{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7BYUF74V3R2O5CNAEE6KO4SZXE","short_pith_number":"pith:7BYUF74V","canonical_record":{"source":{"id":"1703.08435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T14:45:15Z","cross_cats_sorted":["math.OA","math.PR"],"title_canon_sha256":"f85a56751a35b1c6e077c7d308239cdab0a372f9931b288b6514b0d518d711d8","abstract_canon_sha256":"ef63234b39741bade061f789bfb72104a5039d6da6a07a8ac1d78847ca335b83"},"schema_version":"1.0"},"canonical_sha256":"f87142ff95dc74ee89a0213ca77259b908ca7294fccd40d3fce406a4bd98842f","source":{"kind":"arxiv","id":"1703.08435","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08435","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08435v2","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08435","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"7BYUF74V3R2O","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7BYUF74V3R2O5CNA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7BYUF74V","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7BYUF74V3R2O5CNAEE6KO4SZXE","target":"record","payload":{"canonical_record":{"source":{"id":"1703.08435","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T14:45:15Z","cross_cats_sorted":["math.OA","math.PR"],"title_canon_sha256":"f85a56751a35b1c6e077c7d308239cdab0a372f9931b288b6514b0d518d711d8","abstract_canon_sha256":"ef63234b39741bade061f789bfb72104a5039d6da6a07a8ac1d78847ca335b83"},"schema_version":"1.0"},"canonical_sha256":"f87142ff95dc74ee89a0213ca77259b908ca7294fccd40d3fce406a4bd98842f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:39.774792Z","signature_b64":"BhEgha2UUwOspy2KEG+sNQM6xuLfJ+Sw/Qbexvj/5cpmYG0EiYVv7k2zR7oWjhSzFFePeYFXLGJInCB9bIk6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f87142ff95dc74ee89a0213ca77259b908ca7294fccd40d3fce406a4bd98842f","last_reissued_at":"2026-05-18T00:47:39.774226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:39.774226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.08435","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":"2026-05-18T00:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Z6hB0g9xO6tD9S2btIixG4HFM/NwipKw6LfRbxXAaaIM8WpAPOqwEkqzZIC9Vh/xO7VmbSzk/Ihh+rJlrF/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:43:50.936808Z"},"content_sha256":"eb34f988da8a3657a5668e999bc014cd772e0d5708b31da12c4a37a5b444a26b","schema_version":"1.0","event_id":"sha256:eb34f988da8a3657a5668e999bc014cd772e0d5708b31da12c4a37a5b444a26b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7BYUF74V3R2O5CNAEE6KO4SZXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments of the Hermitian Matrix Jacobi process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.PR"],"primary_cat":"math.CO","authors_text":"Luc Deleaval, Nizar Demni","submitted_at":"2017-03-24T14:45:15Z","abstract_excerpt":"In this paper, we compute the expectation of traces of powers of the hermitian matrix Jacobi process for a large enough but fixed size. To proceed, we first derive the semi-group density of its eigenvalues process as a bilinear series of symmetric Jacobi polynomials. Next, we use the expansion of power sums in the Schur polynomial basis and the integral Cauchy-Binet formula in order to determine the partitions having non zero contributions after integration. It turns out that these are hooks of bounded weight and the sought expectation results from the integral of a product of two Schur functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08435","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":"2026-05-18T00:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCHrgvo+ojmb3EJPAGg7582N71S84G1/KOkvUlfk6J6W9J9GrDhZFu0Q5NiXA6pLeuT43RuBM5qi5/Ugdh4KDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:43:50.937480Z"},"content_sha256":"cc6598969deb8855dcccd98a898a12e93ab00eb38ebf0b8e57a675c5249b7c8f","schema_version":"1.0","event_id":"sha256:cc6598969deb8855dcccd98a898a12e93ab00eb38ebf0b8e57a675c5249b7c8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BYUF74V3R2O5CNAEE6KO4SZXE/bundle.json","state_url":"https://pith.science/pith/7