{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KTX6WNQYLOFGJQ653SN5ALZKJD","short_pith_number":"pith:KTX6WNQY","schema_version":"1.0","canonical_sha256":"54efeb36185b8a64c3dddc9bd02f2a48f9b437b211206df26f1c16ac5658507a","source":{"kind":"arxiv","id":"1502.06833","version":1},"attestation_state":"computed","paper":{"title":"Quadratic residues and difference sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack Sonn, Vsevolod F. Lev","submitted_at":"2015-02-24T15:26:36Z","abstract_excerpt":"It has been conjectured by Sarkozy that with finitely many exceptions, the set of quadratic residues modulo a prime $p$ cannot be represented as a sumset $\\{a+b\\colon a\\in A, b\\in B\\}$ with non-singleton sets $A,B\\subset F_p$. The case $A=B$ of this conjecture has been recently established by Shkredov. The analogous problem for differences remains open: is it true that for all sufficiently large primes $p$, the set of quadratic residues modulo $p$ is not of the form $\\{a'-a\"\\colon a',a\"\\in A,\\,a'\\ne a\"\\}$ with $A\\subset F_p$?\n  We attack here a presumably more tractable variant of this problem"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1502.06833","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-02-24T15:26:36Z","cross_cats_sorted":[],"title_canon_sha256":"91ae6dc4123b7f187b4938aa4639d7300edac934b9ffec936c77b6c5fcde9d49","abstract_canon_sha256":"b9ce3afcb2ed702c7c8957db3f7a7db9d4588e8dc5d526d780bb21e6f6f8eb3d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:24.543879Z","signature_b64":"SD7Bl1cZKhkZFbnAOOo+TfdYyEEu2rEKe3XAp18LoLzRrLKu0uwc8zkahHnP2i8uAtsheHKGzadhI9vwIBK1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54efeb36185b8a64c3dddc9bd02f2a48f9b437b211206df26f1c16ac5658507a","last_reissued_at":"2026-05-18T02:26:24.543123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:24.543123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quadratic residues and difference sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jack Sonn, Vsevolod F. Lev","submitted_at":"2015-02-24T15:26:36Z","abstract_excerpt":"It has been conjectured by Sarkozy that with finitely many exceptions, the set of quadratic residues modulo a prime $p$ cannot be represented as a sumset $\\{a+b\\colon a\\in A, b\\in B\\}$ with non-singleton sets $A,B\\subset F_p$. The case $A=B$ of this conjecture has been recently established by Shkredov. The analogous problem for differences remains open: is it true that for all sufficiently large primes $p$, the set of quadratic residues modulo $p$ is not of the form $\\{a'-a\"\\colon a',a\"\\in A,\\,a'\\ne a\"\\}$ with $A\\subset F_p$?\n  We attack here a presumably more tractable variant of this problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06833","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.06833","created_at":"2026-05-18T02:26:24.543249+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.06833v1","created_at":"2026-05-18T02:26:24.543249+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06833","created_at":"2026-05-18T02:26:24.543249+00:00"},{"alias_kind":"pith_short_12","alias_value":"KTX6WNQYLOFG","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_16","alias_value":"KTX6WNQYLOFGJQ65","created_at":"2026-05-18T12:29:29.992203+00:00"},{"alias_kind":"pith_short_8","alias_value":"KTX6WNQY","created_at":"2026-05-18T12:29:29.992203+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD","json":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD.json","graph_json":"https://pith.science/api/pith-number/KTX6WNQYLOFGJQ653SN5ALZKJD/graph.json","events_json":"https://pith.science/api/pith-number/KTX6WNQYLOFGJQ653SN5ALZKJD/events.json","paper":"https://pith.science/paper/KTX6WNQY"},"agent_actions":{"view_html":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD","download_json":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD.json","view_paper":"https://pith.science/paper/KTX6WNQY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.06833&json=true","fetch_graph":"https://pith.science/api/pith-number/KTX6WNQYLOFGJQ653SN5ALZKJD/graph.json","fetch_events":"https://pith.science/api/pith-number/KTX6WNQYLOFGJQ653SN5ALZKJD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD/action/storage_attestation","attest_author":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD/action/author_attestation","sign_citation":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD/action/citation_signature","submit_replication":"https://pith.science/pith/KTX6WNQYLOFGJQ653SN5ALZKJD/action/replication_record"}},"created_at":"2026-05-18T02:26:24.543249+00:00","updated_at":"2026-05-18T02:26:24.543249+00:00"}