{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:3QL4IMYLU2BBZR4BBOK6XCPSSV","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":"ad444560265d6696eac77b03a029960c4915a2212a38fb8f49ec3cf376d91300","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2002-11-20T11:23:51Z","title_canon_sha256":"dff2e3c0c506140b671aac756624eb9b5042cf366cc06ac3d199a75146465be9"},"schema_version":"1.0","source":{"id":"math/0211315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0211315","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0211315v1","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0211315","created_at":"2026-05-18T01:38:29Z"},{"alias_kind":"pith_short_12","alias_value":"3QL4IMYLU2BB","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"3QL4IMYLU2BBZR4B","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"3QL4IMYL","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:f07a6d58f546f3b1905002b4b34df1c53cf0ccdc505e4bd240ab157dde06b71f","target":"graph","created_at":"2026-05-18T01:38:29Z","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 $C$ be a smooth projective curve over $\\mathbb{F}_q$ with function field $K$, $E/K$ a nonconstant elliptic curve and $\\phi:\\mathcal{E}\\to C$ its minimal regular model. For each $P\\in C$ such that $E$ has good reduction at $P$, i.e., the fiber $\\mathcal{E}_P=\\phi^{-1}(P)$ is smooth, the eigenvalues of the zeta-function of $\\mathcal{E}_P$ over the residue field $\\kappa_P$ of $P$ are of the form $q_P^{1/2}e^{i\\theta_P},q_{P}e^{-i\\theta_P}$, where $q_P=q^{\\deg(P)}$ and $0\\le\\theta_P\\le\\pi$. The goal of this note is to determine given an integer $B\\ge 1$, $\\alpha,\\beta\\in[0,\\pi]$ the number of ","authors_text":"Amilcar Pacheco","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2002-11-20T11:23:51Z","title":"On the distribution of the of Frobenius elements on elliptic curves over function fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0211315","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:e62343ae7c5b05de51a07967d117695ade11428d6c9d9c9aff5158cff3e1fdc3","target":"record","created_at":"2026-05-18T01:38:29Z","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":"ad444560265d6696eac77b03a029960c4915a2212a38fb8f49ec3cf376d91300","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2002-11-20T11:23:51Z","title_canon_sha256":"dff2e3c0c506140b671aac756624eb9b5042cf366cc06ac3d199a75146465be9"},"schema_version":"1.0","source":{"id":"math/0211315","kind":"arxiv","version":1}},"canonical_sha256":"dc17c4330ba6821cc7810b95eb89f2957a71057e060d6817c07c21183274ff27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc17c4330ba6821cc7810b95eb89f2957a71057e060d6817c07c21183274ff27","first_computed_at":"2026-05-18T01:38:29.325238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:29.325238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IN7dv6RUR3jdxTXAaz/tjrguj+iGrvyB+VOm/ZVMHIt7Tqt/L/bPoCfSGQsz/TcA1JptOXxU+FmThxq/huS+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:29.325861Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0211315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e62343ae7c5b05de51a07967d117695ade11428d6c9d9c9aff5158cff3e1fdc3","sha256:f07a6d58f546f3b1905002b4b34df1c53cf0ccdc505e4bd240ab157dde06b71f"],"state_sha256":"5a7a28b0bfc795108b3153e847d376043d098877a24a2b44b0d888e347a3104c"}