{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OIMPNCRLLCFK34WKXHIJG3G2NE","short_pith_number":"pith:OIMPNCRL","canonical_record":{"source":{"id":"1710.11402","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-31T10:43:46Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"3ac402ad609027d2f8c97e6fd82f3d25840df94030f549033642ccee7cff24d6","abstract_canon_sha256":"9fe4a04934721ba37cb8f782434a940b8c2f99659f6c7c3c95b3a03bdd5cba7f"},"schema_version":"1.0"},"canonical_sha256":"7218f68a2b588aadf2cab9d0936cda691d59242926538b6b46b5faf3d4944b96","source":{"kind":"arxiv","id":"1710.11402","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11402","created_at":"2026-05-18T00:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11402v3","created_at":"2026-05-18T00:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11402","created_at":"2026-05-18T00:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"OIMPNCRLLCFK","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OIMPNCRLLCFK34WK","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OIMPNCRL","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OIMPNCRLLCFK34WKXHIJG3G2NE","target":"record","payload":{"canonical_record":{"source":{"id":"1710.11402","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-31T10:43:46Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"3ac402ad609027d2f8c97e6fd82f3d25840df94030f549033642ccee7cff24d6","abstract_canon_sha256":"9fe4a04934721ba37cb8f782434a940b8c2f99659f6c7c3c95b3a03bdd5cba7f"},"schema_version":"1.0"},"canonical_sha256":"7218f68a2b588aadf2cab9d0936cda691d59242926538b6b46b5faf3d4944b96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:27.207989Z","signature_b64":"rERnV4z1zIhVMc98vHEm1JEbd9EpYSDwY2qCqygm09w17PgCa2kfPD6Dq+RDqjQwD0j7biOjSzE+JJu5h/y6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7218f68a2b588aadf2cab9d0936cda691d59242926538b6b46b5faf3d4944b96","last_reissued_at":"2026-05-18T00:08:27.207489Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:27.207489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.11402","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":"2026-05-18T00:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6kxMTNcJMWdnX4idgBjXR9I1vFGBv7IbAUnOHhds6sEyFNxxmuO1t3St1IdXJKPXbrYVLTb2AgfBp1N9SGiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:38:52.027247Z"},"content_sha256":"02301b944b9a0c53af64aec034719645623e8676a0a9b586f1d93926175934bc","schema_version":"1.0","event_id":"sha256:02301b944b9a0c53af64aec034719645623e8676a0a9b586f1d93926175934bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OIMPNCRLLCFK34WKXHIJG3G2NE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boolean convolutions and regular variation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Rajat Subhra Hazra, Sukrit Chakraborty","submitted_at":"2017-10-31T10:43:46Z","abstract_excerpt":"In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the notion of classical and free subexponentiality. We show that the distributions with regularly varying tails belong to the class of Boolean subexponential distributions. As an application we also study the behaviour of the Belinschi-Nica map. Breiman's theorem study the classical product convolution between regularly varying measures. We derive an analogous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11402","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":"2026-05-18T00:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/pbGt2ph/qNod17+6wo2cWX4t+c/lGrJkcc/q7jfLJVxiUUetLr0X993Ze8Hy1zPtEvYlQzU61MuwBrKESJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:38:52.027599Z"},"content_sha256":"b7cd2ed1f4198465747ae5b5531edb7acfde0d847e538f9bf3052dee055bbf7a","schema_version":"1.0","event_id":"sha256:b7cd2ed1f4198465747ae5b5531edb7acfde0d847e538f9bf3052dee055bbf7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OIMPNCRLLCFK34WKXHIJG3G2NE/bundle.json","state_url":"https://pith.science/pith/OIMPNCRLLCFK34WKXHIJG3G2NE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OIMPNCRLLCFK34WKXHIJG3G2NE/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":"2026-06-20T22:38:52Z","links":{"resolver":"https://pith.science/pith/OIMPNCRLLCFK34WKXHIJG3G2NE","bundle":"https://pith.science/pith/OIMPNCRLLCFK34WKXHIJG3G2NE/bundle.json","state":"https://pith.science/pith/OIMPNCRLLCFK34WKXHIJG3G2NE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OIMPNCRLLCFK34WKXHIJG3G2NE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OIMPNCRLLCFK34WKXHIJG3G2NE","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":"9fe4a04934721ba37cb8f782434a940b8c2f99659f6c7c3c95b3a03bdd5cba7f","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-31T10:43:46Z","title_canon_sha256":"3ac402ad609027d2f8c97e6fd82f3d25840df94030f549033642ccee7cff24d6"},"schema_version":"1.0","source":{"id":"1710.11402","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.11402","created_at":"2026-05-18T00:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"1710.11402v3","created_at":"2026-05-18T00:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11402","created_at":"2026-05-18T00:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"OIMPNCRLLCFK","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OIMPNCRLLCFK34WK","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OIMPNCRL","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:b7cd2ed1f4198465747ae5b5531edb7acfde0d847e538f9bf3052dee055bbf7a","target":"graph","created_at":"2026-05-18T00:08:27Z","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":"In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the notion of classical and free subexponentiality. We show that the distributions with regularly varying tails belong to the class of Boolean subexponential distributions. As an application we also study the behaviour of the Belinschi-Nica map. Breiman's theorem study the classical product convolution between regularly varying measures. We derive an analogous ","authors_text":"Rajat Subhra Hazra, Sukrit Chakraborty","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-31T10:43:46Z","title":"Boolean convolutions and regular variation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11402","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":"sha256:02301b944b9a0c53af64aec034719645623e8676a0a9b586f1d93926175934bc","target":"record","created_at":"2026-05-18T00:08:27Z","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":"9fe4a04934721ba37cb8f782434a940b8c2f99659f6c7c3c95b3a03bdd5cba7f","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-31T10:43:46Z","title_canon_sha256":"3ac402ad609027d2f8c97e6fd82f3d25840df94030f549033642ccee7cff24d6"},"schema_version":"1.0","source":{"id":"1710.11402","kind":"arxiv","version":3}},"canonical_sha256":"7218f68a2b588aadf2cab9d0936cda691d59242926538b6b46b5faf3d4944b96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7218f68a2b588aadf2cab9d0936cda691d59242926538b6b46b5faf3d4944b96","first_computed_at":"2026-05-18T00:08:27.207489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:27.207489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rERnV4z1zIhVMc98vHEm1JEbd9EpYSDwY2qCqygm09w17PgCa2kfPD6Dq+RDqjQwD0j7biOjSzE+JJu5h/y6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:27.207989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.11402","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02301b944b9a0c53af64aec034719645623e8676a0a9b586f1d93926175934bc","sha256:b7cd2ed1f4198465747ae5b5531edb7acfde0d847e538f9bf3052dee055bbf7a"],"state_sha256":"0798a0f04d3e8ea53e12eade7944455c2f926505d33197b0842820e032fcf4ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MyfJa0mCrJTCd9UeVU02xrnWxPpYh17zFopJu2zFmFRR2pSPDSTlS3GkhQKxWsLelMUMpuA6BFENP9K44SEmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:38:52.029642Z","bundle_sha256":"cee981281a2a690402075e08d21152b58df6be57b9c619b0dcd803c1bdb2a602"}}