{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S7SY4XFUGRWXDHN5VJITO7XWUM","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":"60f9d2ed45df10e7ac44ad3a5247dc1759089da42cf2001ba5607dc331b2dd5a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-26T20:02:00Z","title_canon_sha256":"17f949dd53c566fef9791f08dfb074a43d9605d7b83ddb3526761beaa004ac39"},"schema_version":"1.0","source":{"id":"1709.09243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09243","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09243v2","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09243","created_at":"2026-05-17T23:52:09Z"},{"alias_kind":"pith_short_12","alias_value":"S7SY4XFUGRWX","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S7SY4XFUGRWXDHN5","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S7SY4XFU","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:d65f8d1a5f5fa61413402ea1ac089e5ed7cb17c6af2d4a86918380f5e28c3ebe","target":"graph","created_at":"2026-05-17T23:52:09Z","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":"The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms. Let $X$ be a curve over $\\mathbb{F}_q$, $F$ its function field and $\\mathbb{A}$ the adele ring of $F$. In this paper we will exhibit the first properties for the graph of Hecke operators for $\\mathrm{GL}_n(\\mathbb{A}),$ for every $n \\geq 1.$ This includes a description of the graph in terms of coherent sheaves on $X.$ We provide a numerical condition for two vertices to be connected by an edge. Moreover, we describe how to calculate these graphs in the case of the projective line $X = ","authors_text":"Roberto Alvarenga","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-26T20:02:00Z","title":"On graphs of Hecke operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09243","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":"sha256:6db3c62582e75862fafb48c5440562d43ddc9b37786dc32d91b91397e6c4903c","target":"record","created_at":"2026-05-17T23:52:09Z","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":"60f9d2ed45df10e7ac44ad3a5247dc1759089da42cf2001ba5607dc331b2dd5a","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-26T20:02:00Z","title_canon_sha256":"17f949dd53c566fef9791f08dfb074a43d9605d7b83ddb3526761beaa004ac39"},"schema_version":"1.0","source":{"id":"1709.09243","kind":"arxiv","version":2}},"canonical_sha256":"97e58e5cb4346d719dbdaa51377ef6a32b4b0265cfd9c0d7af85a33462629b26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97e58e5cb4346d719dbdaa51377ef6a32b4b0265cfd9c0d7af85a33462629b26","first_computed_at":"2026-05-17T23:52:09.558532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:09.558532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SVDJGZohSKGm3OFNDXGd3nmgM7qLjCH4WgoqkOhQgyuMqbmYpuwUXzyed2hIiPcnuMh+oCkng1VPkt9D5XX9DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:09.558988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6db3c62582e75862fafb48c5440562d43ddc9b37786dc32d91b91397e6c4903c","sha256:d65f8d1a5f5fa61413402ea1ac089e5ed7cb17c6af2d4a86918380f5e28c3ebe"],"state_sha256":"faf5407b4473ba0572563f564eb2f481733289c4f4203fb6bb6fa430251befe9"}