{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:G4MOFAD5TVMVTH4SD56KK3MGIQ","short_pith_number":"pith:G4MOFAD5","canonical_record":{"source":{"id":"0909.5289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-09-29T08:32:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c29dfc74c0acb135cadb1b593530fb3681140f23eff8ba6227062c01c19f418d","abstract_canon_sha256":"ecad9761d01ac651d5571096ed57da3ae3060e35f0457ad67f89a965c0ac67d1"},"schema_version":"1.0"},"canonical_sha256":"3718e2807d9d59599f921f7ca56d86440fffe6defaf24231a5f8f5072df36b2b","source":{"kind":"arxiv","id":"0909.5289","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5289","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5289v1","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5289","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"G4MOFAD5TVMV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G4MOFAD5TVMVTH4S","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G4MOFAD5","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:G4MOFAD5TVMVTH4SD56KK3MGIQ","target":"record","payload":{"canonical_record":{"source":{"id":"0909.5289","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-09-29T08:32:06Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"c29dfc74c0acb135cadb1b593530fb3681140f23eff8ba6227062c01c19f418d","abstract_canon_sha256":"ecad9761d01ac651d5571096ed57da3ae3060e35f0457ad67f89a965c0ac67d1"},"schema_version":"1.0"},"canonical_sha256":"3718e2807d9d59599f921f7ca56d86440fffe6defaf24231a5f8f5072df36b2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:41.523301Z","signature_b64":"cFt+298SQfM+4ELKC595OlTC0d+4skiKAyye2e31iXndNwbl8EC1jWngqys5yXjBwLXRaMCCCt4q8l/v/WGRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3718e2807d9d59599f921f7ca56d86440fffe6defaf24231a5f8f5072df36b2b","last_reissued_at":"2026-05-18T04:31:41.522850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:41.522850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.5289","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wADTe0RTghafLHZEMViYwVd8ZX+/VjixxHbElxL3fjzDR/X4IGN3TJT+tuyUW5C0prWKaO8YsmS63XwXQ/x3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:03:52.091549Z"},"content_sha256":"4171042d35b8f48a9d2d02b4e5e50e8f9c289dad019ccdb6c2f449cc6807df19","schema_version":"1.0","event_id":"sha256:4171042d35b8f48a9d2d02b4e5e50e8f9c289dad019ccdb6c2f449cc6807df19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:G4MOFAD5TVMVTH4SD56KK3MGIQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moment properties of multivariate infinitely divisible laws and criteria for self-decomposability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Damodar N. Shanbhag, Theofanis Sapatinas","submitted_at":"2009-09-29T08:32:06Z","abstract_excerpt":"Ramachandran (1969, Theorem 8) has shown that for any univariate infinitely divisible distribution and any positive real number $\\alpha$, an absolute moment of order $\\alpha$ relative to the distribution exists (as a finite number) if and only if this is so for a certain truncated version of the corresponding L$\\acute{\\rm e}$vy measure. A generalized version of this result in the case of multivariate infinitely divisible distributions, involving the concept of g-moments, is given by Sato (1999, Theorem 25.3). We extend Ramachandran's theorem to the multivariate case, keeping in mind the immedi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5289","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":"2026-05-18T04:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S/bPZ6yZ6UTizMqYEoNbbbVX2TTkTqZW7XsftR26RrY+wzAnHObC/YXsgVlkN3W+Hl76KGuDvk1YRL95Z3Z1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T15:03:52.091895Z"},"content_sha256":"145d1f193fe23c49ae864c536cb5295dfdc6f83e79d7b54f604a1675ee937648","schema_version":"1.0","event_id":"sha256:145d1f193fe23c49ae864c536cb5295dfdc6f83e79d7b54f604a1675ee937648"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4MOFAD5TVMVTH4SD56KK3MGIQ/bundle.json","state_url":"https://pith.science/pith/G4MOFAD5TVMVTH4SD56KK3MGIQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