{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IK4ZNZMAZHKZEFXGRPKPAVUTHY","short_pith_number":"pith:IK4ZNZMA","canonical_record":{"source":{"id":"1701.02400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T01:15:06Z","cross_cats_sorted":[],"title_canon_sha256":"ee62db8b761f319b3befa45e8fd90558ca3cb5119421a77c6657ae27e9d59871","abstract_canon_sha256":"cf68261a157dbc754605418f2a987642aa759f8c70d572ff0ac4cfe254099fd8"},"schema_version":"1.0"},"canonical_sha256":"42b996e580c9d59216e68bd4f056933e0eddd78835b4bbf601b33c6b168aa639","source":{"kind":"arxiv","id":"1701.02400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02400","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02400v1","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02400","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"IK4ZNZMAZHKZ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IK4ZNZMAZHKZEFXG","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IK4ZNZMA","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IK4ZNZMAZHKZEFXGRPKPAVUTHY","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T01:15:06Z","cross_cats_sorted":[],"title_canon_sha256":"ee62db8b761f319b3befa45e8fd90558ca3cb5119421a77c6657ae27e9d59871","abstract_canon_sha256":"cf68261a157dbc754605418f2a987642aa759f8c70d572ff0ac4cfe254099fd8"},"schema_version":"1.0"},"canonical_sha256":"42b996e580c9d59216e68bd4f056933e0eddd78835b4bbf601b33c6b168aa639","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:04.327442Z","signature_b64":"9eKUr9lEDTz6g/nsHwSd3kSU87QdyyXuIiWdZh4D9d2bIZUcYCvFjkl/jumHig4s/yieiYRluIhi6t8lZUspDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42b996e580c9d59216e68bd4f056933e0eddd78835b4bbf601b33c6b168aa639","last_reissued_at":"2026-05-18T00:53:04.326892Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:04.326892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02400","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":"2026-05-18T00:53:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DmT7qiomVg5jnP2w2aywm6erX/VE4IGp94ka447BJH5JEQm7DTsP86XbN80zk5d3inYqAo7bXKfM0/cQNfsSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:12:20.914976Z"},"content_sha256":"20364d4c69634929ae1d2039c8c3468349eecfabea9a59000c47351358803ea5","schema_version":"1.0","event_id":"sha256:20364d4c69634929ae1d2039c8c3468349eecfabea9a59000c47351358803ea5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IK4ZNZMAZHKZEFXGRPKPAVUTHY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On quasi-infinitely divisible distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Lindner, Ken-iti Sato, Lei Pan","submitted_at":"2017-01-10T01:15:06Z","abstract_excerpt":"A quasi-infinitely divisible distribution on $\\mathbb{R}$ is a probability distribution whose characteristic function allows a L\\'evy-Khintchine type representation with a \"signed L\\'evy measure\", rather than a L\\'evy measure. Quasi-infinitely divisible distributions appear naturally in the factorization of infinitely divisible distributions. Namely, a distribution $\\mu$ is quasi-infinitely divisible if and only if there are two infinitely divisible distributions $\\mu_1$ and $\\mu_2$ such that $\\mu_1 \\ast \\mu = \\mu_2$. The present paper studies certain properties of quasi-infinitely divisible d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02400","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":"2026-05-18T00:53:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IOLvWM9iQmycQ3ADEszEJauY1XX5YXQEZ7NvWrPswcTmpdB1srqBWQG3cMc9X+2If9XBJqXpcsW6bS07XAUgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:12:20.915334Z"},"content_sha256":"6743123a5c6ab3c45a2073408d12dc3511708fcda40a55df9091c7f08cb6882e","schema_version":"1.0","event_id":"sha256:6743123a5c6ab3c45a2073408d12dc3511708fcda40a55df9091c7f08cb6882e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IK4ZNZMAZHKZEFXGRPKPAVUTHY/bundle.json","state_url":"https://pith.science/pith/IK4ZNZMAZHKZEFXGRPKPAVUTHY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IK4ZNZMAZHKZEFXGRPKPAVUTHY/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":"2026-06-25T19:12:20Z","links":{"resolver":"https://pith.science/pith/IK4ZNZMAZHKZEFXGRPKPAVUTHY","bundle":"https://pith.science/pith/IK4ZNZMAZHKZEFXGRPKPAVUTHY/bundle.json","state":"https://pith.science/pith/IK4ZNZMAZHKZEFXGRPKPAVUTHY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IK4ZNZMAZHKZEFXGRPKPAVUTHY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IK4ZNZMAZHKZEFXGRPKPAVUTHY","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":"cf68261a157dbc754605418f2a987642aa759f8c70d572ff0ac4cfe254099fd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T01:15:06Z","title_canon_sha256":"ee62db8b761f319b3befa45e8fd90558ca3cb5119421a77c6657ae27e9d59871"},"schema_version":"1.0","source":{"id":"1701.02400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02400","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02400v1","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02400","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"IK4ZNZMAZHKZ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IK4ZNZMAZHKZEFXG","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IK4ZNZMA","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:6743123a5c6ab3c45a2073408d12dc3511708fcda40a55df9091c7f08cb6882e","target":"graph","created_at":"2026-05-18T00:53:04Z","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"},"paper":{"abstract_excerpt":"A quasi-infinitely divisible distribution on $\\mathbb{R}$ is a probability distribution whose characteristic function allows a L\\'evy-Khintchine type representation with a \"signed L\\'evy measure\", rather than a L\\'evy measure. Quasi-infinitely divisible distributions appear naturally in the factorization of infinitely divisible distributions. Namely, a distribution $\\mu$ is quasi-infinitely divisible if and only if there are two infinitely divisible distributions $\\mu_1$ and $\\mu_2$ such that $\\mu_1 \\ast \\mu = \\mu_2$. The present paper studies certain properties of quasi-infinitely divisible d","authors_text":"Alexander Lindner, Ken-iti Sato, Lei Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T01:15:06Z","title":"On quasi-infinitely divisible distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02400","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":"sha256:20364d4c69634929ae1d2039c8c3468349eecfabea9a59000c47351358803ea5","target":"record","created_at":"2026-05-18T00:53:04Z","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":"cf68261a157dbc754605418f2a987642aa759f8c70d572ff0ac4cfe254099fd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T01:15:06Z","title_canon_sha256":"ee62db8b761f319b3befa45e8fd90558ca3cb5119421a77c6657ae27e9d59871"},"schema_version":"1.0","source":{"id":"1701.02400","kind":"arxiv","version":1}},"canonical_sha256":"42b996e580c9d59216e68bd4f056933e0eddd78835b4bbf601b33c6b168aa639","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42b996e580c9d59216e68bd4f056933e0eddd78835b4bbf601b33c6b168aa639","first_computed_at":"2026-05-18T00:53:04.326892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:04.326892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9eKUr9lEDTz6g/nsHwSd3kSU87QdyyXuIiWdZh4D9d2bIZUcYCvFjkl/jumHig4s/yieiYRluIhi6t8lZUspDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:04.327442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20364d4c69634929ae1d2039c8c3468349eecfabea9a59000c47351358803ea5","sha256:6743123a5c6ab3c45a2073408d12dc3511708fcda40a55df9091c7f08cb6882e"],"state_sha256":"e25f12086caee22d7147dcfe88de3fa1edbac2858437e91aaa11bb92fe64a50b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hyi1PP01efJPEgJzdqlf78hQ9kJWsMGbso/WeMGa52vABNUrk77R/RMf5I8wyG/PZKrmlvmwTIFhLYsOBx30Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:12:20.917330Z","bundle_sha256":"1e055d918aeca8d972113604640f206c386915f4c1d98931dd31fb0bcdf8dcc3"}}