{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:7YMPI63FLLBK5I6IEHMT6R4HPY","short_pith_number":"pith:7YMPI63F","schema_version":"1.0","canonical_sha256":"fe18f47b655ac2aea3c821d93f47877e2bdaf714eba596a73b6760137cd3e2f1","source":{"kind":"arxiv","id":"1607.08816","version":1},"attestation_state":"computed","paper":{"title":"Arithmetic invariant theory and 2-descent for plane quartic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack A. Thorne","submitted_at":"2016-07-29T14:04:45Z","abstract_excerpt":"Given a smooth plane quartic curve C over a field k of characteristic 0, with Jacobian variety J, and a marked rational point P of C(k), we construct a reductive group G and a G-variety X, together with an injection J(k)/2J(k) -> G(k)\\X(k). We do this using the Mumford theta group of J, and a construction of Lurie which passes from Heisenberg groups to Lie algebras."},"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":"1607.08816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-07-29T14:04:45Z","cross_cats_sorted":[],"title_canon_sha256":"cb270c3a3f15f02251929a19583529a3c4e64884c59a3c7cb5a832201dae079d","abstract_canon_sha256":"fb3006cc90e2327cfcd277eb69d1de1e645732951c2f3b5b5395f5d6bc0eafd4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:15.838524Z","signature_b64":"NB13Wapf6wGnWunt1kaw+mus8L079+6PMcxCIPTAlm9gR9tuEOTQYH260e9IAFfnFvvmLD7fo63aZXiaqZClCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe18f47b655ac2aea3c821d93f47877e2bdaf714eba596a73b6760137cd3e2f1","last_reissued_at":"2026-05-18T01:10:15.838061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:15.838061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arithmetic invariant theory and 2-descent for plane quartic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack A. Thorne","submitted_at":"2016-07-29T14:04:45Z","abstract_excerpt":"Given a smooth plane quartic curve C over a field k of characteristic 0, with Jacobian variety J, and a marked rational point P of C(k), we construct a reductive group G and a G-variety X, together with an injection J(k)/2J(k) -> G(k)\\X(k). We do this using the Mumford theta group of J, and a construction of Lurie which passes from Heisenberg groups to Lie algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08816","kind":"arxiv","version":1},"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":"1607.08816","created_at":"2026-05-18T01:10:15.838123+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.08816v1","created_at":"2026-05-18T01:10:15.838123+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08816","created_at":"2026-05-18T01:10:15.838123+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YMPI63FLLBK","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YMPI63FLLBK5I6I","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YMPI63F","created_at":"2026-05-18T12:30:04.600751+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/7YMPI63FLLBK5I6IEHMT6R4HPY","json":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY.json","graph_json":"https://pith.science/api/pith-number/7YMPI63FLLBK5I6IEHMT6R4HPY/graph.json","events_json":"https://pith.science/api/pith-number/7YMPI63FLLBK5I6IEHMT6R4HPY/events.json","paper":"https://pith.science/paper/7YMPI63F"},"agent_actions":{"view_html":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY","download_json":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY.json","view_paper":"https://pith.science/paper/7YMPI63F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.08816&json=true","fetch_graph":"https://pith.science/api/pith-number/7YMPI63FLLBK5I6IEHMT6R4HPY/graph.json","fetch_events":"https://pith.science/api/pith-number/7YMPI63FLLBK5I6IEHMT6R4HPY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY/action/storage_attestation","attest_author":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY/action/author_attestation","sign_citation":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY/action/citation_signature","submit_replication":"https://pith.science/pith/7YMPI63FLLBK5I6IEHMT6R4HPY/action/replication_record"}},"created_at":"2026-05-18T01:10:15.838123+00:00","updated_at":"2026-05-18T01:10:15.838123+00:00"}