{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KR3DCKQRTI5XNDIAGTMQV2M6WW","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":"7382443073c0ad5a4277a4a77ff74dcf412be0ad2d3b3dab97e4ea4a73ac944e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:46:54Z","title_canon_sha256":"83e1e5d7e27b353994dec8d6e3deaa43fce5d2ba26c67266ee4454203c336a3a"},"schema_version":"1.0","source":{"id":"1201.0630","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0630","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0630v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0630","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"KR3DCKQRTI5X","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KR3DCKQRTI5XNDIA","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KR3DCKQR","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:9eb8e8295d76c8a3d267ca9e8bada51d313d7e8e20db23317a2b0b3fd712e10c","target":"graph","created_at":"2026-05-18T04:05:17Z","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":"This short note gives an upper bound on the measure of sets $A\\subset [0,1]$ such that $x+y=3z$ has no solutions in $A$.","authors_text":"Imre Z. Ruzsa, Mate Matolcsi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:46:54Z","title":"Sets with no solutions to $x+y=3z$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0630","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":"sha256:4b3692a9bd1a8a0506e8f9a80d7497388940345f78ee02bb73a9f17bcf4cfb20","target":"record","created_at":"2026-05-18T04:05:17Z","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":"7382443073c0ad5a4277a4a77ff74dcf412be0ad2d3b3dab97e4ea4a73ac944e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-01-03T13:46:54Z","title_canon_sha256":"83e1e5d7e27b353994dec8d6e3deaa43fce5d2ba26c67266ee4454203c336a3a"},"schema_version":"1.0","source":{"id":"1201.0630","kind":"arxiv","version":1}},"canonical_sha256":"5476312a119a3b768d0034d90ae99eb5a778786d7c9f42e340c2cf92e5a6093e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5476312a119a3b768d0034d90ae99eb5a778786d7c9f42e340c2cf92e5a6093e","first_computed_at":"2026-05-18T04:05:17.045793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:17.045793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9gC/TlifPxF7iwg0uszeObAvtDRmxZ5mjzgPcqEXqnxKeFvtF8ayVJwByhI14mKMN774Q7VeFZzc7mEZVMcBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:17.046469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0630","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b3692a9bd1a8a0506e8f9a80d7497388940345f78ee02bb73a9f17bcf4cfb20","sha256:9eb8e8295d76c8a3d267ca9e8bada51d313d7e8e20db23317a2b0b3fd712e10c"],"state_sha256":"02638216fed5aec091966c00e683dde44828df70fe2bb758527e141f01ef2d83"}