{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DUWOVOF7B732GXWLR5KWNTUHIM","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":"895b95dbb26df8be39f8924096b3a1e85cc88abc0b14036c81d371e06520f56f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:46:11Z","title_canon_sha256":"08b04e9e2395eae85716ac53f5fb826c00706e9064a2c257fa2c2af32447f66c"},"schema_version":"1.0","source":{"id":"1705.08760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08760","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08760v1","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08760","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"DUWOVOF7B732","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DUWOVOF7B732GXWL","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DUWOVOF7","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:7973dc949ab6f3215d9a0c2c7f877cd8c3f7c89eeaf44b8e853a72ca2c0135b7","target":"graph","created_at":"2026-05-18T00:43:44Z","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":"For every $\\epsilon > 0$ and $k \\in \\mathbb{N}$, Haight constructed a set $A \\subset \\mathbb{Z}_N$ ($\\mathbb{Z}_N$ stands for the integers modulo $N$) for a suitable $N$, such that $A-A = \\mathbb{Z}_N$ and $|kA| < \\epsilon N$. Recently, Nathanson posed the problem of constructing sets $A \\subset \\mathbb{Z}_N$ for given polynomials $p$ and $q$, such that $p(A) = \\mathbb{Z}_N$ and $|q(A)| < \\epsilon N$, where $p(A)$ is the set $\\{p(a_1, a_2, \\dots, a_n)\\phantom{.}\\colon\\phantom{.}a_1, a_2, \\dots, a_n \\in A\\}$, when $p$ has $n$ variables. In this paper, we give a partial answer to Nathanson's que","authors_text":"Luka Milicevic","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:46:11Z","title":"Small Sets with Large Difference Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08760","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":"sha256:4325f4ddea68a9065f94058ac6dc9bc62444ac6589b49ff2d0a49e1b5e1c5b76","target":"record","created_at":"2026-05-18T00:43:44Z","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":"895b95dbb26df8be39f8924096b3a1e85cc88abc0b14036c81d371e06520f56f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2017-05-24T13:46:11Z","title_canon_sha256":"08b04e9e2395eae85716ac53f5fb826c00706e9064a2c257fa2c2af32447f66c"},"schema_version":"1.0","source":{"id":"1705.08760","kind":"arxiv","version":1}},"canonical_sha256":"1d2ceab8bf0ff7a35ecb8f5566ce87433e3a2dd2612e455edeaba7f547c7cf84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d2ceab8bf0ff7a35ecb8f5566ce87433e3a2dd2612e455edeaba7f547c7cf84","first_computed_at":"2026-05-18T00:43:44.347639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:44.347639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n7wueb2JSmRyLYSiL9cs+tCSUT92/XVCAAK8YZGamm72vJmVGlQzl+PI41uaeHxEV/V1RwC11qLf2468ocfOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:44.348168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4325f4ddea68a9065f94058ac6dc9bc62444ac6589b49ff2d0a49e1b5e1c5b76","sha256:7973dc949ab6f3215d9a0c2c7f877cd8c3f7c89eeaf44b8e853a72ca2c0135b7"],"state_sha256":"805c7e3ee2d709c382aa88ef9cef5de02ee41b777619b1c99d34c254ec740024"}