{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GWHXMIXZSARTD55QMF2VKWNWZH","short_pith_number":"pith:GWHXMIXZ","canonical_record":{"source":{"id":"1205.1575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-08T02:11:56Z","cross_cats_sorted":[],"title_canon_sha256":"f9a27e90e53a1aa9dbc9dd8edaf5727cd7fcd3cc3e53545b43da4c5dda2ca51e","abstract_canon_sha256":"af03a76dee5de0cddbf782cd3359ea51b95e7414ff0fb11aa6d3ede74bce5aa4"},"schema_version":"1.0"},"canonical_sha256":"358f7622f9902331f7b061755559b6c9d2b4b77a1b12323eaf473f04722a75de","source":{"kind":"arxiv","id":"1205.1575","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1575","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1575v3","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1575","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"GWHXMIXZSART","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GWHXMIXZSARTD55Q","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GWHXMIXZ","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GWHXMIXZSARTD55QMF2VKWNWZH","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1575","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-08T02:11:56Z","cross_cats_sorted":[],"title_canon_sha256":"f9a27e90e53a1aa9dbc9dd8edaf5727cd7fcd3cc3e53545b43da4c5dda2ca51e","abstract_canon_sha256":"af03a76dee5de0cddbf782cd3359ea51b95e7414ff0fb11aa6d3ede74bce5aa4"},"schema_version":"1.0"},"canonical_sha256":"358f7622f9902331f7b061755559b6c9d2b4b77a1b12323eaf473f04722a75de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:00.205981Z","signature_b64":"G07mUkLgS80+15ErxvX+bpPZndfY673EPSMmvT6TmwfVWuhhRdsBl9OOXBtB5IwTUiDbWYQjOH/hki0YXgjTAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"358f7622f9902331f7b061755559b6c9d2b4b77a1b12323eaf473f04722a75de","last_reissued_at":"2026-05-18T02:57:00.205363Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:00.205363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1575","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":"2026-05-18T02:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rMfwljtmTSKKs2xokT8Rw3gvFueHPWResAF0/sNBdqXV2hMaAFrU/6TjmN1E+JO1BtRsWLQTllDGZnmpdVvJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:32:03.731045Z"},"content_sha256":"b8c2ab8dfe72276ed0ea11ecf006940c7a4d7524a1f8cecf64e539d5cd755fde","schema_version":"1.0","event_id":"sha256:b8c2ab8dfe72276ed0ea11ecf006940c7a4d7524a1f8cecf64e539d5cd755fde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GWHXMIXZSARTD55QMF2VKWNWZH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical and free infinite divisibility for Boolean stable laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Octavio Arizmendi, Takahiro Hasebe","submitted_at":"2012-05-08T02:11:56Z","abstract_excerpt":"We completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index $\\alpha$ and an asymmetry coefficient $\\rho$. We prove that the Boolean stable law is freely infinitely divisible if and only if one of the following conditions holds: $0<\\alpha\\leq\\frac{1}{2}$; $\\frac{1}{2}<\\alpha\\leq\\frac{2}{3}$ and $2-\\frac{1}{\\alpha}\\leq\\rho \\leq \\frac{1}{\\alpha}-1$; $\\alpha=1,~\\rho=\\frac{1}{2}$. Positive Boolean stable laws corresponding to $\\rho =1$ and $\\alpha \\leq \\frac{1}{2}$ have completely monotonic densities and they are both freely and class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1575","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":"2026-05-18T02:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AL/Qz+2nieibtHahRoo+xRvdFZARbLeJV9DLsZS6C47Y1KZdLOmcX8VNdurlgyXxAMHYMgFCvq1bSUqRREo9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:32:03.731781Z"},"content_sha256":"3134c0c0d4c33af49bfc119d957557e87c84bd101271241da611c1fb39cf2dfb","schema_version":"1.0","event_id":"sha256:3134c0c0d4c33af49bfc119d957557e87c84bd101271241da611c1fb39cf2dfb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GWHXMIXZSARTD55QMF2VKWNWZH/bundle.json","state_url":"https://pith.science/pith/GWHXMIXZSARTD55QMF2VKWNWZH