{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VCTIMIGUG7NOTEIFP5GGUFAG33","short_pith_number":"pith:VCTIMIGU","canonical_record":{"source":{"id":"1102.0813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-03T23:25:31Z","cross_cats_sorted":["math.GR","math.PR"],"title_canon_sha256":"722ff80bc0ba2081b137b852805552424e23e35313768fd29a3754b9a4213abf","abstract_canon_sha256":"53df3dbea3bcb1f066968b135177a1920a389705f452d106dfafff28af308b1e"},"schema_version":"1.0"},"canonical_sha256":"a8a68620d437dae991057f4c6a1406dec0033d42db5f5c432737c061597bcc06","source":{"kind":"arxiv","id":"1102.0813","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0813","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0813v1","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0813","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"VCTIMIGUG7NO","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VCTIMIGUG7NOTEIF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VCTIMIGU","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VCTIMIGUG7NOTEIFP5GGUFAG33","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0813","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-03T23:25:31Z","cross_cats_sorted":["math.GR","math.PR"],"title_canon_sha256":"722ff80bc0ba2081b137b852805552424e23e35313768fd29a3754b9a4213abf","abstract_canon_sha256":"53df3dbea3bcb1f066968b135177a1920a389705f452d106dfafff28af308b1e"},"schema_version":"1.0"},"canonical_sha256":"a8a68620d437dae991057f4c6a1406dec0033d42db5f5c432737c061597bcc06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:03.561965Z","signature_b64":"Bx41gxWaswCypaeULOdiRo5lFE1Ytse03M4UucZLuacSOIB4/Fn1NGBlKRssKPe0z1kKt2wEpY8CQWW9vjKhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8a68620d437dae991057f4c6a1406dec0033d42db5f5c432737c061597bcc06","last_reissued_at":"2026-05-18T04:30:03.561569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:03.561569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0813","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":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hwQ+l1OF/Xr4eT5cUMwfRSLQ8Lnaa3478pDYaMC1NdKJ/NiMmg8VSLxAfCemzFBoPjhCNegJoQmc/OovEWqYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:24:18.854038Z"},"content_sha256":"db88c63a3aa8adab4c74a5a74e72a48f539aaa8dfebd274d8bad70b9c6c0797e","schema_version":"1.0","event_id":"sha256:db88c63a3aa8adab4c74a5a74e72a48f539aaa8dfebd274d8bad70b9c6c0797e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VCTIMIGUG7NOTEIFP5GGUFAG33","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative Independence in the Infinite Braid and Symmetric Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.PR"],"primary_cat":"math.OA","authors_text":"Claus K\\\"ostler, Rolf Gohm","submitted_at":"2011-02-03T23:25:31Z","abstract_excerpt":"This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows to derive factorization properties from symmetries. We explain some of the main ideas of this approach and work out a constructive procedure to use in applications. Finally we illustrate the method by applying it to the theory of group characters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0813","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":"2026-05-18T04:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pagw7syiE0WnlWzW7SGazXhvC9vXQReh0y+8E/gnDntHeDhktarUFo673WpHMSLFgAp2sw/D1HvAT+l3r4irCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:24:18.854724Z"},"content_sha256":"de0caaf25c39e8031c71fab3a7ab896ebe6f3f4471ce5b0091a4fb587b691823","schema_version":"1.0","event_id":"sha256:de0caaf25c39e8031c71fab3a7ab896ebe6f3f4471ce5b0091a4fb587b691823"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCTIMIGUG7NOTEIFP5GGUFAG33/bundle.json","state_url":"https://pith.science/pith/VCTIMIGUG7NOTEIFP5GGUFAG33/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCTIMIGUG7NOTEIFP5GGUFAG33/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":"2026-05-27T18:24:18Z","links":{"resolver":"https://pith.science/pith/VCTIMIGUG7NOTEIFP5GGUFAG33","bundle":"https://pith.science/pith/VCTIMIGUG7NOTEIFP5GGUFAG33/bundle.json","state":"https://pith.science/pith/VCTIMIGUG7NOTEIFP5GGUFAG33/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCTIMIGUG7NOTEIFP5GGUFAG33/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VCTIMIGUG7NOTEIFP5GGUFAG33","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":"53df3dbea3bcb1f066968b135177a1920a389705f452d106dfafff28af308b1e","cross_cats_sorted":["math.GR","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-03T23:25:31Z","title_canon_sha256":"722ff80bc0ba2081b137b852805552424e23e35313768fd29a3754b9a4213abf"},"schema_version":"1.0","source":{"id":"1102.0813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0813","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0813v1","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0813","created_at":"2026-05-18T04:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"VCTIMIGUG7NO","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"VCTIMIGUG7NOTEIF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"VCTIMIGU","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:de0caaf25c39e8031c71fab3a7ab896ebe6f3f4471ce5b0091a4fb587b691823","target":"graph","created_at":"2026-05-18T04:30:03Z","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":"This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows to derive factorization properties from symmetries. We explain some of the main ideas of this approach and work out a constructive procedure to use in applications. Finally we illustrate the method by applying it to the theory of group characters.","authors_text":"Claus K\\\"ostler, Rolf Gohm","cross_cats":["math.GR","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-03T23:25:31Z","title":"Noncommutative Independence in the Infinite Braid and Symmetric Group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0813","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:db88c63a3aa8adab4c74a5a74e72a48f539aaa8dfebd274d8bad70b9c6c0797e","target":"record","created_at":"2026-05-18T04:30:03Z","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":"53df3dbea3bcb1f066968b135177a1920a389705f452d106dfafff28af308b1e","cross_cats_sorted":["math.GR","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-02-03T23:25:31Z","title_canon_sha256":"722ff80bc0ba2081b137b852805552424e23e35313768fd29a3754b9a4213abf"},"schema_version":"1.0","source":{"id":"1102.0813","kind":"arxiv","version":1}},"canonical_sha256":"a8a68620d437dae991057f4c6a1406dec0033d42db5f5c432737c061597bcc06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8a68620d437dae991057f4c6a1406dec0033d42db5f5c432737c061597bcc06","first_computed_at":"2026-05-18T04:30:03.561569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:03.561569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bx41gxWaswCypaeULOdiRo5lFE1Ytse03M4UucZLuacSOIB4/Fn1NGBlKRssKPe0z1kKt2wEpY8CQWW9vjKhAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:03.561965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db88c63a3aa8adab4c74a5a74e72a48f539aaa8dfebd274d8bad70b9c6c0797e","sha256:de0caaf25c39e8031c71fab3a7ab896ebe6f3f4471ce5b0091a4fb587b691823"],"state_sha256":"7e7bcf7ab34df2a9bd9abc269e12c6ebf026e378050e3116a2cbabd32641003e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtYwn5J2IgxLPnn5B5AnEL+vZz12ReLciCVu1Ce1WhxBOlJ0m1ytzODwc9Wkf5u1JcnAO4Empm2mC/OhilN6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:24:18.858263Z","bundle_sha256":"0b8da863708e892941e9cc07254c27ada4e3d8549a3e2e5b97bfd79c4bb9738b"}}