{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3TV5WSU6JUSJ7OELEX5YGXK6JJ","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":"67aa1a9ce1cb11665a9b8db777898cfdae53f6a717a46537fba3d8f581916229","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-06T08:30:07Z","title_canon_sha256":"3b014be2f242674a7cd32d7edab6bc3c5f02b0fb895c4740e42ae3f742ca52f1"},"schema_version":"1.0","source":{"id":"1609.01429","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01429","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01429v2","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01429","created_at":"2026-05-18T00:54:34Z"},{"alias_kind":"pith_short_12","alias_value":"3TV5WSU6JUSJ","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3TV5WSU6JUSJ7OEL","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3TV5WSU6","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:18fbe15918beeeede290dd46e46517375d192b9f4142eb024e4aaa44bd08ce6e","target":"graph","created_at":"2026-05-18T00:54:34Z","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":"A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime p > 3. His proof required deep algebro-geometric techniques, and he expressed interest in finding a more straightforward direct proof. The first author recently gave such a proof of his identities when q = 1 (mod 4), and this paper provides such a proof for the remaining case q = 3 (mod 4). Our proofs are valid for all characteristics p > 2. Along the way we prove some elegant new character sum identities.","authors_text":"John Greene, Ron Evans","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-06T08:30:07Z","title":"Some mixed character sum identities of Katz II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01429","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:f7921d28025f252c6f6637256aae95418c9f2d49ecc5c2cca8a350f3a88120ae","target":"record","created_at":"2026-05-18T00:54:34Z","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":"67aa1a9ce1cb11665a9b8db777898cfdae53f6a717a46537fba3d8f581916229","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-06T08:30:07Z","title_canon_sha256":"3b014be2f242674a7cd32d7edab6bc3c5f02b0fb895c4740e42ae3f742ca52f1"},"schema_version":"1.0","source":{"id":"1609.01429","kind":"arxiv","version":2}},"canonical_sha256":"dcebdb4a9e4d249fb88b25fb835d5e4a66f860544124d6ddd84c73682568bb98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcebdb4a9e4d249fb88b25fb835d5e4a66f860544124d6ddd84c73682568bb98","first_computed_at":"2026-05-18T00:54:34.194971Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:34.194971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9PuWPoNvd04K5cH4MZhPeCbGeIQW5zuNsx7h0t+AOOQg4EeE9zWwJkYcgicF/E4K/ucvuSgnL7P4nKNYpwddBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:34.195690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01429","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7921d28025f252c6f6637256aae95418c9f2d49ecc5c2cca8a350f3a88120ae","sha256:18fbe15918beeeede290dd46e46517375d192b9f4142eb024e4aaa44bd08ce6e"],"state_sha256":"7f55effe992124cdcc170653c0f2e7605807bed05eb20a2791458722ed150b4f"}