{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:35LDU7W7CS2Q27S7Z7CE7H7HEO","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":"86f7e588914d00ee70e8027256efcc1e40a228687681fd393b9b1d0f222f5617","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-01T08:16:08Z","title_canon_sha256":"d61bf89c0b18a087dff6cfc0652e3b675876e2571149992b71e77c3b31eba808"},"schema_version":"1.0","source":{"id":"1504.00137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00137","created_at":"2026-05-18T02:19:44Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00137v1","created_at":"2026-05-18T02:19:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00137","created_at":"2026-05-18T02:19:44Z"},{"alias_kind":"pith_short_12","alias_value":"35LDU7W7CS2Q","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"35LDU7W7CS2Q27S7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"35LDU7W7","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:b6ee9c33f58fb3d26e9d488634f5f73bfabe7afcc1133ca986ffd0aed683d034","target":"graph","created_at":"2026-05-18T02:19:44Z","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 study extremal problems about sets of integers that do not contain sumsets with summands of prescribed size. We analyse both finite sets and infinite sequences. We also study the connections of these problems with extremal problems of graphs and hypergraphs.","authors_text":"Javier Cilleruelo, Rafael Tesoro","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-01T08:16:08Z","title":"On sets free of sumsets with summands of prescribed size"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00137","kind":"arxiv","version":1},"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:c24ed6d162c66f03b7c900871d6acc1300e782d31dee245a4e8fec7494c10172","target":"record","created_at":"2026-05-18T02:19:44Z","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":"86f7e588914d00ee70e8027256efcc1e40a228687681fd393b9b1d0f222f5617","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-01T08:16:08Z","title_canon_sha256":"d61bf89c0b18a087dff6cfc0652e3b675876e2571149992b71e77c3b31eba808"},"schema_version":"1.0","source":{"id":"1504.00137","kind":"arxiv","version":1}},"canonical_sha256":"df563a7edf14b50d7e5fcfc44f9fe723a4dc1690aac088d0b6388f42de4b37da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df563a7edf14b50d7e5fcfc44f9fe723a4dc1690aac088d0b6388f42de4b37da","first_computed_at":"2026-05-18T02:19:44.477516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:44.477516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0v0zv4+G+Gbrpa4Kmoy7bnQxvIKsGcQXU1+5tc36E2xNsv47U1KzdMH+VdMxt9VGcmlumGIXgrZH27i9hHpTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:44.477977Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c24ed6d162c66f03b7c900871d6acc1300e782d31dee245a4e8fec7494c10172","sha256:b6ee9c33f58fb3d26e9d488634f5f73bfabe7afcc1133ca986ffd0aed683d034"],"state_sha256":"821633d9b490279277a569bb6a888a5f8df2615bf1de34622d5f3b2e41d841e5"}