{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GKD4HDXXCJBQSCM4VLUJUCU4B5","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":"ce13c49e006064b7436bca5a6836b1a394baf43fd3d0f8d5fc89d1c4da99817b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-13T18:46:45Z","title_canon_sha256":"91e67729f4d9fb7f52b065bd21caaf5a73e6ce3d238bc47845a06e2d3f946ddc"},"schema_version":"1.0","source":{"id":"1709.04501","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04501","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04501v2","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04501","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"GKD4HDXXCJBQ","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GKD4HDXXCJBQSCM4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GKD4HDXX","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:855e57efa8d84f56af88cba26c8c506c9786057d827f5e69e54d00fcf81692df","target":"graph","created_at":"2026-05-18T00:11:11Z","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 prove results on the structure of a subset of the circle group having positive inner Haar measure and doubling constant close to the minimum. These results go toward a continuous analogue in the circle of Freiman's $3k-4$ theorem from the integer setting. An analogue of this theorem in $\\mathbb{Z}_p$ has been pursued extensively, and we use some recent results in this direction. For instance, obtaining a continuous analogue of a result of Serra and Z\\'emor, we prove that if a subset $A$ of the circle is not too large and has doubling constant at most $2+\\varepsilon$ with $\\varepsilon<10^{-4","authors_text":"Anne de Roton, Pablo Candela","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-13T18:46:45Z","title":"On sets with small sumset in the circle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04501","kind":"arxiv","version":2},"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":"sha256:066be9a2dcb152fa8a6f97af5ec35c14d5d52c78d1a1ca1282eade8501d5122f","target":"record","created_at":"2026-05-18T00:11:11Z","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":"ce13c49e006064b7436bca5a6836b1a394baf43fd3d0f8d5fc89d1c4da99817b","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-13T18:46:45Z","title_canon_sha256":"91e67729f4d9fb7f52b065bd21caaf5a73e6ce3d238bc47845a06e2d3f946ddc"},"schema_version":"1.0","source":{"id":"1709.04501","kind":"arxiv","version":2}},"canonical_sha256":"3287c38ef7124309099caae89a0a9c0f6b3d6d50c2f4026a6b2864da1950e260","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3287c38ef7124309099caae89a0a9c0f6b3d6d50c2f4026a6b2864da1950e260","first_computed_at":"2026-05-18T00:11:11.523808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:11.523808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mR7EcWIL5X6xLe8DO4VoMtOaalnDqWtOM7TlutcBhV+JYoKyTIsvHZL391JTwB5xp6Zi7Svd9UFzQ4EDnbEUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:11.524532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04501","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:066be9a2dcb152fa8a6f97af5ec35c14d5d52c78d1a1ca1282eade8501d5122f","sha256:855e57efa8d84f56af88cba26c8c506c9786057d827f5e69e54d00fcf81692df"],"state_sha256":"5796d623c1dc6afa5c8969d8d892722ca1ca3e173b1b691500cb844ca4966e4a"}