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This approach is inspired by the Birch and Swinnerton-Dyer conjecture.\n  Our observations reveal an oscillatory behavior in the sums, closely associated with the recently discovered phenomena of murmurations of elliptic curv"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2403.17626","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-03-26T12:03:50Z","cross_cats_sorted":[],"title_canon_sha256":"de869550df9a43900583dc0c9e8c0c9be78e43383a2acc9b77d37d6617f1e470","abstract_canon_sha256":"dd329338738e093cdaa3611fb22463107626f21ee7e29b5311b96e3f61a33af4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:53.600710Z","signature_b64":"x0vzerVyjf6u4ITpneYePVb4GSr2bdLV5qk6Z0EOz9gvelErTchjXK2TcG1DJWAAMnVKhPW+FWixaE7M5xhMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dcef114d0c5936b13ae393b152ad10e329703ce4179c63202dc10652b164943","last_reissued_at":"2026-07-05T08:00:53.600142Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:53.600142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Murmurations of Mestre-Nagao sums","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lukas Novak, Matija Kazalicki, Zvonimir Bujanovi\\'c","submitted_at":"2024-03-26T12:03:50Z","abstract_excerpt":"This paper investigates the detection of the rank of elliptic curves with ranks 0 and 1, employing a heuristic known as the Mestre-Nagao sum\n  \\[ S(B) = \\frac{1}{\\log{B}} \\sum_{\\substack{p<B \\\\ \\textrm{good reduction}}} \\frac{a_p(E)\\log{p}}{p}, \\]\nwhere $a_p(E)$ is defined as $p + 1 - \\#E(\\mathbb{F}_p)$ for an elliptic curve $E/\\mathbb{Q}$ with good reduction at prime $p$. This approach is inspired by the Birch and Swinnerton-Dyer conjecture.\n  Our observations reveal an oscillatory behavior in the sums, closely associated with the recently discovered phenomena of murmurations of elliptic curv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.17626","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/2403.17626/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2403.17626","created_at":"2026-07-05T08:00:53.600197+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.17626v1","created_at":"2026-07-05T08:00:53.600197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.17626","created_at":"2026-07-05T08:00:53.600197+00:00"},{"alias_kind":"pith_short_12","alias_value":"FXHPCFGQYWJW","created_at":"2026-07-05T08:00:53.600197+00:00"},{"alias_kind":"pith_short_16","alias_value":"FXHPCFGQYWJWWE5O","created_at":"2026-07-05T08:00:53.600197+00:00"},{"alias_kind":"pith_short_8","alias_value":"FXHPCFGQ","created_at":"2026-07-05T08:00:53.600197+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.14288","citing_title":"How Twist Class Redundancy Drives the Prediction of Traces of Frobenius of Elliptic Curves","ref_index":9,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY","json":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY.json","graph_json":"https://pith.science/api/pith-number/FXHPCFGQYWJWWE5OHE5RKKWRBY/graph.json","events_json":"https://pith.science/api/pith-number/FXHPCFGQYWJWWE5OHE5RKKWRBY/events.json","paper":"https://pith.science/paper/FXHPCFGQ"},"agent_actions":{"view_html":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY","download_json":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY.json","view_paper":"https://pith.science/paper/FXHPCFGQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.17626&json=true","fetch_graph":"https://pith.science/api/pith-number/FXHPCFGQYWJWWE5OHE5RKKWRBY/graph.json","fetch_events":"https://pith.science/api/pith-number/FXHPCFGQYWJWWE5OHE5RKKWRBY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY/action/storage_attestation","attest_author":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY/action/author_attestation","sign_citation":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY/action/citation_signature","submit_replication":"https://pith.science/pith/FXHPCFGQYWJWWE5OHE5RKKWRBY/action/replication_record"}},"created_at":"2026-07-05T08:00:53.600197+00:00","updated_at":"2026-07-05T08:00:53.600197+00:00"}