{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PX5VSL5OEDB6HGC7THTPDKPTNT","short_pith_number":"pith:PX5VSL5O","canonical_record":{"source":{"id":"1412.1280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-03T11:35:00Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d4146fa78bebf7d75d6cce0e1d068e4b10bb861e0ca64acc9efb1f895c95c39e","abstract_canon_sha256":"221c2710449dd7dfcf705aec64598efc3e37c8b2322eda337d17f3ea0e796bae"},"schema_version":"1.0"},"canonical_sha256":"7dfb592fae20c3e3985f99e6f1a9f36cd43997335abe3b1878fb72fd7de0441a","source":{"kind":"arxiv","id":"1412.1280","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1280","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1280v3","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1280","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"PX5VSL5OEDB6","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PX5VSL5OEDB6HGC7","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PX5VSL5O","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PX5VSL5OEDB6HGC7THTPDKPTNT","target":"record","payload":{"canonical_record":{"source":{"id":"1412.1280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-03T11:35:00Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d4146fa78bebf7d75d6cce0e1d068e4b10bb861e0ca64acc9efb1f895c95c39e","abstract_canon_sha256":"221c2710449dd7dfcf705aec64598efc3e37c8b2322eda337d17f3ea0e796bae"},"schema_version":"1.0"},"canonical_sha256":"7dfb592fae20c3e3985f99e6f1a9f36cd43997335abe3b1878fb72fd7de0441a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:11.028965Z","signature_b64":"yl6K/iTo2wnr4l7WPQhjjH/sW6D2w9sQYiok+jq5TnqOmFxXSS78mXn43rPjE35vXNlx8vmYVPNDq0rZXyH1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dfb592fae20c3e3985f99e6f1a9f36cd43997335abe3b1878fb72fd7de0441a","last_reissued_at":"2026-05-18T01:24:11.028311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:11.028311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.1280","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":"2026-05-18T01:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/aV4LjWPiHKYRPALUaKbkqNH3DzevCiw7ktrN8KrVeUYnGvzd+PAtAUY8iCtOalwwN/FmHXSjkGosZ6HOdWUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:54:09.078557Z"},"content_sha256":"ed534d31ae3659d3ea174b0d78c044152a199d256f785c4c5fd0a8983e74ee02","schema_version":"1.0","event_id":"sha256:ed534d31ae3659d3ea174b0d78c044152a199d256f785c4c5fd0a8983e74ee02"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PX5VSL5OEDB6HGC7THTPDKPTNT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operator-valued Jacobi parameters and examples of operator-valued distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OA","authors_text":"John D. Williams, Michael Anshelevich","submitted_at":"2014-12-03T11:35:00Z","abstract_excerpt":"In the setting of distributions taking values in a $C^\\ast$-algebra $\\mathcal{B}$, we define generalized Jacobi parameters and study distributions they generate. These include numerous known examples and one new family, of $\\mathcal{B}$-valued free binomial distributions, for which we are able to compute free convolution powers. Moreover, we develop a convenient combinatorial method for calculating the joint distributions of $\\mathcal{B}$-free random variables with Jacobi parameters, utilizing two-color non-crossing partitions. This leads to several new explicit examples of free convolution co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1280","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":"2026-05-18T01:24:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RJRpnBhXRulW9XwigHE50WzKsqMMZPWE28m/7XzPrYfXW6QIZEWT8MyoJ/c0szGGRvAAOcjp/y8gzejXDfPxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:54:09.079260Z"},"content_sha256":"0bdace488d9945767a0a6a8b5ae016945b7159f5090f56ef54ff197920ac54a4","schema_version":"1.0","event_id":"sha256:0bdace488d9945767a0a6a8b5ae016945b7159f5090f56ef54ff197920ac54a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PX5VSL5OEDB6HGC7THTPDKPTNT/bundle.json","state_url":"https://pith.science/pith/PX5VSL5OEDB6HGC7