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GWHXMIXZSARTD55QMF2VKWNWZH/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":"2026-05-31T07:32:03Z","links":{"resolver":"https://pith.science/pith/GWHXMIXZSARTD55QMF2VKWNWZH","bundle":"https://pith.science/pith/GWHXMIXZSARTD55QMF2VKWNWZH/bundle.json","state":"https://pith.science/pith/GWHXMIXZSARTD55QMF2VKWNWZH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GWHXMIXZSARTD55QMF2VKWNWZH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GWHXMIXZSARTD55QMF2VKWNWZH","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":"af03a76dee5de0cddbf782cd3359ea51b95e7414ff0fb11aa6d3ede74bce5aa4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-08T02:11:56Z","title_canon_sha256":"f9a27e90e53a1aa9dbc9dd8edaf5727cd7fcd3cc3e53545b43da4c5dda2ca51e"},"schema_version":"1.0","source":{"id":"1205.1575","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1575","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1575v3","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1575","created_at":"2026-05-18T02:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"GWHXMIXZSART","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GWHXMIXZSARTD55Q","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GWHXMIXZ","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:3134c0c0d4c33af49bfc119d957557e87c84bd101271241da611c1fb39cf2dfb","target":"graph","created_at":"2026-05-18T02:57:00Z","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 completely determine the free infinite divisibility for the Boolean stable law which is parametrized by a stability index $\\alpha$ and an asymmetry coefficient $\\rho$. We prove that the Boolean stable law is freely infinitely divisible if and only if one of the following conditions holds: $0<\\alpha\\leq\\frac{1}{2}$; $\\frac{1}{2}<\\alpha\\leq\\frac{2}{3}$ and $2-\\frac{1}{\\alpha}\\leq\\rho \\leq \\frac{1}{\\alpha}-1$; $\\alpha=1,~\\rho=\\frac{1}{2}$. Positive Boolean stable laws corresponding to $\\rho =1$ and $\\alpha \\leq \\frac{1}{2}$ have completely monotonic densities and they are both freely and class","authors_text":"Octavio Arizmendi, Takahiro Hasebe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-08T02:11:56Z","title":"Classical and free infinite divisibility for Boolean stable laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1575","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:b8c2ab8dfe72276ed0ea11ecf006940c7a4d7524a1f8cecf64e539d5cd755fde","target":"record","created_at":"2026-05-18T02:57:00Z","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":"af03a76dee5de0cddbf782cd3359ea51b95e7414ff0fb11aa6d3ede74bce5aa4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-08T02:11:56Z","title_canon_sha256":"f9a27e90e53a1aa9dbc9dd8edaf5727cd7fcd3cc3e53545b43da4c5dda2ca51e"},"schema_version":"1.0","source":{"id":"1205.1575","kind":"arxiv","version":3}},"canonical_sha256":"358f7622f9902331f7b061755559b6c9d2b4b77a1b12323eaf473f04722a75de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"358f7622f9902331f7b061755559b6c9d2b4b77a1b12323eaf473f04722a75de","first_computed_at":"2026-05-18T02:57:00.205363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:00.205363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G07mUkLgS80+15ErxvX+bpPZndfY673EPSMmvT6TmwfVWuhhRdsBl9OOXBtB5IwTUiDbWYQjOH/hki0YXgjTAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:00.205981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1575","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8c2ab8dfe72276ed0ea11ecf006940c7a4d7524a1f8cecf64e539d5cd755fde","sha256:3134c0c0d4c33af49bfc119d957557e87c84bd101271241da611c1fb39cf2dfb"],"state_sha256":"094fea7bc684255122424abae8f5d0d89f1ee6d1bd6c7d0d9e6bf3323b0e5724"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Atyzx+UDY0ogXiKugoxIa0cBixkDv4oAsb4cKnxtif7y8KqXHQWkrb7rAWbtq6h37EXxnkB1FMwZSdMBgyJACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:32:03.735010Z","bundle_sha256":"95054e0d653c5483800fa7df1eba6375bd6be0f61a2511111107aaa9d0920644"}}