{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X5IFX6W6RVKNICZU7R77MQ474P","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":"8414bef3d6267c5bd87361e080cae7362f9921dde9d021779f92b205d21601cb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-29T09:54:09Z","title_canon_sha256":"817c6979c3933c0b6a7b9977676f65c87a16d5cc3ee85d874756e0cd0cbee7f2"},"schema_version":"1.0","source":{"id":"1408.6968","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6968","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6968v2","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6968","created_at":"2026-05-18T02:31:35Z"},{"alias_kind":"pith_short_12","alias_value":"X5IFX6W6RVKN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X5IFX6W6RVKNICZU","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X5IFX6W6","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:623a9547e653a0dd969b7c330a86bf2c991d08cae12dc6d97c98d8058fd5b036","target":"graph","created_at":"2026-05-18T02:31:35Z","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":"We describe the analogue of the Sato-Tate conjecture for an abelian variety over a number field; this predicts that the zeta functions of the reductions over various finite fields, when properly normalized, have a limiting distribution predicted by a certain group-theoretic construction related to Hodge theory, Galois images, and endomorphisms. After making precise the definition of the \"Sato-Tate group\" appearing in this conjecture, we describe the classification of Sato-Tate groups of abelian surfaces due to Fite-Kedlaya-Rotger-Sutherland. (These are notes from a three-lecture series present","authors_text":"Kiran S. Kedlaya","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-29T09:54:09Z","title":"Sato-Tate groups of genus 2 curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6968","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:d0c531dcb5508898f8fa99d2c083678a55cfeed11e5eef1419460eea689a48f5","target":"record","created_at":"2026-05-18T02:31:35Z","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":"8414bef3d6267c5bd87361e080cae7362f9921dde9d021779f92b205d21601cb","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-29T09:54:09Z","title_canon_sha256":"817c6979c3933c0b6a7b9977676f65c87a16d5cc3ee85d874756e0cd0cbee7f2"},"schema_version":"1.0","source":{"id":"1408.6968","kind":"arxiv","version":2}},"canonical_sha256":"bf505bfade8d54d40b34fc7ff6439fe3dd7fa36bfa13c91f9e3a4e508da3ba08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf505bfade8d54d40b34fc7ff6439fe3dd7fa36bfa13c91f9e3a4e508da3ba08","first_computed_at":"2026-05-18T02:31:35.698443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:35.698443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3wRh+Utcb4vq5yBtmp1Wpk9ctn6nPwuZbbvfZeDVuRy7rxWY7H+RwM0OHxpBKlIbQSVGiH4CSfKFvzP0teApDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:35.698901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6968","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0c531dcb5508898f8fa99d2c083678a55cfeed11e5eef1419460eea689a48f5","sha256:623a9547e653a0dd969b7c330a86bf2c991d08cae12dc6d97c98d8058fd5b036"],"state_sha256":"47d7b3131845fc5e1bdeaa227dd700bf489b1f72e12fe90a0d96101f76d8a0d3"}