{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:K44TTZHHEPBLJRZRXYQA4EVSIX","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":"19a44d57b22bcbb5aa28efafbb1eefa03edfd21fe1a53df3076fa31ef84df53e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-01-31T13:09:03Z","title_canon_sha256":"5a64578ba2c7fe55438b2827282f2bb813772c87c205a0a3549ae1f21d9170a2"},"schema_version":"1.0","source":{"id":"0902.0065","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0065","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0065v2","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0065","created_at":"2026-05-18T04:34:10Z"},{"alias_kind":"pith_short_12","alias_value":"K44TTZHHEPBL","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"K44TTZHHEPBLJRZR","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"K44TTZHH","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:1c3f28feedf6bfb4f61f1d31aeb4e10ed96e05070700689c0981c0ab6a575f3f","target":"graph","created_at":"2026-05-18T04:34:10Z","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 obtain a characterization of generalized Stieltjes functions of any order \\lambda > 0 in terms of inequalities for their derivatives on (0,\\infty). When \\lambda=1, this provides a new and simple proof of a characterization of Stieltjes functions first obtained by Widder in 1938.","authors_text":"Alan D. Sokal","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-01-31T13:09:03Z","title":"Real-variables characterization of generalized Stieltjes functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0065","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":"sha256:873c4cf7e2ced8726da2490423e4053a10114a0e7957ca16105f70e168d612a9","target":"record","created_at":"2026-05-18T04:34:10Z","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":"19a44d57b22bcbb5aa28efafbb1eefa03edfd21fe1a53df3076fa31ef84df53e","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-01-31T13:09:03Z","title_canon_sha256":"5a64578ba2c7fe55438b2827282f2bb813772c87c205a0a3549ae1f21d9170a2"},"schema_version":"1.0","source":{"id":"0902.0065","kind":"arxiv","version":2}},"canonical_sha256":"573939e4e723c2b4c731be200e12b245e680fb0c5b87babc55bec370f7b31e45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"573939e4e723c2b4c731be200e12b245e680fb0c5b87babc55bec370f7b31e45","first_computed_at":"2026-05-18T04:34:10.220621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:10.220621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rcgxtY6NU7CgCxQcdJ1gbhp4BMYxg5bWP9y51ZnoAq1CkhE45k5+2Auhv/JD1PJX+0BqTZMhn/NfilmK3EoADg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:10.220999Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0065","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:873c4cf7e2ced8726da2490423e4053a10114a0e7957ca16105f70e168d612a9","sha256:1c3f28feedf6bfb4f61f1d31aeb4e10ed96e05070700689c0981c0ab6a575f3f"],"state_sha256":"a013a7a224801e1de370beec54f25b43fbfe908c7be2bd68d88f05fc58eaf55a"}