4MOFAD5TVMVTH4SD56KK3MGIQ/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":"2026-06-30T15:03:52Z","links":{"resolver":"https://pith.science/pith/G4MOFAD5TVMVTH4SD56KK3MGIQ","bundle":"https://pith.science/pith/G4MOFAD5TVMVTH4SD56KK3MGIQ/bundle.json","state":"https://pith.science/pith/G4MOFAD5TVMVTH4SD56KK3MGIQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4MOFAD5TVMVTH4SD56KK3MGIQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:G4MOFAD5TVMVTH4SD56KK3MGIQ","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":"ecad9761d01ac651d5571096ed57da3ae3060e35f0457ad67f89a965c0ac67d1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-09-29T08:32:06Z","title_canon_sha256":"c29dfc74c0acb135cadb1b593530fb3681140f23eff8ba6227062c01c19f418d"},"schema_version":"1.0","source":{"id":"0909.5289","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.5289","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"0909.5289v1","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.5289","created_at":"2026-05-18T04:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"G4MOFAD5TVMV","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G4MOFAD5TVMVTH4S","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G4MOFAD5","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:145d1f193fe23c49ae864c536cb5295dfdc6f83e79d7b54f604a1675ee937648","target":"graph","created_at":"2026-05-18T04:31:41Z","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":"Ramachandran (1969, Theorem 8) has shown that for any univariate infinitely divisible distribution and any positive real number $\\alpha$, an absolute moment of order $\\alpha$ relative to the distribution exists (as a finite number) if and only if this is so for a certain truncated version of the corresponding L$\\acute{\\rm e}$vy measure. A generalized version of this result in the case of multivariate infinitely divisible distributions, involving the concept of g-moments, is given by Sato (1999, Theorem 25.3). We extend Ramachandran's theorem to the multivariate case, keeping in mind the immedi","authors_text":"Damodar N. Shanbhag, Theofanis Sapatinas","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-09-29T08:32:06Z","title":"Moment properties of multivariate infinitely divisible laws and criteria for self-decomposability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.5289","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":"sha256:4171042d35b8f48a9d2d02b4e5e50e8f9c289dad019ccdb6c2f449cc6807df19","target":"record","created_at":"2026-05-18T04:31:41Z","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":"ecad9761d01ac651d5571096ed57da3ae3060e35f0457ad67f89a965c0ac67d1","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2009-09-29T08:32:06Z","title_canon_sha256":"c29dfc74c0acb135cadb1b593530fb3681140f23eff8ba6227062c01c19f418d"},"schema_version":"1.0","source":{"id":"0909.5289","kind":"arxiv","version":1}},"canonical_sha256":"3718e2807d9d59599f921f7ca56d86440fffe6defaf24231a5f8f5072df36b2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3718e2807d9d59599f921f7ca56d86440fffe6defaf24231a5f8f5072df36b2b","first_computed_at":"2026-05-18T04:31:41.522850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:41.522850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cFt+298SQfM+4ELKC595OlTC0d+4skiKAyye2e31iXndNwbl8EC1jWngqys5yXjBwLXRaMCCCt4q8l/v/WGRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:41.523301Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.5289","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4171042d35b8f48a9d2d02b4e5e50e8f9c289dad019ccdb6c2f449cc6807df19","sha256:145d1f193fe23c49ae864c536cb5295dfdc6f83e79d7b54f604a1675ee937648"],"state_sha256":"5ad1d40bbc55e3ef5f6a430a72b57d8f8d1edec5feda3627419a6b8d31b3ec18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IQKwWd4nc7L9HXjlPqq5ofXd9t9OXUrMLd6RDi/LPDMkPHh5lllNO73eSsy8Vhzi4cXozm531dNCdze771EBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T15:03:52.093784Z","bundle_sha256":"7290127575d6173629939a71072592653d7c9457a576f80f681b2bbeb80f78b9"}}