{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ASDXSJKHMDQ7SKZFUT4USGFT6X","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":"8c4cf8a4eac942144b6882b6b153a2231106ccbb28f4e8ed3427057f83356ea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-19T00:47:26Z","title_canon_sha256":"986ad3e3b005ae43286f632525fc3f1ec17cdc4b4ceb2a9c3f9b4df45e2e1565"},"schema_version":"1.0","source":{"id":"1112.4208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4208","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4208v1","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4208","created_at":"2026-05-18T04:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"ASDXSJKHMDQ7","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ASDXSJKHMDQ7SKZF","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ASDXSJKH","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:8d0adea6ee608b8555436bb8feff4d96f6a8aedc3e0d519694562777bca97304","target":"graph","created_at":"2026-05-18T04:06:06Z","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 study the density of the supremum of a strictly stable L\\'evy process. As was proved recently in F. Hubalek and A. Kuznetsov \"A convergent series representation for the density of the supremum of a stable process\" (Elect. Comm. in Probab., 16, 84-95, 2011), for almost all irrational values of the stability parameter $\\alpha$ this density can be represented by an absolutely convergent series. We show that this result is not valid for all irrational values of $\\alpha$: we construct a dense uncountable set of irrational numbers $\\alpha$ for which the series does not converge absolutely. Our se","authors_text":"Alexey Kuznetsov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-19T00:47:26Z","title":"On the density of the supremum of a stable process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4208","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":"sha256:9abc14f9474122dff7bd6fa5e0ef69ec959e21c6ef00d66004a0238fb3df1a39","target":"record","created_at":"2026-05-18T04:06:06Z","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":"8c4cf8a4eac942144b6882b6b153a2231106ccbb28f4e8ed3427057f83356ea2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-19T00:47:26Z","title_canon_sha256":"986ad3e3b005ae43286f632525fc3f1ec17cdc4b4ceb2a9c3f9b4df45e2e1565"},"schema_version":"1.0","source":{"id":"1112.4208","kind":"arxiv","version":1}},"canonical_sha256":"048779254760e1f92b25a4f94918b3f5eabf4b7f8bd650ee9d1b326cbb801ecb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"048779254760e1f92b25a4f94918b3f5eabf4b7f8bd650ee9d1b326cbb801ecb","first_computed_at":"2026-05-18T04:06:06.835589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:06.835589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nOikhxmPSvmVbIkPhwJzJlW9vlD6hn7tHKd41juuNb9H2sHi/Kds98OmkGLPHPxXbyemjBF+x3nmlL3ZEkSrAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:06.836073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9abc14f9474122dff7bd6fa5e0ef69ec959e21c6ef00d66004a0238fb3df1a39","sha256:8d0adea6ee608b8555436bb8feff4d96f6a8aedc3e0d519694562777bca97304"],"state_sha256":"15834225b3e82fde026d008cf7bd7b9b08ff9de5a4048a22cb619e28a82275fd"}