{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CYZ4UJ4IIN2L2ZUQFCGBCITVIF","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":"2dfeb9244f6ba018e39eba3e9a9b0d37aee4e046db0e6494ef32ead776a182c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-11T11:26:09Z","title_canon_sha256":"f0080282830880b0b9d874324d5b12193cca08b3d7246955500359a293ff5c9d"},"schema_version":"1.0","source":{"id":"1312.3119","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3119","created_at":"2026-05-18T03:04:16Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3119v2","created_at":"2026-05-18T03:04:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3119","created_at":"2026-05-18T03:04:16Z"},{"alias_kind":"pith_short_12","alias_value":"CYZ4UJ4IIN2L","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CYZ4UJ4IIN2L2ZUQ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CYZ4UJ4I","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:d2b2e31db08b19dbd76376a4d3ad6cf3ccfcf77cec5f593c8ee436e29383e4a9","target":"graph","created_at":"2026-05-18T03:04:16Z","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":"We improve the results from [EBS10] about the Eisenstein series $E_2(z)=1-24\\sum_{n=1}^\\infty \\frac{nq^n}{1-q^n}$. In particular we show that there exists exactly one (simple) zero in each Ford circle and give an approximation to its location.","authors_text":"\\'Arp\\'ad T\\'oth, Jonas Jermann, \\\"Ozlem Imamo\\=glu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-11T11:26:09Z","title":"Estimates on the zeros of $E_2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3119","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:d3b04cb87c1d07758f967582ff72d0c0319ec8d20007f1c6df4c58c36af0e43b","target":"record","created_at":"2026-05-18T03:04:16Z","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":"2dfeb9244f6ba018e39eba3e9a9b0d37aee4e046db0e6494ef32ead776a182c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-12-11T11:26:09Z","title_canon_sha256":"f0080282830880b0b9d874324d5b12193cca08b3d7246955500359a293ff5c9d"},"schema_version":"1.0","source":{"id":"1312.3119","kind":"arxiv","version":2}},"canonical_sha256":"1633ca27884374bd6690288c112275414c9071eda6e3c538f3ca01917a2f94e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1633ca27884374bd6690288c112275414c9071eda6e3c538f3ca01917a2f94e5","first_computed_at":"2026-05-18T03:04:16.776402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:16.776402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"flSLDyg0CkumQ293DciJIqjzyGbSWOMSWfqSauWrIPbHV383mQ+ib3TvemAgcy9YRIl8SBQ6pG0Jpze/pvwyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:16.776952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3119","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3b04cb87c1d07758f967582ff72d0c0319ec8d20007f1c6df4c58c36af0e43b","sha256:d2b2e31db08b19dbd76376a4d3ad6cf3ccfcf77cec5f593c8ee436e29383e4a9"],"state_sha256":"9b95ca39e2480be682d8374db02e303536bcbf8cad8f09406d78fd11ca63f1c1"}