{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5FXLO4QJE4M6AHJXOTMABGOFG2","short_pith_number":"pith:5FXLO4QJ","canonical_record":{"source":{"id":"1310.4955","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T09:06:26Z","cross_cats_sorted":[],"title_canon_sha256":"a2176297eb809fc910240483979ecc932091685c827a7951d5cf691ccf059245","abstract_canon_sha256":"c44bf15a5609c88e22504900ad56d0944c3be0c2f41432bf45e88af0e70b55c2"},"schema_version":"1.0"},"canonical_sha256":"e96eb772092719e01d3774d80099c5369eebe72cd8b859ded1f0a245df392bb4","source":{"kind":"arxiv","id":"1310.4955","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4955","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4955v4","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4955","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"5FXLO4QJE4M6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5FXLO4QJE4M6AHJX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5FXLO4QJ","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5FXLO4QJE4M6AHJXOTMABGOFG2","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4955","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T09:06:26Z","cross_cats_sorted":[],"title_canon_sha256":"a2176297eb809fc910240483979ecc932091685c827a7951d5cf691ccf059245","abstract_canon_sha256":"c44bf15a5609c88e22504900ad56d0944c3be0c2f41432bf45e88af0e70b55c2"},"schema_version":"1.0"},"canonical_sha256":"e96eb772092719e01d3774d80099c5369eebe72cd8b859ded1f0a245df392bb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:39.221421Z","signature_b64":"82AHJoVSOdtuYMhAmPTyvh9aiz/gfdqusO9nJIGyklDntA9I+x5rSmbpmppDpKUxjmPLUgdANalXRk2BuK8zBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e96eb772092719e01d3774d80099c5369eebe72cd8b859ded1f0a245df392bb4","last_reissued_at":"2026-05-18T02:29:39.220991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:39.220991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4955","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gYoqFOaHj/UTTmq5T4rlUCc0fR4uxYToUdVAv0hkfYEC7Z8RQi9tsAFmBLXMNBJ+gseEGko7v7z0KId7fcWUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:25:09.774769Z"},"content_sha256":"7d2c871d8a00139411ed93738fffddeae4565f82b023b20134150b5606e9cec0","schema_version":"1.0","event_id":"sha256:7d2c871d8a00139411ed93738fffddeae4565f82b023b20134150b5606e9cec0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5FXLO4QJE4M6AHJXOTMABGOFG2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On exponential functionals, harmonic potential measures and undershoots of subordinators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Larbi Alili, V\\'ictor Rivero, Wissem Jedidi","submitted_at":"2013-10-18T09:06:26Z","abstract_excerpt":"We establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in terms of the L\\'evy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating function of an exponential functional $I$ and the so called remainder random variable $R$ associated to it. We provide a realization of the remainder random variable $R$ as an infinite product invol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4955","kind":"arxiv","version":4},"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":"2026-05-18T02:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rAriajaxw5cp/aUAqD1TCksFfZx+GhxpGL/NqLG0KkpIq85mQ5ERYLWz1xOTMbKTGxYyqLE/B1VoHfx2KMqTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:25:09.775137Z"},"content_sha256":"0f775d62c222cf07ca91f0b92a321d21001c7d7d96d618bf4d402f098c3b6787","schema_version":"1.0","event_id":"sha256:0f775d62c222cf07ca91f0b92a321d21001c7d7d96d618bf4d402f098c3b6787"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5FXLO4QJE4M6AHJXOTMABGOFG2/bundle.json","state_url":"https://pith.science/pith/5FXLO4QJE4M6AHJXOTMABGOFG2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5FXLO4QJE4M6AHJXOTMABGOFG2/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":"2026-06-01T08:25:09Z","links":{"resolver":"https://pith.science/pith/5FXLO4QJE4M6AHJXOTMABGOFG2","bundle":"https://pith.science/pith/5FXLO4QJE4M6AHJXOTMABGOFG2/bundle.json","state":"https://pith.science/pith/5FXLO4QJE4M6AHJXOTMABGOFG2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5FXLO4QJE4M6AHJXOTMABGOFG2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5FXLO4QJE4M6AHJXOTMABGOFG2","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":"c44bf15a5609c88e22504900ad56d0944c3be0c2f41432bf45e88af0e70b55c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T09:06:26Z","title_canon_sha256":"a2176297eb809fc910240483979ecc932091685c827a7951d5cf691ccf059245"},"schema_version":"1.0","source":{"id":"1310.4955","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4955","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4955v4","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4955","created_at":"2026-05-18T02:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"5FXLO4QJE4M6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5FXLO4QJE4M6AHJX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5FXLO4QJ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:0f775d62c222cf07ca91f0b92a321d21001c7d7d96d618bf4d402f098c3b6787","target":"graph","created_at":"2026-05-18T02:29:39Z","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 establish a link between the distribution of an exponential functional I and the undershoots of a subordinator, which is given in terms of the associated harmonic potential measure. This allows us to give a necessary and sufficient condition in terms of the L\\'evy measure for the exponential functional to be multiplicative infinitely divisible. We then provide a formula for the moment generating function of an exponential functional $I$ and the so called remainder random variable $R$ associated to it. We provide a realization of the remainder random variable $R$ as an infinite product invol","authors_text":"Larbi Alili, V\\'ictor Rivero, Wissem Jedidi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T09:06:26Z","title":"On exponential functionals, harmonic potential measures and undershoots of subordinators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4955","kind":"arxiv","version":4},"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":"sha256:7d2c871d8a00139411ed93738fffddeae4565f82b023b20134150b5606e9cec0","target":"record","created_at":"2026-05-18T02:29:39Z","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":"c44bf15a5609c88e22504900ad56d0944c3be0c2f41432bf45e88af0e70b55c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-18T09:06:26Z","title_canon_sha256":"a2176297eb809fc910240483979ecc932091685c827a7951d5cf691ccf059245"},"schema_version":"1.0","source":{"id":"1310.4955","kind":"arxiv","version":4}},"canonical_sha256":"e96eb772092719e01d3774d80099c5369eebe72cd8b859ded1f0a245df392bb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e96eb772092719e01d3774d80099c5369eebe72cd8b859ded1f0a245df392bb4","first_computed_at":"2026-05-18T02:29:39.220991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:39.220991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"82AHJoVSOdtuYMhAmPTyvh9aiz/gfdqusO9nJIGyklDntA9I+x5rSmbpmppDpKUxjmPLUgdANalXRk2BuK8zBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:39.221421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4955","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d2c871d8a00139411ed93738fffddeae4565f82b023b20134150b5606e9cec0","sha256:0f775d62c222cf07ca91f0b92a321d21001c7d7d96d618bf4d402f098c3b6787"],"state_sha256":"bb75b6e31115378152c36dba3f0b8cbba46533aa3baffded7bbe72cd83a9aacf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPy5CX20YI20QpKsZtIwYyjHoVsFNBrAZRlAT28G7mKNWq+83VF+qReRO3DdSeciGZYTq/ti0B/t4EdCoCP2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:25:09.777055Z","bundle_sha256":"99d1e5b8edec8d5de3273ebacd85edc91108ad9b3a55a0194c51d6f9612f4c1c"}}