{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O3QTFFGU35OWHDMWBSSSONXDZZ","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":"661b95816cecb70fe1d9e8d66a117711349ba886ff7484018c173b225abd6e6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-16T17:01:17Z","title_canon_sha256":"51e849ab6282c83ba6a9ac1524c43741e676780679d903c78f5b48b7cce871f0"},"schema_version":"1.0","source":{"id":"1412.5082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5082","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5082v1","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5082","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"O3QTFFGU35OW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O3QTFFGU35OWHDMW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O3QTFFGU","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:982e8e055f97908f1bc7f57418ffb5e41e7a08fb018b0a8d6db280a3c9d020aa","target":"graph","created_at":"2026-05-18T02:31:09Z","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":"The study of the additive volume of sets can be reduced to the case of one-dimensional sets. The exact values of the volume of extremal sets are given as a conjecture.","authors_text":"Gregory A. Freiman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-16T17:01:17Z","title":"On the Additive Volume of Sets of Integers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5082","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":"sha256:1cb25b38581a1bcad67568b9573bd082dc423251a50ce76e4b48c972e398d662","target":"record","created_at":"2026-05-18T02:31:09Z","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":"661b95816cecb70fe1d9e8d66a117711349ba886ff7484018c173b225abd6e6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-12-16T17:01:17Z","title_canon_sha256":"51e849ab6282c83ba6a9ac1524c43741e676780679d903c78f5b48b7cce871f0"},"schema_version":"1.0","source":{"id":"1412.5082","kind":"arxiv","version":1}},"canonical_sha256":"76e13294d4df5d638d960ca52736e3ce498f5bb8d7e8d91a5039b0457e3a908c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76e13294d4df5d638d960ca52736e3ce498f5bb8d7e8d91a5039b0457e3a908c","first_computed_at":"2026-05-18T02:31:09.687769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:09.687769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FlEj7jjBrrv1gSHwHroZBfJMJuT19sAHGDRI/zbYgjg41Qj8wLBbj2t5RWLTiEIR2eoo0qMCRY7Qv6PKfTK9Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:09.688457Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cb25b38581a1bcad67568b9573bd082dc423251a50ce76e4b48c972e398d662","sha256:982e8e055f97908f1bc7f57418ffb5e41e7a08fb018b0a8d6db280a3c9d020aa"],"state_sha256":"99be00946e6aa3da40f241aac6245e5b21dd71475fd76b10e906893339994fb0"}