{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VM5H4M4QQHAI5ZIZPFDM4L4KZF","short_pith_number":"pith:VM5H4M4Q","canonical_record":{"source":{"id":"1706.00606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-02T09:43:24Z","cross_cats_sorted":[],"title_canon_sha256":"013fb7a93fd54f1a5df85c971729be26ec74b65cf8fd363960a703d59601c896","abstract_canon_sha256":"471a276c2c137f2fe0a90d5a66e42c7608dede1a36f085b1b2d20f67cef88d3c"},"schema_version":"1.0"},"canonical_sha256":"ab3a7e339081c08ee5197946ce2f8ac9740c5a0eda172b570013dcfcadda2864","source":{"kind":"arxiv","id":"1706.00606","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00606","created_at":"2026-05-18T00:43:12Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00606v1","created_at":"2026-05-18T00:43:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00606","created_at":"2026-05-18T00:43:12Z"},{"alias_kind":"pith_short_12","alias_value":"VM5H4M4QQHAI","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VM5H4M4QQHAI5ZIZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VM5H4M4Q","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VM5H4M4QQHAI5ZIZPFDM4L4KZF","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-02T09:43:24Z","cross_cats_sorted":[],"title_canon_sha256":"013fb7a93fd54f1a5df85c971729be26ec74b65cf8fd363960a703d59601c896","abstract_canon_sha256":"471a276c2c137f2fe0a90d5a66e42c7608dede1a36f085b1b2d20f67cef88d3c"},"schema_version":"1.0"},"canonical_sha256":"ab3a7e339081c08ee5197946ce2f8ac9740c5a0eda172b570013dcfcadda2864","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:12.565959Z","signature_b64":"HmMIER3C02lExC2YKjUeHkh8zPlxqHv9dwS2HWsmEyjCHUrZcxr3EtFMbZtLEmxT+LkDSv2Kwq+LEPfTDNutDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab3a7e339081c08ee5197946ce2f8ac9740c5a0eda172b570013dcfcadda2864","last_reissued_at":"2026-05-18T00:43:12.565377Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:12.565377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00606","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHTPyGjKgLVi7huCAtSFbwWkILsnIjWIaeg7m2aDnACFZEZLU/Wkq1GUd1pIFrPSZFBRGkCTPUNJPRxJPn+ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:15:08.497786Z"},"content_sha256":"7ee8ec60bb5aa157ee1e4e7650e3e26905dd4c8c31c0cb69a27737316d44578a","schema_version":"1.0","event_id":"sha256:7ee8ec60bb5aa157ee1e4e7650e3e26905dd4c8c31c0cb69a27737316d44578a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VM5H4M4QQHAI5ZIZPFDM4L4KZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On generalized Stieltjes functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Henrik L. Pedersen, Stamatis Koumandos","submitted_at":"2017-06-02T09:43:24Z","abstract_excerpt":"It is shown that a function $f$ is a generalized Stieltjes function of order $\\lambda>0$ if and only if $x^{1-\\lambda}(x^{\\lambda-1+k}f(x))^{(k)}$ is completely monotonic for all $k\\geq 0$, thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions $f$ for which $x^{1-\\lambda}(x^{\\lambda-1+k}f(x))^{(k)}$ is completely monotonic for all $k\\leq n$ is obtained in terms of properties of the representing measure of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00606","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nyf99q9uGmOmwcD44mcOO0C7m+fVnTsQ94YltnTtGzKQUhYo7Mx2vbHYu5cOn8EAcX6K+TSCuxwAym6R6FBIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T23:15:08.498131Z"},"content_sha256":"9f53ef79ab4df2bc7e52aa9e93dcab5a67de8aa02c71c77ae0f26405b60109f7","schema_version":"1.0","event_id":"sha256:9f53ef79ab4df2bc7e52aa9e93dcab5a67de8aa02c71c77ae0f26405b60109f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VM5H4M4QQHAI5ZIZPFDM4L4KZF/bundle.json","state_url":"https://pith.science/pith/VM5H4M4QQHAI5ZIZPFDM4L4KZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VM5H4M4QQHAI5ZIZPFDM