{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HKSTONE3TEW4IP5LODQTKKYYMB","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":"fe253778c80de1eadb56e45b29595d4be9e000ffe1ffd510d078495769aebebc","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-27T00:32:39Z","title_canon_sha256":"de5303d33866f6dde687297ab5ed2806dc3a6c7570c862659d173f178dfcec81"},"schema_version":"1.0","source":{"id":"1208.5271","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5271","created_at":"2026-05-18T02:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5271v6","created_at":"2026-05-18T02:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5271","created_at":"2026-05-18T02:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"HKSTONE3TEW4","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HKSTONE3TEW4IP5L","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HKSTONE3","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:8b25144b533151092abfb1251dc73917f319b2f2ac62fc6be62a9d62864664e0","target":"graph","created_at":"2026-05-18T02:21:00Z","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":"The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, Heilbronn, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertaint","authors_text":"Andrew P. Turner, Gizem Karaali, Hong Suh, J. L. Brumbaugh, Luis Alberto Garcia, Madeleine Bulkow, Matt Michal, Patrick S. Fleming, Stephan Ramon Garcia","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-27T00:32:39Z","title":"Supercharacters, exponential sums, and the uncertainty principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5271","kind":"arxiv","version":6},"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":"sha256:341debaef3fb615c45d6fbeec148a266b7719472a6a807ac554f45e67948b0eb","target":"record","created_at":"2026-05-18T02:21:00Z","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":"fe253778c80de1eadb56e45b29595d4be9e000ffe1ffd510d078495769aebebc","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-08-27T00:32:39Z","title_canon_sha256":"de5303d33866f6dde687297ab5ed2806dc3a6c7570c862659d173f178dfcec81"},"schema_version":"1.0","source":{"id":"1208.5271","kind":"arxiv","version":6}},"canonical_sha256":"3aa537349b992dc43fab70e1352b18605647c60d8b4e87f9d3306965c24ff6c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aa537349b992dc43fab70e1352b18605647c60d8b4e87f9d3306965c24ff6c7","first_computed_at":"2026-05-18T02:21:00.012396Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:00.012396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"naMVNSvfDbTvUphXc/RG/oaFQqLzO3YklGvUyS/YatT6lO+Frwou3mVyU7Kmy5UXUUDyDTGfPzeyF+ddifquCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:00.012866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5271","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:341debaef3fb615c45d6fbeec148a266b7719472a6a807ac554f45e67948b0eb","sha256:8b25144b533151092abfb1251dc73917f319b2f2ac62fc6be62a9d62864664e0"],"state_sha256":"83d5c8664e311155e0cb33b6d3af6abf44ac65ec970ddaa8fcb9ee1d7cf3d08c"}