{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZBJKEOSWJ673LPGTCR5AP4U223","short_pith_number":"pith:ZBJKEOSW","canonical_record":{"source":{"id":"1807.09238","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T17:20:09Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"39bcca53ea75ab53e47b7574df928e41d68c5a836d61ead0ae56799004062bab","abstract_canon_sha256":"ced2c565f6ca17e4bb3c85bfe7423cf56407aadc086fbeb2cd51cf4f7be45239"},"schema_version":"1.0"},"canonical_sha256":"c852a23a564fbfb5bcd3147a07f29ad6ef7af373f5d38832aa5cf79c3457c4bd","source":{"kind":"arxiv","id":"1807.09238","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09238","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09238v3","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09238","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZBJKEOSWJ673","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZBJKEOSWJ673LPGT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZBJKEOSW","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZBJKEOSWJ673LPGTCR5AP4U223","target":"record","payload":{"canonical_record":{"source":{"id":"1807.09238","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T17:20:09Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"39bcca53ea75ab53e47b7574df928e41d68c5a836d61ead0ae56799004062bab","abstract_canon_sha256":"ced2c565f6ca17e4bb3c85bfe7423cf56407aadc086fbeb2cd51cf4f7be45239"},"schema_version":"1.0"},"canonical_sha256":"c852a23a564fbfb5bcd3147a07f29ad6ef7af373f5d38832aa5cf79c3457c4bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:40.319803Z","signature_b64":"ehIfhfR9IyRtq74jZYH2dNR/FU1AiJuS2iCpPCHP0AZQvo392meZ2U1P1+alm+rUBoeEFOyZkRDs+IeKFmP2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c852a23a564fbfb5bcd3147a07f29ad6ef7af373f5d38832aa5cf79c3457c4bd","last_reissued_at":"2026-05-17T23:48:40.319176Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:40.319176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.09238","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":"2026-05-17T23:48:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5rrk7cG9evbIPesbU5S+SMnezWDobcFyJD34Kap137UIzol9hDRw0Dlmi663RAVKPL1eAQw0Xgdq29IV2Q5jCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:18:20.866636Z"},"content_sha256":"f372d26927fb5c0ce8e46268bcf98a4333988d9525f3226726d0d671ab3bfff9","schema_version":"1.0","event_id":"sha256:f372d26927fb5c0ce8e46268bcf98a4333988d9525f3226726d0d671ab3bfff9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZBJKEOSWJ673LPGTCR5AP4U223","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markov semi-groups associated with the complex unimodular group $Sl(2,\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.PR","authors_text":"Nizar Demni","submitted_at":"2018-07-24T17:20:09Z","abstract_excerpt":"In this paper, we derive the explicit expressions of two Markov semi-groups constructed by P. Biane in \\cite{Bia1} from the restriction of a particular positive definite function on the complex unimodular group $Sl(2,\\mathbb{C})$ to two commutative subalgebras of its universal $C^{\\star}$-algebra. Our computations use Euclidean Fourier analysis together with the generating function of Laguerre polynomials with index $-1$, and yield absolutely-convergent double series representations of the semi-group densities. In the last part of the paper, we discuss the coincidence, noticed by Biane as well"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09238","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":"2026-05-17T23:48:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u5bA4tAcDPCryEZDcQCiCbxxL/vYn+nPDm/NOmavCFFGJbtqeo4e/NjCe+S+dn8tLvyfxBu5m1/q7N7kkiREAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:18:20.867230Z"},"content_sha256":"002736deed68eda91a7ac27696a35cf1f4b6dd9dbeca677c0352151bc845c1ce","schema_version":"1.0","event_id":"sha256:002736deed68eda91a7ac27696a35cf1f4b6dd9dbeca677c0352151bc845c1ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBJKEOSWJ673LPGTCR5AP4U223/bundle.json","state_url":"https://pith.science/pith/ZBJKEOSWJ673LPGTCR5AP4U223/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBJKEOSWJ673LPGTCR5AP4U223/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":"2026-06-06T21:18:20Z","links":{"resolver":"https://pith.science/pith/ZBJKEOSWJ673LPGTCR5AP4U223","bundle":"https://pith.science/pith/ZBJKEOSWJ673LPGTCR5AP4U223/bundle.json","state":"https://pith.science/pith/ZBJKEOSWJ673LPGTCR5AP4U223/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBJKEOSWJ673LPGTCR5AP4U223/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZBJKEOSWJ673LPGTCR5AP4U223","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":"ced2c565f6ca17e4bb3c85bfe7423cf56407aadc086fbeb2cd51cf4f7be45239","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T17:20:09Z","title_canon_sha256":"39bcca53ea75ab53e47b7574df928e41d68c5a836d61ead0ae56799004062bab"},"schema_version":"1.0","source":{"id":"1807.09238","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09238","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09238v3","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09238","created_at":"2026-05-17T23:48:40Z"},{"alias_kind":"pith_short_12","alias_value":"ZBJKEOSWJ673","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZBJKEOSWJ673LPGT","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZBJKEOSW","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:002736deed68eda91a7ac27696a35cf1f4b6dd9dbeca677c0352151bc845c1ce","target":"graph","created_at":"2026-05-17T23:48:40Z","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":"In this paper, we derive the explicit expressions of two Markov semi-groups constructed by P. Biane in \\cite{Bia1} from the restriction of a particular positive definite function on the complex unimodular group $Sl(2,\\mathbb{C})$ to two commutative subalgebras of its universal $C^{\\star}$-algebra. Our computations use Euclidean Fourier analysis together with the generating function of Laguerre polynomials with index $-1$, and yield absolutely-convergent double series representations of the semi-group densities. In the last part of the paper, we discuss the coincidence, noticed by Biane as well","authors_text":"Nizar Demni","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T17:20:09Z","title":"Markov semi-groups associated with the complex unimodular group $Sl(2,\\mathbb{C})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09238","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:f372d26927fb5c0ce8e46268bcf98a4333988d9525f3226726d0d671ab3bfff9","target":"record","created_at":"2026-05-17T23:48:40Z","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":"ced2c565f6ca17e4bb3c85bfe7423cf56407aadc086fbeb2cd51cf4f7be45239","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T17:20:09Z","title_canon_sha256":"39bcca53ea75ab53e47b7574df928e41d68c5a836d61ead0ae56799004062bab"},"schema_version":"1.0","source":{"id":"1807.09238","kind":"arxiv","version":3}},"canonical_sha256":"c852a23a564fbfb5bcd3147a07f29ad6ef7af373f5d38832aa5cf79c3457c4bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c852a23a564fbfb5bcd3147a07f29ad6ef7af373f5d38832aa5cf79c3457c4bd","first_computed_at":"2026-05-17T23:48:40.319176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:40.319176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ehIfhfR9IyRtq74jZYH2dNR/FU1AiJuS2iCpPCHP0AZQvo392meZ2U1P1+alm+rUBoeEFOyZkRDs+IeKFmP2Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:40.319803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09238","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f372d26927fb5c0ce8e46268bcf98a4333988d9525f3226726d0d671ab3bfff9","sha256:002736deed68eda91a7ac27696a35cf1f4b6dd9dbeca677c0352151bc845c1ce"],"state_sha256":"6a62d6f2db00ca6392dc2ebfcf98cab3fda0c78ad6794906d8805ab64f940489"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rBOcI0esGLrB6TEUITc2W9XyDZ5Tpg2EPp5dmUYnT8kvG5Eb4CrTmm5ErxUy67WSFuA56EdkkBdePPiIZs/rBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:18:20.870147Z","bundle_sha256":"39cb78b560cf938ab42b7fb1e254f7ea9422469e4ebbee26fe1e9499ff5ef49d"}}