{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AIWDU37SLFJE66CR4ICBS5LIQW","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":"722f4b70be5b53ce9b722608e05b8674906ca9ac610ba1883364261150105aea","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-18T12:29:27Z","title_canon_sha256":"c447a8aaf9792ec17b254a1d655e1cf44da506133fc52f93aea2ce24f583a2d6"},"schema_version":"1.0","source":{"id":"1308.3853","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3853","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3853v2","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3853","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"AIWDU37SLFJE","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AIWDU37SLFJE66CR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AIWDU37S","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:b89a66d5dbe3b4e050aba80ba7e6bb8a3d77ccdc5309ab6be6e1f254c2483f56","target":"graph","created_at":"2026-05-18T01:04:50Z","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 a generalization of Frieman's $3k-3$ theorem for the sumset $$ \\Sigma^{l}(A_1,\\ldots,A_k)=\\{a_{j_{1}}+\\cdots+a_{j_{l}}:\\,1\\leq j_{1}<\\cdots<j_{l}\\leq k,\\ a_{j_{s}}\\in A_{j_{s}}\\text{ for all }s\\}. $$","authors_text":"Hao Pan, Shanshan Du","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-18T12:29:27Z","title":"A generalization of Frieman's 3k-3 theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3853","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":"sha256:3c0fc5b98629902d3070261773f87a67daa041ae36132e2aecdac80946440fe7","target":"record","created_at":"2026-05-18T01:04:50Z","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":"722f4b70be5b53ce9b722608e05b8674906ca9ac610ba1883364261150105aea","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-18T12:29:27Z","title_canon_sha256":"c447a8aaf9792ec17b254a1d655e1cf44da506133fc52f93aea2ce24f583a2d6"},"schema_version":"1.0","source":{"id":"1308.3853","kind":"arxiv","version":2}},"canonical_sha256":"022c3a6ff259524f7851e20419756885a2c179e21cb46801030a776ddc822af1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"022c3a6ff259524f7851e20419756885a2c179e21cb46801030a776ddc822af1","first_computed_at":"2026-05-18T01:04:50.844175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.844175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WCc6IlexXaHTSXNlMY30hZUrm8D1UgeQuKlxKpKdFgwdmPB+73PDAs/UEc7sDbO9+4aC0FM5kD/omjW2SGfhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.844694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3853","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c0fc5b98629902d3070261773f87a67daa041ae36132e2aecdac80946440fe7","sha256:b89a66d5dbe3b4e050aba80ba7e6bb8a3d77ccdc5309ab6be6e1f254c2483f56"],"state_sha256":"79df35e0054757266893e995c3913ead1fd359557896437b53e93a6aa95ba4c1"}