{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LZW72IDPAPG2YR4Q53CAN2NFJ7","short_pith_number":"pith:LZW72IDP","canonical_record":{"source":{"id":"1410.7036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T14:47:32Z","cross_cats_sorted":[],"title_canon_sha256":"934fae3129dd32187558353f2f603e13220ad5aba3a1f247c222d62582a95305","abstract_canon_sha256":"203d907111205e0edbccb31860b746be0bf333a6b452a4420d619bffecf009ec"},"schema_version":"1.0"},"canonical_sha256":"5e6dfd206f03cdac4790eec406e9a54fc7741039a3ddf507c7b6b4257e42662d","source":{"kind":"arxiv","id":"1410.7036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7036","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7036v1","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7036","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"LZW72IDPAPG2","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"pith_short_16","alias_value":"LZW72IDPAPG2YR4Q","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"pith_short_8","alias_value":"LZW72IDP","created_at":"2026-07-05T03:25:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LZW72IDPAPG2YR4Q53CAN2NFJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T14:47:32Z","cross_cats_sorted":[],"title_canon_sha256":"934fae3129dd32187558353f2f603e13220ad5aba3a1f247c222d62582a95305","abstract_canon_sha256":"203d907111205e0edbccb31860b746be0bf333a6b452a4420d619bffecf009ec"},"schema_version":"1.0"},"canonical_sha256":"5e6dfd206f03cdac4790eec406e9a54fc7741039a3ddf507c7b6b4257e42662d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:25:08.225358Z","signature_b64":"POBIPnbKp+TMg/q/9OsjtEVyGYYIqE/fCL18uo0t/Tp4FtqwqQrvElOHaMJGpmNHR5ew+Irbo0jSW2s5Ffg5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e6dfd206f03cdac4790eec406e9a54fc7741039a3ddf507c7b6b4257e42662d","last_reissued_at":"2026-07-05T03:25:08.224981Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:25:08.224981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7036","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":"2026-07-05T03:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RVuCQPVZhln4W1VwlOha2Ic/9qq2U4JjZ6HTpAHkWr6CLkz6PiCBB43unIMHaNYZnySvERJmBuPzYRxQvwwrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:54:35.517811Z"},"content_sha256":"ac4894126f5c3ad0ee56360fc806cfdaa5e2b70e4ddda339fde8fbbd45fdc16e","schema_version":"1.0","event_id":"sha256:ac4894126f5c3ad0ee56360fc806cfdaa5e2b70e4ddda339fde8fbbd45fdc16e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LZW72IDPAPG2YR4Q53CAN2NFJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Yet another representation for the sum of reciprocals of the nontrivial zeros of the Riemann zeta-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yuri Matiyasevich","submitted_at":"2014-10-26T14:47:32Z","abstract_excerpt":"The positivity of the sum from the title is the first condition in the well-known criterium for the validity of the Riemann Hypothesis suggested by X.-J. Li. In the paper this value is represented as an infinite sum with positive summands."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7036","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1410.7036/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:25:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkOw/sODQyC143i68eeL1Z1C/pUpZrL/v9+cghrqluO0sOo4zIpK0OoWRIhcePQnt3iFY3Dd1g6VRPcWOodlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:54:35.518422Z"},"content_sha256":"d1dd4581bad2bf45bf260da06afc33b483d0204e31f17786ddc5903f9e4113dc","schema_version":"1.0","event_id":"sha256:d1dd4581bad2bf45bf260da06afc33b483d0204e31f17786ddc5903f9e4113dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZW72IDPAPG2YR4Q53CAN2NFJ7/bundle.json","state_url":"https://pith.science/pith/LZW72IDPAPG2YR4Q53CAN2NFJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZW72IDPAPG2YR4Q53CAN2NFJ7/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":"2026-07-09T05:54:35Z","links":{"resolver":"https://pith.science/pith/LZW72IDPAPG2YR4Q53CAN2NFJ7","bundle":"https://pith.science/pith/LZW72IDPAPG2YR4Q53CAN2NFJ7/bundle.json","state":"https://pith.science/pith/LZW72IDPAPG2YR4Q53CAN2NFJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZW72IDPAPG2YR4Q53CAN2NFJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LZW72IDPAPG2YR4Q53CAN2NFJ7","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":"203d907111205e0edbccb31860b746be0bf333a6b452a4420d619bffecf009ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T14:47:32Z","title_canon_sha256":"934fae3129dd32187558353f2f603e13220ad5aba3a1f247c222d62582a95305"},"schema_version":"1.0","source":{"id":"1410.7036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7036","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7036v1","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7036","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"pith_short_12","alias_value":"LZW72IDPAPG2","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"pith_short_16","alias_value":"LZW72IDPAPG2YR4Q","created_at":"2026-07-05T03:25:08Z"},{"alias_kind":"pith_short_8","alias_value":"LZW72IDP","created_at":"2026-07-05T03:25:08Z"}],"graph_snapshots":[{"event_id":"sha256:d1dd4581bad2bf45bf260da06afc33b483d0204e31f17786ddc5903f9e4113dc","target":"graph","created_at":"2026-07-05T03:25:08Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1410.7036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The positivity of the sum from the title is the first condition in the well-known criterium for the validity of the Riemann Hypothesis suggested by X.-J. Li. In the paper this value is represented as an infinite sum with positive summands.","authors_text":"Yuri Matiyasevich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T14:47:32Z","title":"Yet another representation for the sum of reciprocals of the nontrivial zeros of the Riemann zeta-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7036","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:ac4894126f5c3ad0ee56360fc806cfdaa5e2b70e4ddda339fde8fbbd45fdc16e","target":"record","created_at":"2026-07-05T03:25:08Z","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":"203d907111205e0edbccb31860b746be0bf333a6b452a4420d619bffecf009ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-26T14:47:32Z","title_canon_sha256":"934fae3129dd32187558353f2f603e13220ad5aba3a1f247c222d62582a95305"},"schema_version":"1.0","source":{"id":"1410.7036","kind":"arxiv","version":1}},"canonical_sha256":"5e6dfd206f03cdac4790eec406e9a54fc7741039a3ddf507c7b6b4257e42662d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e6dfd206f03cdac4790eec406e9a54fc7741039a3ddf507c7b6b4257e42662d","first_computed_at":"2026-07-05T03:25:08.224981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:25:08.224981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"POBIPnbKp+TMg/q/9OsjtEVyGYYIqE/fCL18uo0t/Tp4FtqwqQrvElOHaMJGpmNHR5ew+Irbo0jSW2s5Ffg5Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:25:08.225358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac4894126f5c3ad0ee56360fc806cfdaa5e2b70e4ddda339fde8fbbd45fdc16e","sha256:d1dd4581bad2bf45bf260da06afc33b483d0204e31f17786ddc5903f9e4113dc"],"state_sha256":"f4387588427f7c03f7ca0310bedf0483ed4931cebc30da3fc61cc5731a482278"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"23w4ef1fTm8QYVIDZsSNk/IL1CDdq9Ke1mI6H61pmqjjTdsD6xGjx2GQLBJdzOBspDHCySMSvsn8+xH0ygLNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T05:54:35.522221Z","bundle_sha256":"396a578b0ed1878c05887ffa8e348a8b6c9286eb85c3a7fbac6d1156690e3bff"}}