{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:US4T5CN3LNPKP5PZXOOGXOFSO3","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":"1e932c3671b0cd94dfe75b74a2f707feba16527da5ceedb338cadb8db33629df","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-04-28T16:00:34Z","title_canon_sha256":"d05e6c71c945916c6b5e982de5fae2d38d864fd259deede696ee5a764bcac28d"},"schema_version":"1.0","source":{"id":"1705.06569","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06569","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06569v1","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06569","created_at":"2026-05-18T00:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"US4T5CN3LNPK","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"US4T5CN3LNPKP5PZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"US4T5CN3","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:0621c9a082f6a9408aad8049963ce8bef3ec5840eceea429c16b0f6a4a452d2f","target":"graph","created_at":"2026-05-18T00:44:14Z","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 a continuation of our previous work in bi-free harmonic analysis for commuting left and right variables. Here we analyze the bi-free partial S-transform and use the results to study limit theorems and infinite divisibility relative to the multiplicative bi-free convolution.","authors_text":"Hao-Wei Huang, Jiun-Chau Wang","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-04-28T16:00:34Z","title":"Harmonic analysis for the bi-free partial S-transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06569","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:c3350de67dc9ef28283e5d4da71c8dc2efb5f2b1d89a28163129c07f8456c144","target":"record","created_at":"2026-05-18T00:44:14Z","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":"1e932c3671b0cd94dfe75b74a2f707feba16527da5ceedb338cadb8db33629df","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-04-28T16:00:34Z","title_canon_sha256":"d05e6c71c945916c6b5e982de5fae2d38d864fd259deede696ee5a764bcac28d"},"schema_version":"1.0","source":{"id":"1705.06569","kind":"arxiv","version":1}},"canonical_sha256":"a4b93e89bb5b5ea7f5f9bb9c6bb8b276e781631e1641f43be64c783c8481e2b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4b93e89bb5b5ea7f5f9bb9c6bb8b276e781631e1641f43be64c783c8481e2b5","first_computed_at":"2026-05-18T00:44:14.397345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:14.397345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BhaOUhsMn3F/sjITFsXGweQhJ8ocD2LALxzrTM93h0sS/FADyxnFLNrtl5WS67d4x1fi6I57KnK9R7PR4BjzBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:14.397820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06569","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3350de67dc9ef28283e5d4da71c8dc2efb5f2b1d89a28163129c07f8456c144","sha256:0621c9a082f6a9408aad8049963ce8bef3ec5840eceea429c16b0f6a4a452d2f"],"state_sha256":"5caecd39e24471f3d3468c609d1049929985e3580f34abd0c96fc1a7383d92f6"}