BYUF74V3R2O5CNAEE6KO4SZXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BYUF74V3R2O5CNAEE6KO4SZXE/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":"2026-06-06T16:43:50Z","links":{"resolver":"https://pith.science/pith/7BYUF74V3R2O5CNAEE6KO4SZXE","bundle":"https://pith.science/pith/7BYUF74V3R2O5CNAEE6KO4SZXE/bundle.json","state":"https://pith.science/pith/7BYUF74V3R2O5CNAEE6KO4SZXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BYUF74V3R2O5CNAEE6KO4SZXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7BYUF74V3R2O5CNAEE6KO4SZXE","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":"ef63234b39741bade061f789bfb72104a5039d6da6a07a8ac1d78847ca335b83","cross_cats_sorted":["math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T14:45:15Z","title_canon_sha256":"f85a56751a35b1c6e077c7d308239cdab0a372f9931b288b6514b0d518d711d8"},"schema_version":"1.0","source":{"id":"1703.08435","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.08435","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.08435v2","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.08435","created_at":"2026-05-18T00:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"7BYUF74V3R2O","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"7BYUF74V3R2O5CNA","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"7BYUF74V","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:cc6598969deb8855dcccd98a898a12e93ab00eb38ebf0b8e57a675c5249b7c8f","target":"graph","created_at":"2026-05-18T00:47:39Z","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 compute the expectation of traces of powers of the hermitian matrix Jacobi process for a large enough but fixed size. To proceed, we first derive the semi-group density of its eigenvalues process as a bilinear series of symmetric Jacobi polynomials. Next, we use the expansion of power sums in the Schur polynomial basis and the integral Cauchy-Binet formula in order to determine the partitions having non zero contributions after integration. It turns out that these are hooks of bounded weight and the sought expectation results from the integral of a product of two Schur functi","authors_text":"Luc Deleaval, Nizar Demni","cross_cats":["math.OA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T14:45:15Z","title":"Moments of the Hermitian Matrix Jacobi process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.08435","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:eb34f988da8a3657a5668e999bc014cd772e0d5708b31da12c4a37a5b444a26b","target":"record","created_at":"2026-05-18T00:47:39Z","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":"ef63234b39741bade061f789bfb72104a5039d6da6a07a8ac1d78847ca335b83","cross_cats_sorted":["math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-24T14:45:15Z","title_canon_sha256":"f85a56751a35b1c6e077c7d308239cdab0a372f9931b288b6514b0d518d711d8"},"schema_version":"1.0","source":{"id":"1703.08435","kind":"arxiv","version":2}},"canonical_sha256":"f87142ff95dc74ee89a0213ca77259b908ca7294fccd40d3fce406a4bd98842f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f87142ff95dc74ee89a0213ca77259b908ca7294fccd40d3fce406a4bd98842f","first_computed_at":"2026-05-18T00:47:39.774226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:39.774226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BhEgha2UUwOspy2KEG+sNQM6xuLfJ+Sw/Qbexvj/5cpmYG0EiYVv7k2zR7oWjhSzFFePeYFXLGJInCB9bIk6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:39.774792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.08435","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb34f988da8a3657a5668e999bc014cd772e0d5708b31da12c4a37a5b444a26b","sha256:cc6598969deb8855dcccd98a898a12e93ab00eb38ebf0b8e57a675c5249b7c8f"],"state_sha256":"39cd241b49487a77824e881e3f0ef6f32a517dd3e550b07fa40164279a7bcc89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iVZducHC5L3aOY+dTg9MYh/jCK6rZQPyBjxm6fDpuBBzIRRHVbQFOXptlIlFmvikin/IwLje7hdf/QyD0TROAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:43:50.940501Z","bundle_sha256":"822eaa1390b1ca9b02a4d9e225f7071650509f80284fecc3627bf03efcfc4660"}}