{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:X5IFX6W6RVKNICZU7R77MQ474P","short_pith_number":"pith:X5IFX6W6","schema_version":"1.0","canonical_sha256":"bf505bfade8d54d40b34fc7ff6439fe3dd7fa36bfa13c91f9e3a4e508da3ba08","source":{"kind":"arxiv","id":"1408.6968","version":2},"attestation_state":"computed","paper":{"title":"Sato-Tate groups of genus 2 curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Kiran S. Kedlaya","submitted_at":"2014-08-29T09:54:09Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.6968","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-29T09:54:09Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"817c6979c3933c0b6a7b9977676f65c87a16d5cc3ee85d874756e0cd0cbee7f2","abstract_canon_sha256":"8414bef3d6267c5bd87361e080cae7362f9921dde9d021779f92b205d21601cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:35.698901Z","signature_b64":"3wRh+Utcb4vq5yBtmp1Wpk9ctn6nPwuZbbvfZeDVuRy7rxWY7H+RwM0OHxpBKlIbQSVGiH4CSfKFvzP0teApDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf505bfade8d54d40b34fc7ff6439fe3dd7fa36bfa13c91f9e3a4e508da3ba08","last_reissued_at":"2026-05-18T02:31:35.698443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:35.698443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sato-Tate groups of genus 2 curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Kiran S. Kedlaya","submitted_at":"2014-08-29T09:54:09Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6968","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.6968","created_at":"2026-05-18T02:31:35.698513+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.6968v2","created_at":"2026-05-18T02:31:35.698513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6968","created_at":"2026-05-18T02:31:35.698513+00:00"},{"alias_kind":"pith_short_12","alias_value":"X5IFX6W6RVKN","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"X5IFX6W6RVKNICZU","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"X5IFX6W6","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P","json":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P.json","graph_json":"https://pith.science/api/pith-number/X5IFX6W6RVKNICZU7R77MQ474P/graph.json","events_json":"https://pith.science/api/pith-number/X5IFX6W6RVKNICZU7R77MQ474P/events.json","paper":"https://pith.science/paper/X5IFX6W6"},"agent_actions":{"view_html":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P","download_json":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P.json","view_paper":"https://pith.science/paper/X5IFX6W6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.6968&json=true","fetch_graph":"https://pith.science/api/pith-number/X5IFX6W6RVKNICZU7R77MQ474P/graph.json","fetch_events":"https://pith.science/api/pith-number/X5IFX6W6RVKNICZU7R77MQ474P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P/action/storage_attestation","attest_author":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P/action/author_attestation","sign_citation":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P/action/citation_signature","submit_replication":"https://pith.science/pith/X5IFX6W6RVKNICZU7R77MQ474P/action/replication_record"}},"created_at":"2026-05-18T02:31:35.698513+00:00","updated_at":"2026-05-18T02:31:35.698513+00:00"}