{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:OJRPOFPN5TRVLLNOR2UEFY5RZC","short_pith_number":"pith:OJRPOFPN","canonical_record":{"source":{"id":"0911.4139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-11-21T16:27:31Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"1ba575fab75453c89afc58bee68e464de88d897b8937d6425ad853bab42854ef","abstract_canon_sha256":"bfbd706d23e0fd505d0d24e454a0e613bbd62f0c12dc28ce3920bef935991108"},"schema_version":"1.0"},"canonical_sha256":"7262f715edece355adae8ea842e3b1c8848c4fafb979b679a1515a5b8b02c97e","source":{"kind":"arxiv","id":"0911.4139","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4139","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4139v2","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4139","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"OJRPOFPN5TRV","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OJRPOFPN5TRVLLNO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OJRPOFPN","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:OJRPOFPN5TRVLLNOR2UEFY5RZC","target":"record","payload":{"canonical_record":{"source":{"id":"0911.4139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-11-21T16:27:31Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"1ba575fab75453c89afc58bee68e464de88d897b8937d6425ad853bab42854ef","abstract_canon_sha256":"bfbd706d23e0fd505d0d24e454a0e613bbd62f0c12dc28ce3920bef935991108"},"schema_version":"1.0"},"canonical_sha256":"7262f715edece355adae8ea842e3b1c8848c4fafb979b679a1515a5b8b02c97e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:22.570028Z","signature_b64":"xWRfvPxMQ2YWET+RaluTu/NM3R7jpMK5MvmzUswpdNpKxx8V4ji36eQg1RwsEDRcJwiGCeFuUzpCSdoLafYmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7262f715edece355adae8ea842e3b1c8848c4fafb979b679a1515a5b8b02c97e","last_reissued_at":"2026-05-18T04:18:22.569480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:22.569480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.4139","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":"2026-05-18T04:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZeC9LpdZi3PmuA9RM5Q9HLPOK5p2ZN6w/t6nTIj9bA+iaqcZHZcfiJrJMqrk670DM255RRtKHQC86E6zR2RBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:22:10.988698Z"},"content_sha256":"6a8e5f8538418d31a3b7c46626677e4b6a3a50ab17986e9fa381c4729a270151","schema_version":"1.0","event_id":"sha256:6a8e5f8538418d31a3b7c46626677e4b6a3a50ab17986e9fa381c4729a270151"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:OJRPOFPN5TRVLLNOR2UEFY5RZC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional limit theorems for sums of independent geometric L\\'{e}vy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Zakhar Kabluchko","submitted_at":"2009-11-21T16:27:31Z","abstract_excerpt":"Let $\\xi_i$, $i\\in \\mathbb {N}$, be independent copies of a L\\'{e}vy process $\\{\\xi(t),t\\geq0\\}$. Motivated by the results obtained previously in the context of the random energy model, we prove functional limit theorems for the process \\[Z_N(t)=\\sum_{i=1}^N\\mathrm{e}^{\\xi_i(s_N+t)}\\] as $N\\to\\infty$, where $s_N$ is a non-negative sequence converging to $+\\infty$. The limiting process depends heavily on the growth rate of the sequence $s_N$. If $s_N$ grows slowly in the sense that $\\liminf_{N\\to\\infty}\\log N/s_N>\\lambda_2$ for some critical value $\\lambda_2>0$, then the limit is an Ornstein--U"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4139","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":"2026-05-18T04:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ob7/y51Fd9jmX2jyozswSDBVdYT1QH/jppCkyk/HLuGkEyzy18J3JOH+t5so89QeL+jlEhQ6gfnGajvrZc3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:22:10.989154Z"},"content_sha256":"8900f51d6de0fd4ffff49c2e7b486911a81852cf35b6feb584be2cee8a4511b1","schema_version":"1.0","event_id":"sha256:8900f51d6de0fd4ffff49c2e7b486911a81852cf35b6feb584be2cee8a4511b1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJRPOFPN5TRVLLNOR2UEFY5RZC/bundle.json","state_url":"https://pith.science/pith/OJRPOFPN5TRVLLNOR2UEFY5RZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJRPOFPN5TRVLLNOR2UEFY5RZC/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":"2026-05-27T04:22:10Z","links":{"resolver":"https://pith.science/pith/OJRPOFPN5TRVLLNOR2UEFY5RZC","bundle":"https://pith.science/pith/OJRPOFPN5TRVLLNOR2UEFY5RZC/bundle.json","state":"https://pith.science/pith/OJRPOFPN5TRVLLNOR2UEFY5RZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJRPOFPN5TRVLLNOR2UEFY5RZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OJRPOFPN5TRVLLNOR2UEFY5RZC","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":"bfbd706d23e0fd505d0d24e454a0e613bbd62f0c12dc28ce3920bef935991108","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-11-21T16:27:31Z","title_canon_sha256":"1ba575fab75453c89afc58bee68e464de88d897b8937d6425ad853bab42854ef"},"schema_version":"1.0","source":{"id":"0911.4139","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.4139","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"0911.4139v2","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.4139","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"OJRPOFPN5TRV","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OJRPOFPN5TRVLLNO","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OJRPOFPN","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:8900f51d6de0fd4ffff49c2e7b486911a81852cf35b6feb584be2cee8a4511b1","target":"graph","created_at":"2026-05-18T04:18:22Z","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":"Let $\\xi_i$, $i\\in \\mathbb {N}$, be independent copies of a L\\'{e}vy process $\\{\\xi(t),t\\geq0\\}$. Motivated by the results obtained previously in the context of the random energy model, we prove functional limit theorems for the process \\[Z_N(t)=\\sum_{i=1}^N\\mathrm{e}^{\\xi_i(s_N+t)}\\] as $N\\to\\infty$, where $s_N$ is a non-negative sequence converging to $+\\infty$. The limiting process depends heavily on the growth rate of the sequence $s_N$. If $s_N$ grows slowly in the sense that $\\liminf_{N\\to\\infty}\\log N/s_N>\\lambda_2$ for some critical value $\\lambda_2>0$, then the limit is an Ornstein--U","authors_text":"Zakhar Kabluchko","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-11-21T16:27:31Z","title":"Functional limit theorems for sums of independent geometric L\\'{e}vy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.4139","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":"sha256:6a8e5f8538418d31a3b7c46626677e4b6a3a50ab17986e9fa381c4729a270151","target":"record","created_at":"2026-05-18T04:18:22Z","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":"bfbd706d23e0fd505d0d24e454a0e613bbd62f0c12dc28ce3920bef935991108","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-11-21T16:27:31Z","title_canon_sha256":"1ba575fab75453c89afc58bee68e464de88d897b8937d6425ad853bab42854ef"},"schema_version":"1.0","source":{"id":"0911.4139","kind":"arxiv","version":2}},"canonical_sha256":"7262f715edece355adae8ea842e3b1c8848c4fafb979b679a1515a5b8b02c97e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7262f715edece355adae8ea842e3b1c8848c4fafb979b679a1515a5b8b02c97e","first_computed_at":"2026-05-18T04:18:22.569480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:22.569480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xWRfvPxMQ2YWET+RaluTu/NM3R7jpMK5MvmzUswpdNpKxx8V4ji36eQg1RwsEDRcJwiGCeFuUzpCSdoLafYmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:22.570028Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.4139","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a8e5f8538418d31a3b7c46626677e4b6a3a50ab17986e9fa381c4729a270151","sha256:8900f51d6de0fd4ffff49c2e7b486911a81852cf35b6feb584be2cee8a4511b1"],"state_sha256":"a66be63dcd514294ecc9b9376026afa03d1a26e35a8c3312a1c2bb880db7a514"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/AY8akFf7hR1saDR0F35+41CJP9qRVGwgzADurTqgT3IBU7XTdMdy9cTnYJYGUmh/Co8Y/QAG2NTiwcMJQOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:22:10.991950Z","bundle_sha256":"c63179b04c96eb2a150ae0a0139fe460b0c2eb104eebedd6bd318b38a688476e"}}