{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:ZFJARJSEFWVZF7EO7QACLQOWDS","short_pith_number":"pith:ZFJARJSE","canonical_record":{"source":{"id":"2102.01214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-02-01T22:34:33Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c207c2c3adb0fa6eaace6a05e5e422af85666fe4a163eb0f896288c2a4e311a3","abstract_canon_sha256":"b98bd159e1c8ed2086799dc3f150ac435bef4e26a2f8c479616ca86412d2248f"},"schema_version":"1.0"},"canonical_sha256":"c95208a6442dab92fc8efc0025c1d61c8cec280e115fc7068e8be0ad044e9244","source":{"kind":"arxiv","id":"2102.01214","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.01214","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"2102.01214v2","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.01214","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZFJARJSEFWVZ","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZFJARJSEFWVZF7EO","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZFJARJSE","created_at":"2026-07-05T02:31:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:ZFJARJSEFWVZF7EO7QACLQOWDS","target":"record","payload":{"canonical_record":{"source":{"id":"2102.01214","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-02-01T22:34:33Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c207c2c3adb0fa6eaace6a05e5e422af85666fe4a163eb0f896288c2a4e311a3","abstract_canon_sha256":"b98bd159e1c8ed2086799dc3f150ac435bef4e26a2f8c479616ca86412d2248f"},"schema_version":"1.0"},"canonical_sha256":"c95208a6442dab92fc8efc0025c1d61c8cec280e115fc7068e8be0ad044e9244","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:31:04.018085Z","signature_b64":"fcan5yb170OlU7bYhA2AtJRSpt+5ecgzMpH9tSkCuQaK0PK9ZLqm+sDJJdeOAMUB93nG45R2IZbrJqElZyxKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c95208a6442dab92fc8efc0025c1d61c8cec280e115fc7068e8be0ad044e9244","last_reissued_at":"2026-07-05T02:31:04.017531Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:31:04.017531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.01214","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"udZU9gMjGb017Ch/GJjP6oQQOoiJeZp/KjIvp8lzFJnFlXtw2ii8JpUZt3qIwNLVuqjYSWexq83766F0DjQUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:34:48.630563Z"},"content_sha256":"beaa8ba743f50e139e0b19857466f55ecf755e5f160fe71479f541a59ffe6a75","schema_version":"1.0","event_id":"sha256:beaa8ba743f50e139e0b19857466f55ecf755e5f160fe71479f541a59ffe6a75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:ZFJARJSEFWVZF7EO7QACLQOWDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tree convolution for probability distributions with unbounded support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.OA","authors_text":"David Jekel, Ethan Davis, Zhichao Wang","submitted_at":"2021-02-01T22:34:33Z","abstract_excerpt":"We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in \"An operad of non-commutative independences defined by trees\" (Dissertationes Mathematicae, 2020, doi:10.4064/dm797-6-2020), which generalize the free, boolean, monotone, and orthogonal convolutions. In particular, for each rooted subtree $\\mathcal{T}$ of the $N$-regular tree (with vertices labeled by alternating strings), we define the convolution $\\boxplus_{\\mathcal{T}}(\\mu_1,\\dots,\\mu_N)$ for arbitrary probability measures $\\mu_1$, ..., $\\mu_N$ on $\\mathbb{R}$ using a certain fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.01214","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.01214/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pGiuoravOa+rwPmMOZO2jyZ0KyLhi3oPQH2hfWb1DY8ac28j0FjyBEw+G0Kvqq3VDfq7++EFJaqgacd45+UwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T18:34:48.631951Z"},"content_sha256":"50ca52e5b27ca9b0b6171f25b98c18401805ca4c1737982cc771fa9c0ca87e92","schema_version":"1.0","event_id":"sha256:50ca52e5b27ca9b0b6171f25b98c18401805ca4c1737982cc771fa9c0ca87e92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFJARJSEFWVZF7EO7QACLQOWDS/bundle.json","state_url":"https://pith.science/pith/ZFJARJSEFWVZF7EO7QACLQOWDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFJARJSEFWVZF7EO7QACLQOWDS/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":"2026-08-05T18:34:48Z","links":{"resolver":"https://pith.science/pith/ZFJARJSEFWVZF7EO7QACLQOWDS","bundle":"https://pith.science/pith/ZFJARJSEFWVZF7EO7QACLQOWDS/bundle.json","state":"https://pith.science/pith/ZFJARJSEFWVZF7EO7QACLQOWDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFJARJSEFWVZF7EO7QACLQOWDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ZFJARJSEFWVZF7EO7QACLQOWDS","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":"b98bd159e1c8ed2086799dc3f150ac435bef4e26a2f8c479616ca86412d2248f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-02-01T22:34:33Z","title_canon_sha256":"c207c2c3adb0fa6eaace6a05e5e422af85666fe4a163eb0f896288c2a4e311a3"},"schema_version":"1.0","source":{"id":"2102.01214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.01214","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"2102.01214v2","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.01214","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"ZFJARJSEFWVZ","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZFJARJSEFWVZF7EO","created_at":"2026-07-05T02:31:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZFJARJSE","created_at":"2026-07-05T02:31:04Z"}],"graph_snapshots":[{"event_id":"sha256:50ca52e5b27ca9b0b6171f25b98c18401805ca4c1737982cc771fa9c0ca87e92","target":"graph","created_at":"2026-07-05T02:31:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2102.01214/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the complex-analytic viewpoint on the tree convolutions studied by the second author and Weihua Liu in \"An operad of non-commutative independences defined by trees\" (Dissertationes Mathematicae, 2020, doi:10.4064/dm797-6-2020), which generalize the free, boolean, monotone, and orthogonal convolutions. In particular, for each rooted subtree $\\mathcal{T}$ of the $N$-regular tree (with vertices labeled by alternating strings), we define the convolution $\\boxplus_{\\mathcal{T}}(\\mu_1,\\dots,\\mu_N)$ for arbitrary probability measures $\\mu_1$, ..., $\\mu_N$ on $\\mathbb{R}$ using a certain fi","authors_text":"David Jekel, Ethan Davis, Zhichao Wang","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-02-01T22:34:33Z","title":"Tree convolution for probability distributions with unbounded support"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.01214","kind":"arxiv","version":2},"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:beaa8ba743f50e139e0b19857466f55ecf755e5f160fe71479f541a59ffe6a75","target":"record","created_at":"2026-07-05T02:31:04Z","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":"b98bd159e1c8ed2086799dc3f150ac435bef4e26a2f8c479616ca86412d2248f","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-02-01T22:34:33Z","title_canon_sha256":"c207c2c3adb0fa6eaace6a05e5e422af85666fe4a163eb0f896288c2a4e311a3"},"schema_version":"1.0","source":{"id":"2102.01214","kind":"arxiv","version":2}},"canonical_sha256":"c95208a6442dab92fc8efc0025c1d61c8cec280e115fc7068e8be0ad044e9244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c95208a6442dab92fc8efc0025c1d61c8cec280e115fc7068e8be0ad044e9244","first_computed_at":"2026-07-05T02:31:04.017531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:31:04.017531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fcan5yb170OlU7bYhA2AtJRSpt+5ecgzMpH9tSkCuQaK0PK9ZLqm+sDJJdeOAMUB93nG45R2IZbrJqElZyxKCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:31:04.018085Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.01214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:beaa8ba743f50e139e0b19857466f55ecf755e5f160fe71479f541a59ffe6a75","sha256:50ca52e5b27ca9b0b6171f25b98c18401805ca4c1737982cc771fa9c0ca87e92"],"state_sha256":"fb1393dcdfbff7646d5affdb34eed702db035ef461147a385e596d5c2a4b46df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f9UkIGXpthWKA5h2dnTPU0+XnygFpmA1pVkvhxIvazUXbBsENsiEp57iJWKsL/v6bDh9oXaIziGeaVxbTAl/BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T18:34:48.641765Z","bundle_sha256":"ebc012f570f92345e283a92eb1029a1446fc7fcd84b99d2487219bfe8954641f"}}