{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:FMYTG66MRPBRBCGREOARX4UMGV","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":"03012b5650af41f15bbfd87c99697ed457a16b1e86cf9cf3b88d9186ecc33ec9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-02-14T03:04:48Z","title_canon_sha256":"5b715467fee0cd00a556bff0ae2795bec0bcd71d1ea624b5930b74d9de274e9e"},"schema_version":"1.0","source":{"id":"1902.05195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.05195","created_at":"2026-05-17T23:54:01Z"},{"alias_kind":"arxiv_version","alias_value":"1902.05195v1","created_at":"2026-05-17T23:54:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.05195","created_at":"2026-05-17T23:54:01Z"},{"alias_kind":"pith_short_12","alias_value":"FMYTG66MRPBR","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"FMYTG66MRPBRBCGR","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"FMYTG66M","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:a7d2899dfd00593e3a675249389fb7050c3c2a522e51b24181ed05a366e64364","target":"graph","created_at":"2026-05-17T23:54:01Z","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":"Let $p$ be a prime and let $A$ be a subset of $\\mathbb{F}_p$ with $A=-A$ and $|A\\setminus\\{0\\}| \\leq 2\\log_3(p)$. Then there is an element of $\\mathbb{F}_p$ which has a unique representation as a difference of two elements of $A$.","authors_text":"Bernhard Schmidt, Tai Do Duc","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-02-14T03:04:48Z","title":"Unique Differences in Symmetric Subsets of $\\mathbb{F}_p$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05195","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":"sha256:2ad4538cde4b82d31af9a12bec4fa26f0eae35f4a1950dbe5a1b794a20a2d352","target":"record","created_at":"2026-05-17T23:54:01Z","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":"03012b5650af41f15bbfd87c99697ed457a16b1e86cf9cf3b88d9186ecc33ec9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2019-02-14T03:04:48Z","title_canon_sha256":"5b715467fee0cd00a556bff0ae2795bec0bcd71d1ea624b5930b74d9de274e9e"},"schema_version":"1.0","source":{"id":"1902.05195","kind":"arxiv","version":1}},"canonical_sha256":"2b31337bcc8bc31088d123811bf28c35745841cf65c0ad579598fccf6eaaa10c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b31337bcc8bc31088d123811bf28c35745841cf65c0ad579598fccf6eaaa10c","first_computed_at":"2026-05-17T23:54:01.630556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:01.630556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fYIk8UY4JCeaIArmWK3M23JlYxfh7oLweX/6hcgyo42vewgJhPuV8WYhyOsSkn9QwTzSpszCsIVKGzyFO6wACQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:01.631218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.05195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ad4538cde4b82d31af9a12bec4fa26f0eae35f4a1950dbe5a1b794a20a2d352","sha256:a7d2899dfd00593e3a675249389fb7050c3c2a522e51b24181ed05a366e64364"],"state_sha256":"6e99aae3ee92517f8887beeea32103d8b59dcde1590ae41b06204616142ddbe9"}