{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:OOW52RRUK6LI54JNGSYLPEMS2A","short_pith_number":"pith:OOW52RRU","canonical_record":{"source":{"id":"1012.0093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-01T04:45:31Z","cross_cats_sorted":[],"title_canon_sha256":"d8e345f9eef819fc43e4bdce0162f50b2d5ed66ea90c9b26b769f8b638bee099","abstract_canon_sha256":"2449177f0401a78f55960e946e348a371ea844cf19d610030c00fc5bd3cb0dd6"},"schema_version":"1.0"},"canonical_sha256":"73addd463457968ef12d34b0b79192d006c3be601b144adacaea09ef7eb859e0","source":{"kind":"arxiv","id":"1012.0093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0093","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0093v1","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0093","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"OOW52RRUK6LI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OOW52RRUK6LI54JN","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OOW52RRU","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:OOW52RRUK6LI54JNGSYLPEMS2A","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-01T04:45:31Z","cross_cats_sorted":[],"title_canon_sha256":"d8e345f9eef819fc43e4bdce0162f50b2d5ed66ea90c9b26b769f8b638bee099","abstract_canon_sha256":"2449177f0401a78f55960e946e348a371ea844cf19d610030c00fc5bd3cb0dd6"},"schema_version":"1.0"},"canonical_sha256":"73addd463457968ef12d34b0b79192d006c3be601b144adacaea09ef7eb859e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:18.961856Z","signature_b64":"v/mmR30k9ru+DNH2k6M3AGUsJadZM35vOHQDsmNbKOBt7nGfrHqyQNtVPeX+A1csb0JCkIpFOlxoUMyZ6YIqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73addd463457968ef12d34b0b79192d006c3be601b144adacaea09ef7eb859e0","last_reissued_at":"2026-05-18T04:34:18.961372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:18.961372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0093","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":"2026-05-18T04:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0GNrq2aAwoDivkkLBP3eSjsayXTk1VLyhzSzFshvDUt9svG4OhrhuJbNhvWQ8hWoiaqTi0TpFpiCz4sWG94CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:13:56.737740Z"},"content_sha256":"2b9e89a1fd4203fee3f0ce45bf36ddc58f919d8e04b736dbe31c722797b2f5c9","schema_version":"1.0","event_id":"sha256:2b9e89a1fd4203fee3f0ce45bf36ddc58f919d8e04b736dbe31c722797b2f5c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:OOW52RRUK6LI54JNGSYLPEMS2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Description of limits of ranges of iterations of stochastic integral mappings of infinitely divisible distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ken-iti Sato","submitted_at":"2010-12-01T04:45:31Z","abstract_excerpt":"For infinitely divisible distributions $\\rho$ on $\\mathbb{R}^d$ the stochastic integral mapping $\\Phi_f\\rho$ is defined as the distribution of improper stochastic integral $\\int_0^{\\infty-} f(s) dX_s^{(\\rho)}$, where $f(s)$ is a non-random function and $\\{X_s^{(\\rho)}\\}$ is a L\\'evy process on $\\mathbb{R}^d$ with distribution $\\rho$ at time 1. For three families of functions $f$ with parameters, the limits of the nested sequences of the ranges of the iterations $\\Phi_f^n$ are shown to be some subclasses, with explicit description, of the class $L_{\\infty}$ of completely selfdecomposable distri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0093","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":"2026-05-18T04:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBnPn8fd7XLCgsCRq292JChH7cvlTbPbr30czOMclWeqE2fun2air31cFGGI2u6ObAGZl++stXM9BI4mjQgBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:13:56.738082Z"},"content_sha256":"140c88f225bbcd732d3e62d8a8c08563dd55c3899abee6aa533d0d27fa69b0f1","schema_version":"1.0","event_id":"sha256:140c88f225bbcd732d3e62d8a8c08563dd55c3899abee6aa533d0d27fa69b0f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OOW52RRUK6LI54JNGSYLPEMS2A/bundle.json","state_url":"https://pith.science/pith/OOW52RRUK6LI54JNGSYLPEMS2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OOW52RRUK6LI54JNGSYLPEMS2A/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":"2026-06-25T19:13:56Z","links":{"resolver":"https://pith.science/pith/OOW52RRUK6LI54JNGSYLPEMS2A","bundle":"https://pith.science/pith/OOW52RRUK6LI54JNGSYLPEMS2A/bundle.json","state":"https://pith.science/pith/OOW52RRUK6LI54JNGSYLPEMS2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OOW52RRUK6LI54JNGSYLPEMS2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OOW52RRUK6LI54JNGSYLPEMS2A","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":"2449177f0401a78f55960e946e348a371ea844cf19d610030c00fc5bd3cb0dd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-01T04:45:31Z","title_canon_sha256":"d8e345f9eef819fc43e4bdce0162f50b2d5ed66ea90c9b26b769f8b638bee099"},"schema_version":"1.0","source":{"id":"1012.0093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0093","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0093v1","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0093","created_at":"2026-05-18T04:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"OOW52RRUK6LI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OOW52RRUK6LI54JN","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OOW52RRU","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:140c88f225bbcd732d3e62d8a8c08563dd55c3899abee6aa533d0d27fa69b0f1","target":"graph","created_at":"2026-05-18T04:34:18Z","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":"For infinitely divisible distributions $\\rho$ on $\\mathbb{R}^d$ the stochastic integral mapping $\\Phi_f\\rho$ is defined as the distribution of improper stochastic integral $\\int_0^{\\infty-} f(s) dX_s^{(\\rho)}$, where $f(s)$ is a non-random function and $\\{X_s^{(\\rho)}\\}$ is a L\\'evy process on $\\mathbb{R}^d$ with distribution $\\rho$ at time 1. For three families of functions $f$ with parameters, the limits of the nested sequences of the ranges of the iterations $\\Phi_f^n$ are shown to be some subclasses, with explicit description, of the class $L_{\\infty}$ of completely selfdecomposable distri","authors_text":"Ken-iti Sato","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-01T04:45:31Z","title":"Description of limits of ranges of iterations of stochastic integral mappings of infinitely divisible distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0093","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":"sha256:2b9e89a1fd4203fee3f0ce45bf36ddc58f919d8e04b736dbe31c722797b2f5c9","target":"record","created_at":"2026-05-18T04:34:18Z","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":"2449177f0401a78f55960e946e348a371ea844cf19d610030c00fc5bd3cb0dd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-01T04:45:31Z","title_canon_sha256":"d8e345f9eef819fc43e4bdce0162f50b2d5ed66ea90c9b26b769f8b638bee099"},"schema_version":"1.0","source":{"id":"1012.0093","kind":"arxiv","version":1}},"canonical_sha256":"73addd463457968ef12d34b0b79192d006c3be601b144adacaea09ef7eb859e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73addd463457968ef12d34b0b79192d006c3be601b144adacaea09ef7eb859e0","first_computed_at":"2026-05-18T04:34:18.961372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:18.961372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v/mmR30k9ru+DNH2k6M3AGUsJadZM35vOHQDsmNbKOBt7nGfrHqyQNtVPeX+A1csb0JCkIpFOlxoUMyZ6YIqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:18.961856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b9e89a1fd4203fee3f0ce45bf36ddc58f919d8e04b736dbe31c722797b2f5c9","sha256:140c88f225bbcd732d3e62d8a8c08563dd55c3899abee6aa533d0d27fa69b0f1"],"state_sha256":"3de2dd7878c2dbf622a0b64dea51990fa8d014818a8b40eca04ec3466cceec14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYiwvMbRW6O65Yamq/x+A8bO1U0YZKXpxGcrvdBDfVeqSrrNk3GUITagMvbdlyqo+ZfiNnfP4UkA0PoXDw24Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:13:56.740071Z","bundle_sha256":"c52b709014dc5c8380b9724caafae196e4ee07bb787806eb669c33bfc2bc4543"}}