{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WUAUNXU44QKNDWZBDRRDXGMG7F","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":"1fc6d2a9b61c90f43a87d4af781950e7d7f6c8c2972689593903840a9f1419c7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-10-01T11:40:19Z","title_canon_sha256":"22a6a3d70319ca726558d232f0611c8fac315cf6c9f2c085c99f029c83ea94e4"},"schema_version":"1.0","source":{"id":"1310.0252","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0252","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0252v1","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0252","created_at":"2026-05-18T00:52:02Z"},{"alias_kind":"pith_short_12","alias_value":"WUAUNXU44QKN","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WUAUNXU44QKNDWZB","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WUAUNXU4","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:48b547c5c5d51d308e11a5a06e45b92b3a2c76cba10f047083cf6e43b5ed1fb0","target":"graph","created_at":"2026-05-18T00:52:02Z","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 revisit the product convolution semigroup of probability densities e_c(t),c>0 on the positive half-line with moments (n!)^c and determine the asymptotic behaviour of e_c(t) for large and small t>0. This shows that (n!)^c is indeterminate as Stieltjes moment sequence if and only if c>2","authors_text":"Christian Berg, Jos\\'e Luis L\\'opez","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-10-01T11:40:19Z","title":"Asymptotic behaviour of the Urbanik semigroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0252","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":"sha256:30659eda921f6da24fcfc563b070f7fca7553c05a7ef809e79e11299fa7f39bb","target":"record","created_at":"2026-05-18T00:52:02Z","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":"1fc6d2a9b61c90f43a87d4af781950e7d7f6c8c2972689593903840a9f1419c7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-10-01T11:40:19Z","title_canon_sha256":"22a6a3d70319ca726558d232f0611c8fac315cf6c9f2c085c99f029c83ea94e4"},"schema_version":"1.0","source":{"id":"1310.0252","kind":"arxiv","version":1}},"canonical_sha256":"b50146de9ce414d1db211c623b9986f94ed4b48e9f36a04d1a7d8feb058cd519","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b50146de9ce414d1db211c623b9986f94ed4b48e9f36a04d1a7d8feb058cd519","first_computed_at":"2026-05-18T00:52:02.437022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:02.437022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/uMWonNm0BdzKt0sPvox0yk9o9He0uNOibo/6ftZ65NKq+N5NXe+hIlUlE5btVSZVYJHQ25uggvllkLXcMSkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:02.437765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0252","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30659eda921f6da24fcfc563b070f7fca7553c05a7ef809e79e11299fa7f39bb","sha256:48b547c5c5d51d308e11a5a06e45b92b3a2c76cba10f047083cf6e43b5ed1fb0"],"state_sha256":"e799f5689320c219e53d35e0ba96bc212e10104147e70a0191cd2dd13148bb59"}