{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:DLY7LIMQNEX2MCH4BMYSGQY652","short_pith_number":"pith:DLY7LIMQ","schema_version":"1.0","canonical_sha256":"1af1f5a190692fa608fc0b3123431eeea045c725b409d6511815ef3df14cdfbd","source":{"kind":"arxiv","id":"1001.1230","version":1},"attestation_state":"computed","paper":{"title":"On Wiener-Hopf factors for stable processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Piotr Graczyk, Tomasz Jakubowski","submitted_at":"2010-01-08T09:36:01Z","abstract_excerpt":"We give a series representation of the logarithm of the bivariate Laplace exponent $\\kappa$ of $\\alpha$-stable processes for almost all $\\alpha \\in (0,2]$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1001.1230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-08T09:36:01Z","cross_cats_sorted":[],"title_canon_sha256":"5b8bd7cc817d8a2be14762162bf4da740e8de8eedef05414eafa14f1e152537c","abstract_canon_sha256":"a225c6236fce33e843ee275d354f7440d46ef0815064edef04bde952fff27116"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:03.834038Z","signature_b64":"3sGkkYwKm8oLSkA/fHXrp+QIJEp3p0fd/JwApTPFGF4K0mNGGtXMOLWurYri+sVmqJWr0kTFx1TgPSNsBrbfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1af1f5a190692fa608fc0b3123431eeea045c725b409d6511815ef3df14cdfbd","last_reissued_at":"2026-05-18T02:10:03.833375Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:03.833375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Wiener-Hopf factors for stable processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Piotr Graczyk, Tomasz Jakubowski","submitted_at":"2010-01-08T09:36:01Z","abstract_excerpt":"We give a series representation of the logarithm of the bivariate Laplace exponent $\\kappa$ of $\\alpha$-stable processes for almost all $\\alpha \\in (0,2]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1230","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1001.1230","created_at":"2026-05-18T02:10:03.833489+00:00"},{"alias_kind":"arxiv_version","alias_value":"1001.1230v1","created_at":"2026-05-18T02:10:03.833489+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1230","created_at":"2026-05-18T02:10:03.833489+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLY7LIMQNEX2","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLY7LIMQNEX2MCH4","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLY7LIMQ","created_at":"2026-05-18T12:26:06.534383+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652","json":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652.json","graph_json":"https://pith.science/api/pith-number/DLY7LIMQNEX2MCH4BMYSGQY652/graph.json","events_json":"https://pith.science/api/pith-number/DLY7LIMQNEX2MCH4BMYSGQY652/events.json","paper":"https://pith.science/paper/DLY7LIMQ"},"agent_actions":{"view_html":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652","download_json":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652.json","view_paper":"https://pith.science/paper/DLY7LIMQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1001.1230&json=true","fetch_graph":"https://pith.science/api/pith-number/DLY7LIMQNEX2MCH4BMYSGQY652/graph.json","fetch_events":"https://pith.science/api/pith-number/DLY7LIMQNEX2MCH4BMYSGQY652/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652/action/storage_attestation","attest_author":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652/action/author_attestation","sign_citation":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652/action/citation_signature","submit_replication":"https://pith.science/pith/DLY7LIMQNEX2MCH4BMYSGQY652/action/replication_record"}},"created_at":"2026-05-18T02:10:03.833489+00:00","updated_at":"2026-05-18T02:10:03.833489+00:00"}