{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UFFXMUIMYMORGHODXRYYZWG2NL","short_pith_number":"pith:UFFXMUIM","canonical_record":{"source":{"id":"1408.3251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-14T11:18:19Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0171824eff9ddc0f3728ac1d235372fd3b01ebca4d5ea8a3b6fdc5ef01c0474d","abstract_canon_sha256":"4268b2e202c8444b7cf0ef33ab09efdd75cc3d9aa3759dfbaf35e4f7e493f07e"},"schema_version":"1.0"},"canonical_sha256":"a14b76510cc31d131dc3bc718cd8da6ae8adc18816d2cfd347ed72ed5b3c4a6b","source":{"kind":"arxiv","id":"1408.3251","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3251","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3251v1","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3251","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"UFFXMUIMYMOR","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UFFXMUIMYMORGHOD","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UFFXMUIM","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UFFXMUIMYMORGHODXRYYZWG2NL","target":"record","payload":{"canonical_record":{"source":{"id":"1408.3251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-14T11:18:19Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0171824eff9ddc0f3728ac1d235372fd3b01ebca4d5ea8a3b6fdc5ef01c0474d","abstract_canon_sha256":"4268b2e202c8444b7cf0ef33ab09efdd75cc3d9aa3759dfbaf35e4f7e493f07e"},"schema_version":"1.0"},"canonical_sha256":"a14b76510cc31d131dc3bc718cd8da6ae8adc18816d2cfd347ed72ed5b3c4a6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:59.951173Z","signature_b64":"DP4dOGKXpHSQv68KibQ9xaehtYbKvFOiDxjzoELQm99DvjO9Wwktv/nOL7MDbnR4ZTwXgGvQiyfqBrWP5aE3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a14b76510cc31d131dc3bc718cd8da6ae8adc18816d2cfd347ed72ed5b3c4a6b","last_reissued_at":"2026-05-18T01:55:59.950779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:59.950779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.3251","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":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goLk4ow9kw1xDmUsl5vBrGb+lKdpVYpQHT3tmvUh1iVSYhMqwHDFrNfKPLH5CO0oCd85XRkRukwr8ZKjihWABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:05:52.987725Z"},"content_sha256":"789bd91149917b169322947fbb2ac4d1270c99950dfb2878f94f2a88a1f0cf29","schema_version":"1.0","event_id":"sha256:789bd91149917b169322947fbb2ac4d1270c99950dfb2878f94f2a88a1f0cf29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UFFXMUIMYMORGHODXRYYZWG2NL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorics of Bi-Freeness with Amalgamation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Brent Nelson, Ian Charlesworth, Paul Skoufranis","submitted_at":"2014-08-14T11:18:19Z","abstract_excerpt":"In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence. Further, we develop a multiplicative convolution for operator-valued random variables and explore ways to construct bi-free pairs of B-faces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3251","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":"2026-05-18T01:55:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PrRtpgntL+s61QsVgwGvEscl1EN5YzvkH2n0USvLBD+xzeg4nc+nxKDhBNhBfiKhO9N4grycqvX8tF39ewc8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:05:52.988071Z"},"content_sha256":"5614fbc8e1fdd7dcbe52274dbf9b52e0922b9eef4424f54e6fbf9208d1c9f078","schema_version":"1.0","event_id":"sha256:5614fbc8e1fdd7dcbe52274dbf9b52e0922b9eef4424f54e6fbf9208d1c9f078"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFFXMUIMYMORGHODXRYYZWG2NL/bundle.json","state_url":"https://pith.science/pith/UFFXMUIMYMORGHODXRYYZWG2NL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFFXMUIMYMORGHODXRYYZWG2NL/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":"2026-06-26T09:05:52Z","links":{"resolver":"https://pith.science/pith/UFFXMUIMYMORGHODXRYYZWG2NL","bundle":"https://pith.science/pith/UFFXMUIMYMORGHODXRYYZWG2NL/bundle.json","state":"https://pith.science/pith/UFFXMUIMYMORGHODXRYYZWG2NL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFFXMUIMYMORGHODXRYYZWG2NL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UFFXMUIMYMORGHODXRYYZWG2NL","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":"4268b2e202c8444b7cf0ef33ab09efdd75cc3d9aa3759dfbaf35e4f7e493f07e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-14T11:18:19Z","title_canon_sha256":"0171824eff9ddc0f3728ac1d235372fd3b01ebca4d5ea8a3b6fdc5ef01c0474d"},"schema_version":"1.0","source":{"id":"1408.3251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3251","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3251v1","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3251","created_at":"2026-05-18T01:55:59Z"},{"alias_kind":"pith_short_12","alias_value":"UFFXMUIMYMOR","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UFFXMUIMYMORGHOD","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UFFXMUIM","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:5614fbc8e1fdd7dcbe52274dbf9b52e0922b9eef4424f54e6fbf9208d1c9f078","target":"graph","created_at":"2026-05-18T01:55:59Z","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 develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence. Further, we develop a multiplicative convolution for operator-valued random variables and explore ways to construct bi-free pairs of B-faces.","authors_text":"Brent Nelson, Ian Charlesworth, Paul Skoufranis","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-14T11:18:19Z","title":"Combinatorics of Bi-Freeness with Amalgamation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3251","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":"sha256:789bd91149917b169322947fbb2ac4d1270c99950dfb2878f94f2a88a1f0cf29","target":"record","created_at":"2026-05-18T01:55:59Z","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":"4268b2e202c8444b7cf0ef33ab09efdd75cc3d9aa3759dfbaf35e4f7e493f07e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-14T11:18:19Z","title_canon_sha256":"0171824eff9ddc0f3728ac1d235372fd3b01ebca4d5ea8a3b6fdc5ef01c0474d"},"schema_version":"1.0","source":{"id":"1408.3251","kind":"arxiv","version":1}},"canonical_sha256":"a14b76510cc31d131dc3bc718cd8da6ae8adc18816d2cfd347ed72ed5b3c4a6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a14b76510cc31d131dc3bc718cd8da6ae8adc18816d2cfd347ed72ed5b3c4a6b","first_computed_at":"2026-05-18T01:55:59.950779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:59.950779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DP4dOGKXpHSQv68KibQ9xaehtYbKvFOiDxjzoELQm99DvjO9Wwktv/nOL7MDbnR4ZTwXgGvQiyfqBrWP5aE3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:59.951173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:789bd91149917b169322947fbb2ac4d1270c99950dfb2878f94f2a88a1f0cf29","sha256:5614fbc8e1fdd7dcbe52274dbf9b52e0922b9eef4424f54e6fbf9208d1c9f078"],"state_sha256":"c4e496cc27455040c59d789c3652fdf709df9bde958d42f5b52aa64e528e3124"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UESJDxaCI6bIKiHXXP6QTYPrFtAwIX4CMgLyhQ6LtKByv4vAnNLsT+EKNgRWGeooQQHIggapLtkk01rEMUHPAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:05:52.990005Z","bundle_sha256":"0194e51cdb62d6fc5c82b40f5cfcf615f1d3211afafb858b107c7209f9c6b0c4"}}