{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D5IQRFHIE2YZTPTPUFMHIQ4MNR","short_pith_number":"pith:D5IQRFHI","canonical_record":{"source":{"id":"1009.1510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-08T11:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"19ba231015a6f5c810bec644b0f8dd39a09628ab44a2ff6254310e528e36e959","abstract_canon_sha256":"1b4e6d5bca54fd5b5d7ac6a6c453b151a8be846bc26dc1d388b2246df9c3da6b"},"schema_version":"1.0"},"canonical_sha256":"1f510894e826b199be6fa15874438c6c499bbedf11a514749dd277b67f6b2be4","source":{"kind":"arxiv","id":"1009.1510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1510","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1510v2","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1510","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"D5IQRFHIE2YZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5IQRFHIE2YZTPTP","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5IQRFHI","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D5IQRFHIE2YZTPTPUFMHIQ4MNR","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-08T11:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"19ba231015a6f5c810bec644b0f8dd39a09628ab44a2ff6254310e528e36e959","abstract_canon_sha256":"1b4e6d5bca54fd5b5d7ac6a6c453b151a8be846bc26dc1d388b2246df9c3da6b"},"schema_version":"1.0"},"canonical_sha256":"1f510894e826b199be6fa15874438c6c499bbedf11a514749dd277b67f6b2be4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:45.175098Z","signature_b64":"MIFV+MQfM6DDwThvpOQlDEr/iJe4T/5+JP8NxFk49bfU/3c/H8+7ijNMncMGX6XyAzfuuc62v4iGLsPJ0gc6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f510894e826b199be6fa15874438c6c499bbedf11a514749dd277b67f6b2be4","last_reissued_at":"2026-05-18T03:05:45.174522Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:45.174522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1510","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g4JG4LbaxwSCKO7ny1GBZXh9zjKW8LKDRRKqJ+qFHoU9JuQHn7dL1RhFDIB+cKT8D6ElYX7FqhRXaMRwnW1jBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:51:53.551282Z"},"content_sha256":"f6d31d2394db52f9906e3ba33e5ed1ed21e30bde565dd427d7c45cb97eca1245","schema_version":"1.0","event_id":"sha256:f6d31d2394db52f9906e3ba33e5ed1ed21e30bde565dd427d7c45cb97eca1245"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D5IQRFHIE2YZTPTPUFMHIQ4MNR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytic continuations of Fourier and Stieltjes transforms and generalized moments of probability measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Takahiro Hasebe","submitted_at":"2010-09-08T11:54:44Z","abstract_excerpt":"We consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two ways to generalize moments accordingly to Fourier and Stieltjes transforms; however these two turn out to coincide. As applications, we give short proofs of the convergence of probability measures to Cauchy distributions with respect to tensor, free, Boolean and monotone convolutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1510","kind":"arxiv","version":2},"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":"2026-05-18T03:05:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hglRUhx1+IHynTN6fEGnkOdzT3O3PEPgC5CVdMGOkBL27nwdRvBR8pYf7nqS6PC1fnN4UY93uZuMPfq/HvNyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:51:53.552042Z"},"content_sha256":"fcf37c86e4903c6080b4a4c9b8aeaf80010c3b9a8c330fbc8125ab876f1c0d57","schema_version":"1.0","event_id":"sha256:fcf37c86e4903c6080b4a4c9b8aeaf80010c3b9a8c330fbc8125ab876f1c0d57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5IQRFHIE2YZTPTPUFMHIQ4MNR/bundle.json","state_url":"https://pith.science/pith/D5IQRFHIE2YZTPTPUFMHIQ4MNR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5IQRFHIE2YZTPTPUFMHIQ4MNR/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":"2026-05-31T14:51:53Z","links":{"resolver":"https://pith.science/pith/D5IQRFHIE2YZTPTPUFMHIQ4MNR","bundle":"https://pith.science/pith/D5IQRFHIE2YZTPTPUFMHIQ4MNR/bundle.json","state":"https://pith.science/pith/D5IQRFHIE2YZTPTPUFMHIQ4MNR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5IQRFHIE2YZTPTPUFMHIQ4MNR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D5IQRFHIE2YZTPTPUFMHIQ4MNR","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":"1b4e6d5bca54fd5b5d7ac6a6c453b151a8be846bc26dc1d388b2246df9c3da6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-08T11:54:44Z","title_canon_sha256":"19ba231015a6f5c810bec644b0f8dd39a09628ab44a2ff6254310e528e36e959"},"schema_version":"1.0","source":{"id":"1009.1510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1510","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1510v2","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1510","created_at":"2026-05-18T03:05:45Z"},{"alias_kind":"pith_short_12","alias_value":"D5IQRFHIE2YZ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5IQRFHIE2YZTPTP","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5IQRFHI","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:fcf37c86e4903c6080b4a4c9b8aeaf80010c3b9a8c330fbc8125ab876f1c0d57","target":"graph","created_at":"2026-05-18T03:05:45Z","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 consider analytic continuations of Fourier transforms and Stieltjes transforms. This enables us to define what we call complex moments for some class of probability measures which do not have moments in the usual sense. There are two ways to generalize moments accordingly to Fourier and Stieltjes transforms; however these two turn out to coincide. As applications, we give short proofs of the convergence of probability measures to Cauchy distributions with respect to tensor, free, Boolean and monotone convolutions.","authors_text":"Takahiro Hasebe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-08T11:54:44Z","title":"Analytic continuations of Fourier and Stieltjes transforms and generalized moments of probability measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1510","kind":"arxiv","version":2},"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:f6d31d2394db52f9906e3ba33e5ed1ed21e30bde565dd427d7c45cb97eca1245","target":"record","created_at":"2026-05-18T03:05:45Z","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":"1b4e6d5bca54fd5b5d7ac6a6c453b151a8be846bc26dc1d388b2246df9c3da6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-08T11:54:44Z","title_canon_sha256":"19ba231015a6f5c810bec644b0f8dd39a09628ab44a2ff6254310e528e36e959"},"schema_version":"1.0","source":{"id":"1009.1510","kind":"arxiv","version":2}},"canonical_sha256":"1f510894e826b199be6fa15874438c6c499bbedf11a514749dd277b67f6b2be4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f510894e826b199be6fa15874438c6c499bbedf11a514749dd277b67f6b2be4","first_computed_at":"2026-05-18T03:05:45.174522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:45.174522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MIFV+MQfM6DDwThvpOQlDEr/iJe4T/5+JP8NxFk49bfU/3c/H8+7ijNMncMGX6XyAzfuuc62v4iGLsPJ0gc6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:45.175098Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6d31d2394db52f9906e3ba33e5ed1ed21e30bde565dd427d7c45cb97eca1245","sha256:fcf37c86e4903c6080b4a4c9b8aeaf80010c3b9a8c330fbc8125ab876f1c0d57"],"state_sha256":"9a4f0f2d66f8441662a0472d7a549863cf589472d24dfd9babbc98d54ff547f8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r+1RPMN1u9f7ZlswOGMzvScBBTCyvtU6wq8HyzHlaOfMXgiDqFLJZJCPmaC2BCQiQtrCA/vdzuJZiZ7PTPB8DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:51:53.556280Z","bundle_sha256":"9681c7c7d3ebacb98a5ac5aff1bc805836de171744bd9fb703c7d5a852dd815b"}}