{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JN6H2VHEAVX6CQGNUAR5PIQBN4","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":"f440e846a8dc7c5d26ec5fbf5ef1769eed48a58aac14ce64f226f270240d625e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-24T01:26:28Z","title_canon_sha256":"61df6125282d041ef840d4c45d19c990c5617c31405c3e7e72b7ea478d05f098"},"schema_version":"1.0","source":{"id":"1411.6321","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6321","created_at":"2026-05-18T02:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6321v1","created_at":"2026-05-18T02:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6321","created_at":"2026-05-18T02:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"JN6H2VHEAVX6","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JN6H2VHEAVX6CQGN","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JN6H2VHE","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:6863979d86310dc3a81f374ce90422dbd1ff8171742dc4e3e7415ee927d24109","target":"graph","created_at":"2026-05-18T02:33:00Z","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 obtain bounds on the number of maximal torsion cosets for algebraic subvarieties of n-tori, defined over the rationals, using model theoretic methods.","authors_text":"Chris Smyth, Iskander Aliev, Tristram de Piro","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-24T01:26:28Z","title":"Bounding the Number of Maximal Torsion Cosets on Subvarieties of Algebraic Tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6321","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":"sha256:13671059144bac90391049d6ce0b85d8ec424120078d1ff0501a382903b11a29","target":"record","created_at":"2026-05-18T02:33:00Z","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":"f440e846a8dc7c5d26ec5fbf5ef1769eed48a58aac14ce64f226f270240d625e","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-11-24T01:26:28Z","title_canon_sha256":"61df6125282d041ef840d4c45d19c990c5617c31405c3e7e72b7ea478d05f098"},"schema_version":"1.0","source":{"id":"1411.6321","kind":"arxiv","version":1}},"canonical_sha256":"4b7c7d54e4056fe140cda023d7a2016f32ed0d2eb1846c2101811fe7cfcfb33d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7c7d54e4056fe140cda023d7a2016f32ed0d2eb1846c2101811fe7cfcfb33d","first_computed_at":"2026-05-18T02:33:00.287904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:00.287904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MnLQdiBCEd35UqNnyuEEILTPjS4pvaGwAqPofZwIiSRQ0dluYXE1fC8d1mebXWDd/WFmjJxtlee2/+qrVTCfAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:00.288264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6321","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13671059144bac90391049d6ce0b85d8ec424120078d1ff0501a382903b11a29","sha256:6863979d86310dc3a81f374ce90422dbd1ff8171742dc4e3e7415ee927d24109"],"state_sha256":"4fef9e7a9309af3d735b1d3701948d6d4bffd27b93d7e13b0cea3edcec71ac28"}