{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VV2KVLCM27JLTKTJY4FT5LFWZQ","short_pith_number":"pith:VV2KVLCM","schema_version":"1.0","canonical_sha256":"ad74aaac4cd7d2b9aa69c70b3eacb6cc1abfa0ff1cda83e28dadb55e65c089f6","source":{"kind":"arxiv","id":"1810.12791","version":2},"attestation_state":"computed","paper":{"title":"Logarithmic bounds for Roth's theorem via almost-periodicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Olof Sisask, Thomas F. Bloom","submitted_at":"2018-10-30T14:57:48Z","abstract_excerpt":"We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if $A \\subset \\{1,2,\\ldots,N\\}$ is free of three-term progressions, then $\\lvert A\\rvert \\leq N/(\\log N)^{1-o(1)}$. Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity."},"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":"1810.12791","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2018-10-30T14:57:48Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"6567544cbd7d90b4aa7f37f5985f3923c484cea7cb6dcc3eec2498b3c3db8691","abstract_canon_sha256":"eaf9fe1c1b23e052d6291937ed89c26371ee8bfa036065a6b2381467f10c1627"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:41.440535Z","signature_b64":"tD9UFeEnhs5/HIU2HsZobt0oDVPd7G5b6IoiN8nJQrYXduA7rk+LmV4zcGRrgCdBNNYMfmZ/g9HAIq3c2FrRCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad74aaac4cd7d2b9aa69c70b3eacb6cc1abfa0ff1cda83e28dadb55e65c089f6","last_reissued_at":"2026-05-17T23:46:41.439764Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:41.439764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logarithmic bounds for Roth's theorem via almost-periodicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Olof Sisask, Thomas F. Bloom","submitted_at":"2018-10-30T14:57:48Z","abstract_excerpt":"We give a new proof of logarithmic bounds for Roth's theorem on arithmetic progressions, namely that if $A \\subset \\{1,2,\\ldots,N\\}$ is free of three-term progressions, then $\\lvert A\\rvert \\leq N/(\\log N)^{1-o(1)}$. Unlike previous proofs, this is almost entirely done in physical space using almost-periodicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12791","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":"1810.12791","created_at":"2026-05-17T23:46:41.439890+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.12791v2","created_at":"2026-05-17T23:46:41.439890+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12791","created_at":"2026-05-17T23:46:41.439890+00:00"},{"alias_kind":"pith_short_12","alias_value":"VV2KVLCM27JL","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VV2KVLCM27JLTKTJ","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VV2KVLCM","created_at":"2026-05-18T12:32:59.047623+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/VV2KVLCM27JLTKTJY4FT5LFWZQ","json":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ.json","graph_json":"https://pith.science/api/pith-number/VV2KVLCM27JLTKTJY4FT5LFWZQ/graph.json","events_json":"https://pith.science/api/pith-number/VV2KVLCM27JLTKTJY4FT5LFWZQ/events.json","paper":"https://pith.science/paper/VV2KVLCM"},"agent_actions":{"view_html":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ","download_json":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ.json","view_paper":"https://pith.science/paper/VV2KVLCM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.12791&json=true","fetch_graph":"https://pith.science/api/pith-number/VV2KVLCM27JLTKTJY4FT5LFWZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VV2KVLCM27JLTKTJY4FT5LFWZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ/action/storage_attestation","attest_author":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ/action/author_attestation","sign_citation":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ/action/citation_signature","submit_replication":"https://pith.science/pith/VV2KVLCM27JLTKTJY4FT5LFWZQ/action/replication_record"}},"created_at":"2026-05-17T23:46:41.439890+00:00","updated_at":"2026-05-17T23:46:41.439890+00:00"}