THTPDKPTNT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PX5VSL5OEDB6HGC7THTPDKPTNT/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":"2026-05-28T22:54:09Z","links":{"resolver":"https://pith.science/pith/PX5VSL5OEDB6HGC7THTPDKPTNT","bundle":"https://pith.science/pith/PX5VSL5OEDB6HGC7THTPDKPTNT/bundle.json","state":"https://pith.science/pith/PX5VSL5OEDB6HGC7THTPDKPTNT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PX5VSL5OEDB6HGC7THTPDKPTNT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PX5VSL5OEDB6HGC7THTPDKPTNT","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":"221c2710449dd7dfcf705aec64598efc3e37c8b2322eda337d17f3ea0e796bae","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-03T11:35:00Z","title_canon_sha256":"d4146fa78bebf7d75d6cce0e1d068e4b10bb861e0ca64acc9efb1f895c95c39e"},"schema_version":"1.0","source":{"id":"1412.1280","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.1280","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"arxiv_version","alias_value":"1412.1280v3","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.1280","created_at":"2026-05-18T01:24:11Z"},{"alias_kind":"pith_short_12","alias_value":"PX5VSL5OEDB6","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PX5VSL5OEDB6HGC7","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PX5VSL5O","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:0bdace488d9945767a0a6a8b5ae016945b7159f5090f56ef54ff197920ac54a4","target":"graph","created_at":"2026-05-18T01:24:11Z","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 the setting of distributions taking values in a $C^\\ast$-algebra $\\mathcal{B}$, we define generalized Jacobi parameters and study distributions they generate. These include numerous known examples and one new family, of $\\mathcal{B}$-valued free binomial distributions, for which we are able to compute free convolution powers. Moreover, we develop a convenient combinatorial method for calculating the joint distributions of $\\mathcal{B}$-free random variables with Jacobi parameters, utilizing two-color non-crossing partitions. This leads to several new explicit examples of free convolution co","authors_text":"John D. Williams, Michael Anshelevich","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-03T11:35:00Z","title":"Operator-valued Jacobi parameters and examples of operator-valued distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1280","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:ed534d31ae3659d3ea174b0d78c044152a199d256f785c4c5fd0a8983e74ee02","target":"record","created_at":"2026-05-18T01:24:11Z","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":"221c2710449dd7dfcf705aec64598efc3e37c8b2322eda337d17f3ea0e796bae","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-12-03T11:35:00Z","title_canon_sha256":"d4146fa78bebf7d75d6cce0e1d068e4b10bb861e0ca64acc9efb1f895c95c39e"},"schema_version":"1.0","source":{"id":"1412.1280","kind":"arxiv","version":3}},"canonical_sha256":"7dfb592fae20c3e3985f99e6f1a9f36cd43997335abe3b1878fb72fd7de0441a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dfb592fae20c3e3985f99e6f1a9f36cd43997335abe3b1878fb72fd7de0441a","first_computed_at":"2026-05-18T01:24:11.028311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:11.028311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yl6K/iTo2wnr4l7WPQhjjH/sW6D2w9sQYiok+jq5TnqOmFxXSS78mXn43rPjE35vXNlx8vmYVPNDq0rZXyH1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:11.028965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.1280","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed534d31ae3659d3ea174b0d78c044152a199d256f785c4c5fd0a8983e74ee02","sha256:0bdace488d9945767a0a6a8b5ae016945b7159f5090f56ef54ff197920ac54a4"],"state_sha256":"c22a3cb7c1c830de6b3a3a02eccac3f9e3b7216a614656f2a5eb63cc370c4249"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDPdJOwwxUm3ONyz/4yBrh1dzxD5ych2uPxkVVo28+fI80guoR4fOsMGrq2S+d5IwOh7xsbZSfY60hBVTp8+DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:54:09.082534Z","bundle_sha256":"522088f21df8cc0a6f157be0537a8e415df121d0dc38d878363ddf28a3c96d20"}}