{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IDHMWRK5V6BGI3XR3IXHY3K6PJ","short_pith_number":"pith:IDHMWRK5","canonical_record":{"source":{"id":"1510.03420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-11T18:30:14Z","cross_cats_sorted":[],"title_canon_sha256":"8b9793d62005d1b1b512098e386233ce93d1aec4505583431b2ea4df2a3abc58","abstract_canon_sha256":"8b66990b5539c9270505415338dfe4a287f3e7d12e2e952f78474397aa3af0ca"},"schema_version":"1.0"},"canonical_sha256":"40cecb455daf82646ef1da2e7c6d5e7a7a13ae18f790d89caf4e1da8879b2a35","source":{"kind":"arxiv","id":"1510.03420","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03420","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03420v2","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03420","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"pith_short_12","alias_value":"IDHMWRK5V6BG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IDHMWRK5V6BGI3XR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IDHMWRK5","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IDHMWRK5V6BGI3XR3IXHY3K6PJ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-11T18:30:14Z","cross_cats_sorted":[],"title_canon_sha256":"8b9793d62005d1b1b512098e386233ce93d1aec4505583431b2ea4df2a3abc58","abstract_canon_sha256":"8b66990b5539c9270505415338dfe4a287f3e7d12e2e952f78474397aa3af0ca"},"schema_version":"1.0"},"canonical_sha256":"40cecb455daf82646ef1da2e7c6d5e7a7a13ae18f790d89caf4e1da8879b2a35","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:16.694678Z","signature_b64":"e6se6Xc7k55vwM71W90iNJXuBbXA2IerxzRC0QxAmlZ7brz7fHCIPB5+984w8aE3CxDct2LbwbjqOS6E8LENDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40cecb455daf82646ef1da2e7c6d5e7a7a13ae18f790d89caf4e1da8879b2a35","last_reissued_at":"2026-05-18T01:20:16.693967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:16.693967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03420","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQwIqHhBWXz/2NESdG/m4e47iS957LbbdqBuyedNDcZp1FzIrqHcHsPDwKUfLcHXCsMUGgnPglbeB6dyWcl7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:00:47.156834Z"},"content_sha256":"573fba442b64adfb5133eaef440ef9f201420c273760e8ccdd10e68634a59ce7","schema_version":"1.0","event_id":"sha256:573fba442b64adfb5133eaef440ef9f201420c273760e8ccdd10e68634a59ce7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IDHMWRK5V6BGI3XR3IXHY3K6PJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Power Sums of Positive Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ruiming Zhang","submitted_at":"2015-10-11T18:30:14Z","abstract_excerpt":"In this work we establish a necessary and sufficient condition for a genus $0$ entire function $f(z)$ has only positive zeros by applying Hausdorff moment problem and Mergelyan's theorem, the obtained criterion is very much reminiscent of Xian-Jin Li's criterion on the Riemann hypothesis. We also apply this criterion to the Riemann hypothesis and the generalized Riemann hypothesis for certain Dirichlet $L$-series of real primitive characters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03420","kind":"arxiv","version":2},"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":"2026-05-18T01:20:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ITvumv0PsdmuUGseurTS+IqIoLeHQsXk/wwY91HhLBhKVXMCbW/YaGgQnUhhCnpW70yr3oWuyMrHIwHJ/Yb2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:00:47.157173Z"},"content_sha256":"82f10e539f2f523ea2c1a130c21d9f19cfeb544b2664c46d4b7406486667d863","schema_version":"1.0","event_id":"sha256:82f10e539f2f523ea2c1a130c21d9f19cfeb544b2664c46d4b7406486667d863"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDHMWRK5V6BGI3XR3IXHY3K6PJ/bundle.json","state_url":"https://pith.science/pith/IDHMWRK5V6BGI3XR3IXHY3K6PJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDHMWRK5V6BGI3XR3IXHY3K6PJ/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":"2026-06-21T22:00:47Z","links":{"resolver":"https://pith.science/pith/IDHMWRK5V6BGI3XR3IXHY3K6PJ","bundle":"https://pith.science/pith/IDHMWRK5V6BGI3XR3IXHY3K6PJ/bundle.json","state":"https://pith.science/pith/IDHMWRK5V6BGI3XR3IXHY3K6PJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDHMWRK5V6BGI3XR3IXHY3K6PJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IDHMWRK5V6BGI3XR3IXHY3K6PJ","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":"8b66990b5539c9270505415338dfe4a287f3e7d12e2e952f78474397aa3af0ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-11T18:30:14Z","title_canon_sha256":"8b9793d62005d1b1b512098e386233ce93d1aec4505583431b2ea4df2a3abc58"},"schema_version":"1.0","source":{"id":"1510.03420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03420","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03420v2","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03420","created_at":"2026-05-18T01:20:16Z"},{"alias_kind":"pith_short_12","alias_value":"IDHMWRK5V6BG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IDHMWRK5V6BGI3XR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IDHMWRK5","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:82f10e539f2f523ea2c1a130c21d9f19cfeb544b2664c46d4b7406486667d863","target":"graph","created_at":"2026-05-18T01:20:16Z","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":"In this work we establish a necessary and sufficient condition for a genus $0$ entire function $f(z)$ has only positive zeros by applying Hausdorff moment problem and Mergelyan's theorem, the obtained criterion is very much reminiscent of Xian-Jin Li's criterion on the Riemann hypothesis. We also apply this criterion to the Riemann hypothesis and the generalized Riemann hypothesis for certain Dirichlet $L$-series of real primitive characters.","authors_text":"Ruiming Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-11T18:30:14Z","title":"On Power Sums of Positive Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03420","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":"sha256:573fba442b64adfb5133eaef440ef9f201420c273760e8ccdd10e68634a59ce7","target":"record","created_at":"2026-05-18T01:20:16Z","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":"8b66990b5539c9270505415338dfe4a287f3e7d12e2e952f78474397aa3af0ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-11T18:30:14Z","title_canon_sha256":"8b9793d62005d1b1b512098e386233ce93d1aec4505583431b2ea4df2a3abc58"},"schema_version":"1.0","source":{"id":"1510.03420","kind":"arxiv","version":2}},"canonical_sha256":"40cecb455daf82646ef1da2e7c6d5e7a7a13ae18f790d89caf4e1da8879b2a35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40cecb455daf82646ef1da2e7c6d5e7a7a13ae18f790d89caf4e1da8879b2a35","first_computed_at":"2026-05-18T01:20:16.693967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:16.693967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e6se6Xc7k55vwM71W90iNJXuBbXA2IerxzRC0QxAmlZ7brz7fHCIPB5+984w8aE3CxDct2LbwbjqOS6E8LENDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:16.694678Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:573fba442b64adfb5133eaef440ef9f201420c273760e8ccdd10e68634a59ce7","sha256:82f10e539f2f523ea2c1a130c21d9f19cfeb544b2664c46d4b7406486667d863"],"state_sha256":"9b7cccec91ceefc770f4a61ab7e3103fdaa1be7b758d93bec8ca94035e16fb1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yRlQgC+XH25sCEsYh7m5tOEKvMjtHa+IWdgGhZzMqs6jCEgeay4UUoBtbiutWGTjFh0BNLsauKRKspo6k+/mCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:00:47.159348Z","bundle_sha256":"689da96c2bb6dafaa510184b151a014f8ac12617e8ba97617de885c3022c0eed"}}