{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CPABAPHKS5ZCRKK53FJFDL3QOO","short_pith_number":"pith:CPABAPHK","canonical_record":{"source":{"id":"1304.1713","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-05T13:53:37Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"0ac9ddcedaaae00ec8506c73e3b2d27d22a8d57e2053194141706845efd2a5d2","abstract_canon_sha256":"5c602430d82dc1b8a3795188ae01f230616fb702cba54372a964bbceb4741dbd"},"schema_version":"1.0"},"canonical_sha256":"13c0103cea977228a95dd95251af7073bd809d3e978f8a8bc3c6a44767ebebc2","source":{"kind":"arxiv","id":"1304.1713","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1713","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1713v3","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1713","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"CPABAPHKS5ZC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CPABAPHKS5ZCRKK5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CPABAPHK","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CPABAPHKS5ZCRKK53FJFDL3QOO","target":"record","payload":{"canonical_record":{"source":{"id":"1304.1713","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-05T13:53:37Z","cross_cats_sorted":["math.CO","math.OA"],"title_canon_sha256":"0ac9ddcedaaae00ec8506c73e3b2d27d22a8d57e2053194141706845efd2a5d2","abstract_canon_sha256":"5c602430d82dc1b8a3795188ae01f230616fb702cba54372a964bbceb4741dbd"},"schema_version":"1.0"},"canonical_sha256":"13c0103cea977228a95dd95251af7073bd809d3e978f8a8bc3c6a44767ebebc2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:45.959503Z","signature_b64":"UsG1GOzj7G1dymP65uAJa1xSjzMQVV0wnUwl1+3Q8/stSYPGDgoEgCeZrR39zssgoRZmPAnP17AD6uqHhp9OAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13c0103cea977228a95dd95251af7073bd809d3e978f8a8bc3c6a44767ebebc2","last_reissued_at":"2026-05-18T03:13:45.958975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:45.958975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.1713","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":"2026-05-18T03:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lFCTXstOUGebe+wYoATuq75IfACVp/iYphpffy2ea3kOYjvqkXVvyAvVo4GqyEVyJ6n7wB5GK3IP43Y5zEEfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:27:02.642592Z"},"content_sha256":"411d2b71c6e043de517dc609bd7ab461a309b1f55f434e4ca1bc6c0c6ae6e5cb","schema_version":"1.0","event_id":"sha256:411d2b71c6e043de517dc609bd7ab461a309b1f55f434e4ca1bc6c0c6ae6e5cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CPABAPHKS5ZCRKK53FJFDL3QOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free Convolution Operators and Free Hall Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OA"],"primary_cat":"math.PR","authors_text":"Guillaume C\\'ebron","submitted_at":"2013-04-05T13:53:37Z","abstract_excerpt":"We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free convolution. It also permits us to characterize the free Segal-Bargmann transform and the free Hall transform introduced by Biane, in a manner which is closer to classical definitions. Finally, we use this extension of polynomial calculus to prove two asymptotic results on random matrices: the convergence for each fixed time, as N tends to infinity, of the *-distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1713","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":"2026-05-18T03:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rw8+xseNai3VcCfr7zCP8/sDMolumUPSqoYCXqusDj9r12yD3xixS4sWzrVoY5w6NcSxfhHLo4WJLoVCySQCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:27:02.642947Z"},"content_sha256":"52f25dad2618966297c14a43f48844e4f04710615c282a972a474f6c16ab6b64","schema_version":"1.0","event_id":"sha256:52f25dad2618966297c14a43f48844e4f04710615c282a972a474f6c16ab6b64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CPABAPHKS5ZCRKK53FJFDL3QOO/bundle.json","state_url":"https://pith.science/pith/CPABAPHKS5ZCRKK53FJFDL3QOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CPABAPHKS5ZCRKK53FJFDL3QOO/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":"2026-06-22T14:27:02Z","links":{"resolver":"https://pith.science/pith/CPABAPHKS5ZCRKK53FJFDL3QOO","bundle":"https://pith.science/pith/CPABAPHKS5ZCRKK53FJFDL3QOO/bundle.json","state":"https://pith.science/pith/CPABAPHKS5ZCRKK53FJFDL3QOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CPABAPHKS5ZCRKK53FJFDL3QOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CPABAPHKS5ZCRKK53FJFDL3QOO","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":"5c602430d82dc1b8a3795188ae01f230616fb702cba54372a964bbceb4741dbd","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-05T13:53:37Z","title_canon_sha256":"0ac9ddcedaaae00ec8506c73e3b2d27d22a8d57e2053194141706845efd2a5d2"},"schema_version":"1.0","source":{"id":"1304.1713","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1713","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1713v3","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1713","created_at":"2026-05-18T03:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"CPABAPHKS5ZC","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CPABAPHKS5ZCRKK5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CPABAPHK","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:52f25dad2618966297c14a43f48844e4f04710615c282a972a474f6c16ab6b64","target":"graph","created_at":"2026-05-18T03:13:45Z","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":"We define an extension of the polynomial calculus on a W*-probability space by introducing an abstract algebra which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free convolution. It also permits us to characterize the free Segal-Bargmann transform and the free Hall transform introduced by Biane, in a manner which is closer to classical definitions. Finally, we use this extension of polynomial calculus to prove two asymptotic results on random matrices: the convergence for each fixed time, as N tends to infinity, of the *-distrib","authors_text":"Guillaume C\\'ebron","cross_cats":["math.CO","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-05T13:53:37Z","title":"Free Convolution Operators and Free Hall Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1713","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":"sha256:411d2b71c6e043de517dc609bd7ab461a309b1f55f434e4ca1bc6c0c6ae6e5cb","target":"record","created_at":"2026-05-18T03:13:45Z","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":"5c602430d82dc1b8a3795188ae01f230616fb702cba54372a964bbceb4741dbd","cross_cats_sorted":["math.CO","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-05T13:53:37Z","title_canon_sha256":"0ac9ddcedaaae00ec8506c73e3b2d27d22a8d57e2053194141706845efd2a5d2"},"schema_version":"1.0","source":{"id":"1304.1713","kind":"arxiv","version":3}},"canonical_sha256":"13c0103cea977228a95dd95251af7073bd809d3e978f8a8bc3c6a44767ebebc2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13c0103cea977228a95dd95251af7073bd809d3e978f8a8bc3c6a44767ebebc2","first_computed_at":"2026-05-18T03:13:45.958975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:45.958975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UsG1GOzj7G1dymP65uAJa1xSjzMQVV0wnUwl1+3Q8/stSYPGDgoEgCeZrR39zssgoRZmPAnP17AD6uqHhp9OAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:45.959503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1713","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:411d2b71c6e043de517dc609bd7ab461a309b1f55f434e4ca1bc6c0c6ae6e5cb","sha256:52f25dad2618966297c14a43f48844e4f04710615c282a972a474f6c16ab6b64"],"state_sha256":"f5aeb6368df3c958fe4b5f00f21ac25c6f6ec6baac692fdfa211e6fb890d1226"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lABWeS/LWCuP7WloAn9aqVlK4U1tBm9n8HLL3CjVD/XTE0x/4PSraCzP8Yu2ZaSi1FwEj5V59+6EkpSX8kJODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:27:02.644925Z","bundle_sha256":"a49d7e598504cff7e88ab70f38bedf541acd06e7ee99691b789a8986f893107e"}}