{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HYJIWIMUFG6Z2DOMQR6YM4ZGJL","short_pith_number":"pith:HYJIWIMU","schema_version":"1.0","canonical_sha256":"3e128b219429bd9d0dcc847d8673264ac9e55a08033f5f92ba4d06ead9b12062","source":{"kind":"arxiv","id":"1606.03495","version":2},"attestation_state":"computed","paper":{"title":"On exponential sums over orbits in $\\mathbb{F}_p^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.NT","authors_text":"Sarah Peluse","submitted_at":"2016-06-10T22:24:04Z","abstract_excerpt":"This paper proves a bound for exponential sums over orbits of vectors in $\\mathbb{F}_p^d$ under subgroups of $\\rm{GL}_d(\\mathbb{F}_p)$. The main tool is a classification theorem for approximate groups due to Gill, Helfgott, Pyber, and Szab\\'o."},"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":"1606.03495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-10T22:24:04Z","cross_cats_sorted":["math.CO","math.GR"],"title_canon_sha256":"2fede5f892e465e0d171e5f8eb7c650437d78685571e7192b61baddcbaaa9002","abstract_canon_sha256":"9f125fc83d98618793869bb0865d54d08b02a15aa1452b8f68bd39a4b0f8dc5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:16.622595Z","signature_b64":"ar9t1eKKwZqKjB1a4rsRBy7+pchqE2BdBGWGf2ppB4hqIaGsouJkgDlaUqjN7PBMFDCfysWLK7tJ0uh2I1koAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e128b219429bd9d0dcc847d8673264ac9e55a08033f5f92ba4d06ead9b12062","last_reissued_at":"2026-05-18T01:08:16.621946Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:16.621946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On exponential sums over orbits in $\\mathbb{F}_p^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.NT","authors_text":"Sarah Peluse","submitted_at":"2016-06-10T22:24:04Z","abstract_excerpt":"This paper proves a bound for exponential sums over orbits of vectors in $\\mathbb{F}_p^d$ under subgroups of $\\rm{GL}_d(\\mathbb{F}_p)$. The main tool is a classification theorem for approximate groups due to Gill, Helfgott, Pyber, and Szab\\'o."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03495","kind":"arxiv","version":2},"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":"1606.03495","created_at":"2026-05-18T01:08:16.622065+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.03495v2","created_at":"2026-05-18T01:08:16.622065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03495","created_at":"2026-05-18T01:08:16.622065+00:00"},{"alias_kind":"pith_short_12","alias_value":"HYJIWIMUFG6Z","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"HYJIWIMUFG6Z2DOM","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"HYJIWIMU","created_at":"2026-05-18T12:30:22.444734+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/HYJIWIMUFG6Z2DOMQR6YM4ZGJL","json":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL.json","graph_json":"https://pith.science/api/pith-number/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/graph.json","events_json":"https://pith.science/api/pith-number/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/events.json","paper":"https://pith.science/paper/HYJIWIMU"},"agent_actions":{"view_html":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL","download_json":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL.json","view_paper":"https://pith.science/paper/HYJIWIMU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.03495&json=true","fetch_graph":"https://pith.science/api/pith-number/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/graph.json","fetch_events":"https://pith.science/api/pith-number/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/action/storage_attestation","attest_author":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/action/author_attestation","sign_citation":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/action/citation_signature","submit_replication":"https://pith.science/pith/HYJIWIMUFG6Z2DOMQR6YM4ZGJL/action/replication_record"}},"created_at":"2026-05-18T01:08:16.622065+00:00","updated_at":"2026-05-18T01:08:16.622065+00:00"}