{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XX47ICWZ4GQSULAH5FJCYN3VYT","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":"8a6494682cc0fea40a62e2bd617b77e3e2424f86ea5fa8860701be49db7bd3bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-20T16:50:52Z","title_canon_sha256":"58b68476bcc2d5dc2144f7241f2b305bc8bda17164805b9fac50f21e5f8aed26"},"schema_version":"1.0","source":{"id":"1309.5321","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5321","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5321v2","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5321","created_at":"2026-05-18T03:07:44Z"},{"alias_kind":"pith_short_12","alias_value":"XX47ICWZ4GQS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XX47ICWZ4GQSULAH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XX47ICWZ","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:c33b45f560af36780414607d4c0d2055b3108b7b9772fabca86b001a37bf5f4f","target":"graph","created_at":"2026-05-18T03:07:44Z","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":"We show that the hitting times for points of real $\\alpha-$stable L\\'evy processes ($1<\\alpha\\le 2$) are unimodal random variables. The argument relies on strong unimodality and several recent multiplicative identities in law. In the symmetric case we use a factorization of Yano et al., whereas in the completely asymmetric case we apply an identity of the second author. The method extends to the general case thanks to a fractional moment evaluation due to Kuznetsov et al.","authors_text":"Julien Letemplier (LPP), LPTMS), Thomas Simon (LPP","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-20T16:50:52Z","title":"Unimodality of hitting times for stable processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5321","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":"sha256:1355810811d05948cb3c56c50f33616900ff2f8042dd69a39b046ad126f7791b","target":"record","created_at":"2026-05-18T03:07:44Z","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":"8a6494682cc0fea40a62e2bd617b77e3e2424f86ea5fa8860701be49db7bd3bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-20T16:50:52Z","title_canon_sha256":"58b68476bcc2d5dc2144f7241f2b305bc8bda17164805b9fac50f21e5f8aed26"},"schema_version":"1.0","source":{"id":"1309.5321","kind":"arxiv","version":2}},"canonical_sha256":"bdf9f40ad9e1a12a2c07e9522c3775c4e01b13e1de3aa87548fbb3e702d98344","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdf9f40ad9e1a12a2c07e9522c3775c4e01b13e1de3aa87548fbb3e702d98344","first_computed_at":"2026-05-18T03:07:44.115070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:44.115070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PuIChKT1SGK5HFsVxUOaDhM+hznSh9+xPFVKOIiVeyGkHQJvGGbaxKLJ0iBeoduW0x1luB6BHpOliTW/WWPvCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:44.115563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5321","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1355810811d05948cb3c56c50f33616900ff2f8042dd69a39b046ad126f7791b","sha256:c33b45f560af36780414607d4c0d2055b3108b7b9772fabca86b001a37bf5f4f"],"state_sha256":"03ab4a2001a144c06e477aabcb746dd7da978cc18e6e9ddac5449f14f385affb"}