{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:CFJBQTB73VDCRFLRDIFUTQRQRZ","short_pith_number":"pith:CFJBQTB7","schema_version":"1.0","canonical_sha256":"1152184c3fdd462895711a0b49c2308e60bc931b8f776914e9a7efa8081bf437","source":{"kind":"arxiv","id":"1805.06847","version":1},"attestation_state":"computed","paper":{"title":"Quantitative structure of stable sets in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"C. Terry, J. Wolf","submitted_at":"2018-05-17T16:32:15Z","abstract_excerpt":"We prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was recently obtained by the first author in joint work with Conant and Pillay, using model-theoretic techniques. In contrast, the approach in the present paper is highly quantitative and relies on several key ingredients from arithmetic combinatorics."},"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":"1805.06847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-05-17T16:32:15Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"b0c5861ce182d4d4de3e327299e59b63206817f2f3781d9b6c8bff6ca1e79152","abstract_canon_sha256":"edc9edd9e115c2c85bcabe0616d603c2b9e9309031a9e570b9fe0fb359c77465"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:43.146638Z","signature_b64":"qZiGz4y+sPI/g2bMLOISXmABN/mI1/Ec7cLFAIlBaOutqQKwU4OleD0rErlBUJcIDRvLusRzQW2GRLdagDoCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1152184c3fdd462895711a0b49c2308e60bc931b8f776914e9a7efa8081bf437","last_reissued_at":"2026-05-18T00:15:43.146041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:43.146041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative structure of stable sets in finite abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"C. Terry, J. Wolf","submitted_at":"2018-05-17T16:32:15Z","abstract_excerpt":"We prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was recently obtained by the first author in joint work with Conant and Pillay, using model-theoretic techniques. In contrast, the approach in the present paper is highly quantitative and relies on several key ingredients from arithmetic combinatorics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06847","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":"1805.06847","created_at":"2026-05-18T00:15:43.146146+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.06847v1","created_at":"2026-05-18T00:15:43.146146+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06847","created_at":"2026-05-18T00:15:43.146146+00:00"},{"alias_kind":"pith_short_12","alias_value":"CFJBQTB73VDC","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CFJBQTB73VDCRFLR","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CFJBQTB7","created_at":"2026-05-18T12:32:16.446611+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/CFJBQTB73VDCRFLRDIFUTQRQRZ","json":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ.json","graph_json":"https://pith.science/api/pith-number/CFJBQTB73VDCRFLRDIFUTQRQRZ/graph.json","events_json":"https://pith.science/api/pith-number/CFJBQTB73VDCRFLRDIFUTQRQRZ/events.json","paper":"https://pith.science/paper/CFJBQTB7"},"agent_actions":{"view_html":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ","download_json":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ.json","view_paper":"https://pith.science/paper/CFJBQTB7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.06847&json=true","fetch_graph":"https://pith.science/api/pith-number/CFJBQTB73VDCRFLRDIFUTQRQRZ/graph.json","fetch_events":"https://pith.science/api/pith-number/CFJBQTB73VDCRFLRDIFUTQRQRZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/action/storage_attestation","attest_author":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/action/author_attestation","sign_citation":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/action/citation_signature","submit_replication":"https://pith.science/pith/CFJBQTB73VDCRFLRDIFUTQRQRZ/action/replication_record"}},"created_at":"2026-05-18T00:15:43.146146+00:00","updated_at":"2026-05-18T00:15:43.146146+00:00"}