256":"322f212477d937829bf286d79d8bdd6b35fd8a9b88aa686e7b3a07d63844e6cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/4pqbOgfu4dF4b/o+6qkc8alVVqIGzZ/4vaSFCz/SCqbqfI8Q5nCZWdZwKA+91ZZa91GcngbEK8cONVk9NdDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:52:59.204448Z","bundle_sha256":"aaeceaf2721dfcac2203cdb5b6b81e79e863abe9984ff284186db817fecb83c5"}}