4L4KZF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T23:15:08Z","links":{"resolver":"https://pith.science/pith/VM5H4M4QQHAI5ZIZPFDM4L4KZF","bundle":"https://pith.science/pith/VM5H4M4QQHAI5ZIZPFDM4L4KZF/bundle.json","state":"https://pith.science/pith/VM5H4M4QQHAI5ZIZPFDM4L4KZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VM5H4M4QQHAI5ZIZPFDM4L4KZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VM5H4M4QQHAI5ZIZPFDM4L4KZF","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":"471a276c2c137f2fe0a90d5a66e42c7608dede1a36f085b1b2d20f67cef88d3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-02T09:43:24Z","title_canon_sha256":"013fb7a93fd54f1a5df85c971729be26ec74b65cf8fd363960a703d59601c896"},"schema_version":"1.0","source":{"id":"1706.00606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00606","created_at":"2026-05-18T00:43:12Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00606v1","created_at":"2026-05-18T00:43:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00606","created_at":"2026-05-18T00:43:12Z"},{"alias_kind":"pith_short_12","alias_value":"VM5H4M4QQHAI","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VM5H4M4QQHAI5ZIZ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VM5H4M4Q","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:9f53ef79ab4df2bc7e52aa9e93dcab5a67de8aa02c71c77ae0f26405b60109f7","target":"graph","created_at":"2026-05-18T00:43:12Z","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":"It is shown that a function $f$ is a generalized Stieltjes function of order $\\lambda>0$ if and only if $x^{1-\\lambda}(x^{\\lambda-1+k}f(x))^{(k)}$ is completely monotonic for all $k\\geq 0$, thereby complementing a result due to Sokal. Furthermore, a characterization of those completely monotonic functions $f$ for which $x^{1-\\lambda}(x^{\\lambda-1+k}f(x))^{(k)}$ is completely monotonic for all $k\\leq n$ is obtained in terms of properties of the representing measure of $f$.","authors_text":"Henrik L. Pedersen, Stamatis Koumandos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-02T09:43:24Z","title":"On generalized Stieltjes functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00606","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":"sha256:7ee8ec60bb5aa157ee1e4e7650e3e26905dd4c8c31c0cb69a27737316d44578a","target":"record","created_at":"2026-05-18T00:43:12Z","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":"471a276c2c137f2fe0a90d5a66e42c7608dede1a36f085b1b2d20f67cef88d3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-06-02T09:43:24Z","title_canon_sha256":"013fb7a93fd54f1a5df85c971729be26ec74b65cf8fd363960a703d59601c896"},"schema_version":"1.0","source":{"id":"1706.00606","kind":"arxiv","version":1}},"canonical_sha256":"ab3a7e339081c08ee5197946ce2f8ac9740c5a0eda172b570013dcfcadda2864","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab3a7e339081c08ee5197946ce2f8ac9740c5a0eda172b570013dcfcadda2864","first_computed_at":"2026-05-18T00:43:12.565377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:12.565377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HmMIER3C02lExC2YKjUeHkh8zPlxqHv9dwS2HWsmEyjCHUrZcxr3EtFMbZtLEmxT+LkDSv2Kwq+LEPfTDNutDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:12.565959Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ee8ec60bb5aa157ee1e4e7650e3e26905dd4c8c31c0cb69a27737316d44578a","sha256:9f53ef79ab4df2bc7e52aa9e93dcab5a67de8aa02c71c77ae0f26405b60109f7"],"state_sha256":"4d83d66cf59c4711acacf16ddb67e3e9cf2525dcfac607f4b01bb3a5ece00e9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzq+Ip4dNJIBJrO28/T5Zr0Dg3NanNTYslfyiwUajvm6OGXXti7qC7uHQZfSoT59jsWLkBAK1VYSiF+n0rnZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T23:15:08.500063Z","bundle_sha256":"c059431a924046ee0d147e5a977b6c8ac8ef202d7e684563bd7b043306331b20"}}