{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YBNGD4XJ43JASLEZJ4TMF27GXX","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":"c6da1fd610827f3d695077395417a8828fb597fac32a8a858e96905a3d701da4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-27T14:29:55Z","title_canon_sha256":"676a7e63380f9e159fda51062a0fe63f47f08f8a4548740df91dbb8ae1f201ab"},"schema_version":"1.0","source":{"id":"1510.07918","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07918","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07918v2","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07918","created_at":"2026-05-18T00:42:13Z"},{"alias_kind":"pith_short_12","alias_value":"YBNGD4XJ43JA","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YBNGD4XJ43JASLEZ","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YBNGD4XJ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:5eedbd7f3f7d1de2a7f2b11bff03c6d55f4772839417275370614952b47629ba","target":"graph","created_at":"2026-05-18T00:42:13Z","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 $E \\subseteq \\mathbb{F}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements, which satisfies $|E| > q$. There exist $x,y \\in E$ such that $|E \\cdot (y-x)| > q/2.$ In particular, $(E+E) \\cdot (E-E) = \\mathbb{F}_q$.","authors_text":"Giorgis Petridis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-27T14:29:55Z","title":"On the Number of Dot Products Determined by a Large Set and One of its Translates in Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07918","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:c4c7d62b5365b1d14fc79b50f1731d30c126f5d2f8a53e7ba55871b419e402f4","target":"record","created_at":"2026-05-18T00:42:13Z","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":"c6da1fd610827f3d695077395417a8828fb597fac32a8a858e96905a3d701da4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-27T14:29:55Z","title_canon_sha256":"676a7e63380f9e159fda51062a0fe63f47f08f8a4548740df91dbb8ae1f201ab"},"schema_version":"1.0","source":{"id":"1510.07918","kind":"arxiv","version":2}},"canonical_sha256":"c05a61f2e9e6d2092c994f26c2ebe6bdefdbf2664307f2ef9630062a3a84931d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c05a61f2e9e6d2092c994f26c2ebe6bdefdbf2664307f2ef9630062a3a84931d","first_computed_at":"2026-05-18T00:42:13.439085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:13.439085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6goosKMfWpJAHtAy4n4E70e5pWmAzw6z/AxbgqdgLxdIr4RM6v2j+rJZ3yL17IdikpQSerOAGMNRqtHk+xroBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:13.439627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07918","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4c7d62b5365b1d14fc79b50f1731d30c126f5d2f8a53e7ba55871b419e402f4","sha256:5eedbd7f3f7d1de2a7f2b11bff03c6d55f4772839417275370614952b47629ba"],"state_sha256":"22ad6dcb47dccfffaa7486d091bc60919e45037553e6dca3c007655699d4c840"}