{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KYESBDBTFBFGMMS3U3AJ752CRY","short_pith_number":"pith:KYESBDBT","canonical_record":{"source":{"id":"1203.4142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-14T17:49:39Z","cross_cats_sorted":[],"title_canon_sha256":"1e236f7db6ac667e5a7308b6c698e8832c69ea7ad59d21058ae87826eeb52e33","abstract_canon_sha256":"765a273e882ceb01975f81444313d9a42ae805f1b79ffbe9f5ce3009b6ae2cbf"},"schema_version":"1.0"},"canonical_sha256":"5609208c33284a66325ba6c09ff7428e08b94825f284a29352a9fc54e9ac84f0","source":{"kind":"arxiv","id":"1203.4142","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4142","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4142v1","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4142","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"KYESBDBTFBFG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KYESBDBTFBFGMMS3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KYESBDBT","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KYESBDBTFBFGMMS3U3AJ752CRY","target":"record","payload":{"canonical_record":{"source":{"id":"1203.4142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-14T17:49:39Z","cross_cats_sorted":[],"title_canon_sha256":"1e236f7db6ac667e5a7308b6c698e8832c69ea7ad59d21058ae87826eeb52e33","abstract_canon_sha256":"765a273e882ceb01975f81444313d9a42ae805f1b79ffbe9f5ce3009b6ae2cbf"},"schema_version":"1.0"},"canonical_sha256":"5609208c33284a66325ba6c09ff7428e08b94825f284a29352a9fc54e9ac84f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:48.217175Z","signature_b64":"Mj2w+gBlgWudr1EPHl8cxzvptx72Ajy8wwOpttazHdPbRAXexl8bSm5p9QAvmoZV3HFXSkpeThYPEB0Sf7hCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5609208c33284a66325ba6c09ff7428e08b94825f284a29352a9fc54e9ac84f0","last_reissued_at":"2026-05-18T03:59:48.216691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:48.216691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.4142","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":"2026-05-18T03:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9+v41qxFrRwpyyOYFgjYFovgkGuZZwslomDGvV756V69NfmB+JL6mwRA/EWIBphgiCPMeUVzXzhD3Q+qCrTgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:37:20.078734Z"},"content_sha256":"a7b565cd2992204f0aaa861540bce38bd29a39b44e32ddc2d6612de43eb0c73e","schema_version":"1.0","event_id":"sha256:a7b565cd2992204f0aaa861540bce38bd29a39b44e32ddc2d6612de43eb0c73e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KYESBDBTFBFGMMS3U3AJ752CRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Yaroslav D. Sergeyev","submitted_at":"2012-03-14T17:49:39Z","abstract_excerpt":"The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number of items, in this paper, we look at the Riemann Hypothesis using a new applied approach to infinity allowing one to easily execute numerical computations with various infinite and infinitesimal numbers in accordance with the principle `The part is less than the whole' observed in the physical world around us. The new approach allows one to work with functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4142","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":"2026-05-18T03:59:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RinDJdndCVudG9JyijByL+5pk2/N0ykeQVd1ln2nOQANonbb1eoOlZ3dcS/dgH5/sdZCkLD7h08NHmAWZULrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:37:20.079452Z"},"content_sha256":"6880f6ba5314b0f21e81eb9b506afb53113d1f6542fb922c2ce34efdaa0896d4","schema_version":"1.0","event_id":"sha256:6880f6ba5314b0f21e81eb9b506afb53113d1f6542fb922c2ce34efdaa0896d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KYESBDBTFBFGMMS3U3AJ752CRY/bundle.json","state_url":"https://pith.science/pith/KYESBDBTFBFGMMS3U3AJ752CRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KYESBDBTFBFGMMS3U3AJ752CRY/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":"2026-05-27T08:37:20Z","links":{"resolver":"https://pith.science/pith/KYESBDBTFBFGMMS3U3AJ752CRY","bundle":"https://pith.science/pith/KYESBDBTFBFGMMS3U3AJ752CRY/bundle.json","state":"https://pith.science/pith/KYESBDBTFBFGMMS3U3AJ752CRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KYESBDBTFBFGMMS3U3AJ752CRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KYESBDBTFBFGMMS3U3AJ752CRY","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":"765a273e882ceb01975f81444313d9a42ae805f1b79ffbe9f5ce3009b6ae2cbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-14T17:49:39Z","title_canon_sha256":"1e236f7db6ac667e5a7308b6c698e8832c69ea7ad59d21058ae87826eeb52e33"},"schema_version":"1.0","source":{"id":"1203.4142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.4142","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"arxiv_version","alias_value":"1203.4142v1","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.4142","created_at":"2026-05-18T03:59:48Z"},{"alias_kind":"pith_short_12","alias_value":"KYESBDBTFBFG","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KYESBDBTFBFGMMS3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KYESBDBT","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:6880f6ba5314b0f21e81eb9b506afb53113d1f6542fb922c2ce34efdaa0896d4","target":"graph","created_at":"2026-05-18T03:59:48Z","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":"The Riemann Hypothesis has been of central interest to mathematicians for a long time and many unsuccessful attempts have been made to either prove or disprove it. Since the Riemann zeta function is defined as a sum of the infinite number of items, in this paper, we look at the Riemann Hypothesis using a new applied approach to infinity allowing one to easily execute numerical computations with various infinite and infinitesimal numbers in accordance with the principle `The part is less than the whole' observed in the physical world around us. The new approach allows one to work with functions","authors_text":"Yaroslav D. Sergeyev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-14T17:49:39Z","title":"On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4142","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:a7b565cd2992204f0aaa861540bce38bd29a39b44e32ddc2d6612de43eb0c73e","target":"record","created_at":"2026-05-18T03:59:48Z","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":"765a273e882ceb01975f81444313d9a42ae805f1b79ffbe9f5ce3009b6ae2cbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2012-03-14T17:49:39Z","title_canon_sha256":"1e236f7db6ac667e5a7308b6c698e8832c69ea7ad59d21058ae87826eeb52e33"},"schema_version":"1.0","source":{"id":"1203.4142","kind":"arxiv","version":1}},"canonical_sha256":"5609208c33284a66325ba6c09ff7428e08b94825f284a29352a9fc54e9ac84f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5609208c33284a66325ba6c09ff7428e08b94825f284a29352a9fc54e9ac84f0","first_computed_at":"2026-05-18T03:59:48.216691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:48.216691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mj2w+gBlgWudr1EPHl8cxzvptx72Ajy8wwOpttazHdPbRAXexl8bSm5p9QAvmoZV3HFXSkpeThYPEB0Sf7hCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:48.217175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.4142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7b565cd2992204f0aaa861540bce38bd29a39b44e32ddc2d6612de43eb0c73e","sha256:6880f6ba5314b0f21e81eb9b506afb53113d1f6542fb922c2ce34efdaa0896d4"],"state_sha256":"7471583e6fe0af79b78ef1d614deed0a1e6ee8779143813189aa278b58c6928a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vmWO+cuLu6f/ibOM2TCRpGyWZZpnk3YDBKuhDqq37tdPXJdzivrWrZJeG0eV2Tbl2GnV+DfdTyn9eOIjZJ1uDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:37:20.083700Z","bundle_sha256":"a19c712804e245f079a92012f3cea288354a60e3442719cea8d4cf1ecb5f6e55"}}