{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2JPSSCCW3XGHZ2SGFE6NZQRGCD","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":"dad948d64cc8f1e75483c077a57d2eb5ff4918eb37f9cc107fbcc2e9800540b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T17:48:32Z","title_canon_sha256":"8ce44058b0e46965fd72988509a2527ff47185163bb8692e8070ee6d05f5a24a"},"schema_version":"1.0","source":{"id":"1504.00902","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00902","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00902v4","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00902","created_at":"2026-05-18T01:16:33Z"},{"alias_kind":"pith_short_12","alias_value":"2JPSSCCW3XGH","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2JPSSCCW3XGHZ2SG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2JPSSCCW","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:fa7bd7079e5a81c4755bbc846e70ecbe41c1f1639051257cae0d8534d2cf7ebe","target":"graph","created_at":"2026-05-18T01:16:33Z","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":"Let $A$ be an abelian variety over $\\mathbb{Q}$ of dimension $g$ such that the image of its associated absolute Galois representation $\\rho_A$ is open in $\\operatorname{GSp}_{2g}(\\hat{\\mathbb{Z}})$. We investigate the arithmetic of the traces $a_{1, p}$ of the Frobenius at $p$ in $\\operatorname{Gal}(\\overline{\\mathbb{Q}}/\\mathbb{Q})$ under $\\rho_A$, modulo varying primes $p$. In particular, we obtain upper bounds for the counting function $\\#\\{p \\leq x: a_{1, p} = t\\}$ and we prove an Erd\\\"os-Kac type theorem for the number of prime factors of $a_{1, p}$. We also formulate a conjecture about t","authors_text":"Alice Silverberg, Alina Carmen Cojocaru, Katherine E. Stange, Rachel Davis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T17:48:32Z","title":"Arithmetic properties of the Frobenius traces defined by a rational abelian variety (with two appendices by J-P. Serre)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00902","kind":"arxiv","version":4},"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":"sha256:3ff66fd2d0fc1fb26cd70c80e857a44f9cc933b5a419f7d581b867fd1d26eccb","target":"record","created_at":"2026-05-18T01:16:33Z","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":"dad948d64cc8f1e75483c077a57d2eb5ff4918eb37f9cc107fbcc2e9800540b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-03T17:48:32Z","title_canon_sha256":"8ce44058b0e46965fd72988509a2527ff47185163bb8692e8070ee6d05f5a24a"},"schema_version":"1.0","source":{"id":"1504.00902","kind":"arxiv","version":4}},"canonical_sha256":"d25f290856ddcc7cea46293cdcc22610ff343384259eff4a5626e0ff5b212575","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d25f290856ddcc7cea46293cdcc22610ff343384259eff4a5626e0ff5b212575","first_computed_at":"2026-05-18T01:16:33.429500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:33.429500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dsq2fpsFfz9hqahXI3xQaAEn4USt2i0vgqn/ETEgAcBq+aVLkk+CLZFiab0S4udQMAxI86jESz2fZvwUP5TsDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:33.430150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00902","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ff66fd2d0fc1fb26cd70c80e857a44f9cc933b5a419f7d581b867fd1d26eccb","sha256:fa7bd7079e5a81c4755bbc846e70ecbe41c1f1639051257cae0d8534d2cf7ebe"],"state_sha256":"b9417ddcd0f6f8b2cfb1debd6b08b49b9ec08e1a2f4c21ac95da72bcf2fc3f03"}