{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FP5T7L2G4MMK27LBVB4MRF3UWZ","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":"2333b885218aa99cfb02cef55875057801c1af57329a579a91735e98257a6fef","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-30T20:32:33Z","title_canon_sha256":"1f6475fe3838779ea36044408a752c8f0684ede84f2f6ad91e613058d587b0dc"},"schema_version":"1.0","source":{"id":"1011.0104","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0104","created_at":"2026-05-18T03:39:29Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0104v3","created_at":"2026-05-18T03:39:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0104","created_at":"2026-05-18T03:39:29Z"},{"alias_kind":"pith_short_12","alias_value":"FP5T7L2G4MMK","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FP5T7L2G4MMK27LB","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FP5T7L2G","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:2c8b0082342fb60b81194fe1f9770d9a73b57431f6ce34e4ccc56bb567976703","target":"graph","created_at":"2026-05-18T03:39:29Z","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 show that if A is a subset of {1,...,N} contains no non-trivial three-term arithmetic progressions then |A|=O(N/ log^{1-o(1)} N). The approach is somewhat different from that used in arXiv:1007.5444.","authors_text":"Tom Sanders","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-30T20:32:33Z","title":"On Roth's theorem on progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0104","kind":"arxiv","version":3},"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":"sha256:1796b51dc1e1b292499bfab0ddcc4bbefef38695b97ff899afd3836802e12ca1","target":"record","created_at":"2026-05-18T03:39:29Z","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":"2333b885218aa99cfb02cef55875057801c1af57329a579a91735e98257a6fef","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-10-30T20:32:33Z","title_canon_sha256":"1f6475fe3838779ea36044408a752c8f0684ede84f2f6ad91e613058d587b0dc"},"schema_version":"1.0","source":{"id":"1011.0104","kind":"arxiv","version":3}},"canonical_sha256":"2bfb3faf46e318ad7d61a878c89774b654707c8e30fcabd47cbaa73ac6509fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2bfb3faf46e318ad7d61a878c89774b654707c8e30fcabd47cbaa73ac6509fd4","first_computed_at":"2026-05-18T03:39:29.439304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:29.439304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gORjxQnr47d8VV2svq65jykTZxGPtDPYCxD1CyieLiHpnUS3wvSNv/Dh/zZ0ONqqVLxmjrhhvBhuy8Jjcz2IAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:29.440083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0104","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1796b51dc1e1b292499bfab0ddcc4bbefef38695b97ff899afd3836802e12ca1","sha256:2c8b0082342fb60b81194fe1f9770d9a73b57431f6ce34e4ccc56bb567976703"],"state_sha256":"47002af3ef3a966bf16572a39c669e48b3d2e59dec8cb9dc76b72098e40ec237"}