{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LMLTMDZURDKBBANF72W5HQ3EAG","short_pith_number":"pith:LMLTMDZU","canonical_record":{"source":{"id":"1201.5867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-27T19:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"a59fed28d9b130a1d72811accc63f2a4b1530548d12655a848f9cda0e0214e42","abstract_canon_sha256":"d304c3c51d491e669b60b2a5d2dc069d96fa0e45a8b78eb358ed58f9183f3566"},"schema_version":"1.0"},"canonical_sha256":"5b17360f3488d41081a5feadd3c36401b745088e53be9c16a752091b0307c190","source":{"kind":"arxiv","id":"1201.5867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5867","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5867v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5867","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"LMLTMDZURDKB","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LMLTMDZURDKBBANF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LMLTMDZU","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LMLTMDZURDKBBANF72W5HQ3EAG","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-27T19:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"a59fed28d9b130a1d72811accc63f2a4b1530548d12655a848f9cda0e0214e42","abstract_canon_sha256":"d304c3c51d491e669b60b2a5d2dc069d96fa0e45a8b78eb358ed58f9183f3566"},"schema_version":"1.0"},"canonical_sha256":"5b17360f3488d41081a5feadd3c36401b745088e53be9c16a752091b0307c190","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:44.339876Z","signature_b64":"AnOs8s8D6V6ze2lpFtCoGZZ2rYQbEPqH38CwkOUfme4EXDLIdxjcBN55RvzDy9Kv6B/wpeSHj3955ugqcIWYDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b17360f3488d41081a5feadd3c36401b745088e53be9c16a752091b0307c190","last_reissued_at":"2026-05-18T04:03:44.339385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:44.339385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5867","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":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYipOFxSpTc0s06dRseNiVohAtv1zLtxA6SwdMhSv0r2+b5b+jF93xRt1DlWUu/DQSoJX8PH1BwQ3CBWiMQ+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:05:54.170005Z"},"content_sha256":"a6ac8672f54873c4bf0793cf3c39c553eab9f6fed57dbf8f754064b62ff8f422","schema_version":"1.0","event_id":"sha256:a6ac8672f54873c4bf0793cf3c39c553eab9f6fed57dbf8f754064b62ff8f422"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LMLTMDZURDKBBANF72W5HQ3EAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wiener-Hopf factorization for a family of Levy processes related to theta functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexey Kuznetsov","submitted_at":"2012-01-27T19:16:53Z","abstract_excerpt":"In this paper we study the Wiener-Hopf factorization for a class of L\\'evy processes with double-sided jumps, characterized by the fact that the density of the L\\'evy measure is given by an infinite series of exponential functions with positive coefficients. We express the Wiener-Hopf factors as infinite products over roots of a certain transcendental equation, and provide a series representation for the distribution of the supremum/infimum process evaluated at an independent exponential time. We also introduce five eight-parameter families of L\\'evy processes, defined by the fact that the den"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5867","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":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TaHZRm3HDleXV1XVomOPFCngA0W2H0YuRhWfTaA1BnX5G/9uuqnVUJW2lvevYWoCKs7UJbITGfsb4mdnCCSVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:05:54.170371Z"},"content_sha256":"722f8dd97c8efff1bcbc8495b27a6ced42ad392a73642ef2a73e550e783590eb","schema_version":"1.0","event_id":"sha256:722f8dd97c8efff1bcbc8495b27a6ced42ad392a73642ef2a73e550e783590eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMLTMDZURDKBBANF72W5HQ3EAG/bundle.json","state_url":"https://pith.science/pith/LMLTMDZURDKBBANF72W5HQ3EAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMLTMDZURDKBBANF72W5HQ3EAG/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":"2026-05-28T10:05:54Z","links":{"resolver":"https://pith.science/pith/LMLTMDZURDKBBANF72W5HQ3EAG","bundle":"https://pith.science/pith/LMLTMDZURDKBBANF72W5HQ3EAG/bundle.json","state":"https://pith.science/pith/LMLTMDZURDKBBANF72W5HQ3EAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMLTMDZURDKBBANF72W5HQ3EAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LMLTMDZURDKBBANF72W5HQ3EAG","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":"d304c3c51d491e669b60b2a5d2dc069d96fa0e45a8b78eb358ed58f9183f3566","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-27T19:16:53Z","title_canon_sha256":"a59fed28d9b130a1d72811accc63f2a4b1530548d12655a848f9cda0e0214e42"},"schema_version":"1.0","source":{"id":"1201.5867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5867","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5867v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5867","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"LMLTMDZURDKB","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LMLTMDZURDKBBANF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LMLTMDZU","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:722f8dd97c8efff1bcbc8495b27a6ced42ad392a73642ef2a73e550e783590eb","target":"graph","created_at":"2026-05-18T04:03:44Z","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":"In this paper we study the Wiener-Hopf factorization for a class of L\\'evy processes with double-sided jumps, characterized by the fact that the density of the L\\'evy measure is given by an infinite series of exponential functions with positive coefficients. We express the Wiener-Hopf factors as infinite products over roots of a certain transcendental equation, and provide a series representation for the distribution of the supremum/infimum process evaluated at an independent exponential time. We also introduce five eight-parameter families of L\\'evy processes, defined by the fact that the den","authors_text":"Alexey Kuznetsov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-27T19:16:53Z","title":"Wiener-Hopf factorization for a family of Levy processes related to theta functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5867","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:a6ac8672f54873c4bf0793cf3c39c553eab9f6fed57dbf8f754064b62ff8f422","target":"record","created_at":"2026-05-18T04:03:44Z","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":"d304c3c51d491e669b60b2a5d2dc069d96fa0e45a8b78eb358ed58f9183f3566","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-27T19:16:53Z","title_canon_sha256":"a59fed28d9b130a1d72811accc63f2a4b1530548d12655a848f9cda0e0214e42"},"schema_version":"1.0","source":{"id":"1201.5867","kind":"arxiv","version":1}},"canonical_sha256":"5b17360f3488d41081a5feadd3c36401b745088e53be9c16a752091b0307c190","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b17360f3488d41081a5feadd3c36401b745088e53be9c16a752091b0307c190","first_computed_at":"2026-05-18T04:03:44.339385Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:44.339385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AnOs8s8D6V6ze2lpFtCoGZZ2rYQbEPqH38CwkOUfme4EXDLIdxjcBN55RvzDy9Kv6B/wpeSHj3955ugqcIWYDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:44.339876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6ac8672f54873c4bf0793cf3c39c553eab9f6fed57dbf8f754064b62ff8f422","sha256:722f8dd97c8efff1bcbc8495b27a6ced42ad392a73642ef2a73e550e783590eb"],"state_sha256":"3edc201fbd47df901b07e767b251e3b5dea5fba432521bab5dbf885be2eec02f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QV73wXU8EdcoKOB3B2OaeHlRER8kEm4ULb8Eu8DHGsHeIAjRzXg7iibgICpnCfah8k3JFsnbpEtC8XJPnSi+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:05:54.172348Z","bundle_sha256":"82f3370f204f7dfb66603681dd22dacd8870f02ead438816927cc3e0886fe674"}}