{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K4XX7KG3CU6B6AZYVDE3AUDFMT","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":"71cc4a47c7b6b7dd4d505819eb7eeebebf89b677862c40aced665ac851ce08dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-17T22:06:39Z","title_canon_sha256":"471b4e7b5b2855f72238197f923136bfef42d755d525362fba9eb296df35eb5f"},"schema_version":"1.0","source":{"id":"2605.17674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17674","created_at":"2026-05-20T00:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17674v1","created_at":"2026-05-20T00:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17674","created_at":"2026-05-20T00:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"K4XX7KG3CU6B","created_at":"2026-05-20T00:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"K4XX7KG3CU6B6AZY","created_at":"2026-05-20T00:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"K4XX7KG3","created_at":"2026-05-20T00:04:52Z"}],"graph_snapshots":[{"event_id":"sha256:54c78a185de85bebd051d4c10841cf99dfdb8171d9ab87a1d1a593ea83e67a96","target":"graph","created_at":"2026-05-20T00:04:52Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The finite transcendence of Frobenius traces for elliptic curves over Q without the assumption of complex multiplication."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the method developed by Luca and Zudilin for the CM case extends directly to the non-CM setting and to higher-dimensional abelian varieties."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Establishes finite transcendence of Frobenius traces for non-CM elliptic curves over Q and extends the result to some abelian varieties over Q."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Frobenius traces for elliptic curves over the rationals remain finitely transcendental even without complex multiplication."}],"snapshot_sha256":"8fe09ce437c48a2288a802370c687b93be02e55d7f4220d59a60a0aeb3d4036e"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"35e994108f409f340c0c46c03a5c63221652da8a2b05241a6b90bf0e182d1d0f"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.457853Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:20:57.451806Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T21:51:59.386170Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T21:49:44.261020Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.532421Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:21:57.446472Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.17674/integrity.json","findings":[],"snapshot_sha256":"d282c101dcab8fffe5f29d7c76da16fc5a64d59efbd3ae587092f70185c99210","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The first purpose of this paper is to give the fnite transcendence of Frobenius traces for elliptic curves over $\\mathbb{Q}$ without the assumption of complex multiplication (CM). This result generalizes the previous work by Luca and Zudilin, who obtained similar transcendence results specifically for the CM case. The second purpose is to give the finite transcendence of Frobenius traces for several principally polarized abelian varieties over $\\mathbb{Q}$, by using Luca--Zudilin's method.","authors_text":"Yuto Tsuruta","cross_cats":[],"headline":"Frobenius traces for elliptic curves over the rationals remain finitely transcendental even without complex multiplication.","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-17T22:06:39Z","title":"On the finite transcendence of Frobenius traces for abelian varieties over $\\mathbb{Q}$"},"references":{"count":14,"internal_anchors":2,"resolved_work":14,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"A. Aizenbud, and N. Avni,Counting points of schemes over finite rings and counting represen- tations of arithmetic lattices, Duke Math. J.,167(2018), no. 14, 2721–2743","work_id":"fe209d8b-30b3-4785-a83a-c5d8494ce601","year":2018},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"T. Anzawa, and H. Funakura,Congruences of the𝑞-Fibonacci sequence related with its tran- scendence, Ramanujan J.,63, No.4 (2024) 1057–1072","work_id":"ac501655-1aa4-4fa9-a558-22d114205952","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"T. Barnet-Lamb, D. Geraghty, M. Harris, and R. Taylor,A family of Calabi-Yau varieties and potential automorphy II., Publ. Res. Inst. Math. Sci.,47(2011) no. 1, 29–98","work_id":"682283de-1bb4-431a-a5c4-7b3458cbf9ff","year":2011},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Deligne,La conjecture de Weil.I., Inst","work_id":"30d35ddc-c21e-41d0-a0fc-c16754fe2cb3","year":1974},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"F. Luca, and W. Zudilin,Irrationality and transcendence questions in the ‘poor man’s adèle ring’, Ramanujan J.,67, No.88 (2025)","work_id":"127670cc-1f4e-4dc3-9055-0bae66ca5949","year":2025}],"snapshot_sha256":"39982e00d001c3dc5eabc4919727b3dbe6a6a3253119e19f60f99737e3a5e9fe"},"source":{"id":"2605.17674","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:15:52.190788Z","id":"509a2ef5-91e4-42e0-9f25-fdf7195740fc","model_set":{"reader":"grok-4.3"},"one_line_summary":"Establishes finite transcendence of Frobenius traces for non-CM elliptic curves over Q and extends the result to some abelian varieties over Q.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Frobenius traces for elliptic curves over the rationals remain finitely transcendental even without complex multiplication.","strongest_claim":"The finite transcendence of Frobenius traces for elliptic curves over Q without the assumption of complex multiplication.","weakest_assumption":"That the method developed by Luca and Zudilin for the CM case extends directly to the non-CM setting and to higher-dimensional abelian varieties."}},"verdict_id":"509a2ef5-91e4-42e0-9f25-fdf7195740fc"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6cba32894d5bfb9930979670ece9da1758c684b5531d0d12a49a67c269e0408a","target":"record","created_at":"2026-05-20T00:04:52Z","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":"71cc4a47c7b6b7dd4d505819eb7eeebebf89b677862c40aced665ac851ce08dd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-17T22:06:39Z","title_canon_sha256":"471b4e7b5b2855f72238197f923136bfef42d755d525362fba9eb296df35eb5f"},"schema_version":"1.0","source":{"id":"2605.17674","kind":"arxiv","version":1}},"canonical_sha256":"572f7fa8db153c1f0338a8c9b0506564c9132509a5e651cc4be8a72da1f9a02f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"572f7fa8db153c1f0338a8c9b0506564c9132509a5e651cc4be8a72da1f9a02f","first_computed_at":"2026-05-20T00:04:52.079234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:52.079234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ikWSM8XRCoUfa/Z1J6mfE3Of9ws+SpNjBj6HOhiiRjyW5M5c4Ptxkko1CnbTwkrvlYgEFjBvVUBiQA9Q4ZRBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:52.080169Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cba32894d5bfb9930979670ece9da1758c684b5531d0d12a49a67c269e0408a","sha256:54c78a185de85bebd051d4c10841cf99dfdb8171d9ab87a1d1a593ea83e67a96"],"state_sha256":"1b8c64e0c2591c14e9468cf65c94c354ca625ff1bd83d6e311b21c44cc9567d7"}