{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IY6CFVEI2ZYLI5XRCG7SVFY6BP","short_pith_number":"pith:IY6CFVEI","canonical_record":{"source":{"id":"1305.3405","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-15T09:52:33Z","cross_cats_sorted":[],"title_canon_sha256":"c0512fcf485d04bf89895bf2260065d32ecd27138068349177fb9f8d2a6eaa16","abstract_canon_sha256":"95c5c61693bd61828c405c848719063ce293bdc0c950af827f467f08054e7186"},"schema_version":"1.0"},"canonical_sha256":"463c22d488d670b476f111bf2a971e0bd40bb932dc5c1b18af753de10ed72962","source":{"kind":"arxiv","id":"1305.3405","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3405","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3405v3","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3405","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"IY6CFVEI2ZYL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IY6CFVEI2ZYLI5XR","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IY6CFVEI","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IY6CFVEI2ZYLI5XRCG7SVFY6BP","target":"record","payload":{"canonical_record":{"source":{"id":"1305.3405","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-15T09:52:33Z","cross_cats_sorted":[],"title_canon_sha256":"c0512fcf485d04bf89895bf2260065d32ecd27138068349177fb9f8d2a6eaa16","abstract_canon_sha256":"95c5c61693bd61828c405c848719063ce293bdc0c950af827f467f08054e7186"},"schema_version":"1.0"},"canonical_sha256":"463c22d488d670b476f111bf2a971e0bd40bb932dc5c1b18af753de10ed72962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:10.595509Z","signature_b64":"nxVNpTeRsgZdEPPRXyt63cIN0vCH0iHYnj4tN2BveJFWZw4H22YhQz3HPjN1ykPELF4NNLuPCyAjwD0EsrWKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"463c22d488d670b476f111bf2a971e0bd40bb932dc5c1b18af753de10ed72962","last_reissued_at":"2026-05-18T00:09:10.594894Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:10.594894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.3405","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+/kXrx/Iohyr4Slv0ksb102gx21kfjU44EnmBWZOIx6b14PSRp6uZzamWaxUErOi81R8smc0KBXJO73bFyWGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:54:09.006162Z"},"content_sha256":"7fb793ece316cecbfa57d41114eb3fad570df8c0b8dc69d9a9537b1aa1ecc6f4","schema_version":"1.0","event_id":"sha256:7fb793ece316cecbfa57d41114eb3fad570df8c0b8dc69d9a9537b1aa1ecc6f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IY6CFVEI2ZYLI5XRCG7SVFY6BP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the distribution of Jacobi sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Qing Lu, Weizhe Zheng, Zhiyong Zheng","submitted_at":"2013-05-15T09:52:33Z","abstract_excerpt":"Let $\\mathbf{F}_q$ be a finite field of $q$ elements. For multiplicative characters $\\chi_1,\\dots, \\chi_m$ of $\\mathbf{F}_q^\\times$, we let $J(\\chi_1,\\dots, \\chi_m)$ denote the Jacobi sum. Nicholas Katz and Zhiyong Zheng showed that for $m=2$, the normalized Jacobi sum $q^{-1/2}J(\\chi_1,\\chi_2)$ ($\\chi_1\\chi_2$ nontrivial) is asymptotically equidistributed on the unit circle as $q\\to \\infty$, when $\\chi_1$ and $\\chi_2$ run through all nontrivial multiplicative characters of $\\mathbf{F}_q^\\times$. In this paper, we show a similar property for $m\\ge 2$. More generally, we show that the normalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3405","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T5CoEuRFDOYIe3TjCavEcCYtw/LuJqGCzYjpYNuijDXQBPRPLopYfn8ddgBP7CGykxzjqr+q4f0P7tY4e3+qDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:54:09.006820Z"},"content_sha256":"93957b4868e3074d604d310cd29ffd8c5b18e7727e26559850fd8ff6bde8c72a","schema_version":"1.0","event_id":"sha256:93957b4868e3074d604d310cd29ffd8c5b18e7727e26559850fd8ff6bde8c72a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IY6CFVEI2ZYLI5XRCG7SVFY6BP/bundle.json","state_url":"https://pith.science/pith/IY6CFVEI2ZYLI5XRCG7SVFY6BP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IY6CFVEI2ZYLI5XRCG7SVFY6BP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T13:54:09Z","links":{"resolver":"https://pith.science/pith/IY6CFVEI2ZYLI5XRCG7SVFY6BP","bundle":"https://pith.science/pith/IY6CFVEI2ZYLI5XRCG7SVFY6BP/bundle.json","state":"https://pith.science/pith/IY6CFVEI2ZYLI5XRCG7SVFY6BP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IY6CFVEI2ZYLI5XRCG7SVFY6BP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IY6CFVEI2ZYLI5XRCG7SVFY6BP","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":"95c5c61693bd61828c405c848719063ce293bdc0c950af827f467f08054e7186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-15T09:52:33Z","title_canon_sha256":"c0512fcf485d04bf89895bf2260065d32ecd27138068349177fb9f8d2a6eaa16"},"schema_version":"1.0","source":{"id":"1305.3405","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3405","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3405v3","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3405","created_at":"2026-05-18T00:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"IY6CFVEI2ZYL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IY6CFVEI2ZYLI5XR","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IY6CFVEI","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:93957b4868e3074d604d310cd29ffd8c5b18e7727e26559850fd8ff6bde8c72a","target":"graph","created_at":"2026-05-18T00:09:10Z","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":"Let $\\mathbf{F}_q$ be a finite field of $q$ elements. For multiplicative characters $\\chi_1,\\dots, \\chi_m$ of $\\mathbf{F}_q^\\times$, we let $J(\\chi_1,\\dots, \\chi_m)$ denote the Jacobi sum. Nicholas Katz and Zhiyong Zheng showed that for $m=2$, the normalized Jacobi sum $q^{-1/2}J(\\chi_1,\\chi_2)$ ($\\chi_1\\chi_2$ nontrivial) is asymptotically equidistributed on the unit circle as $q\\to \\infty$, when $\\chi_1$ and $\\chi_2$ run through all nontrivial multiplicative characters of $\\mathbf{F}_q^\\times$. In this paper, we show a similar property for $m\\ge 2$. More generally, we show that the normalize","authors_text":"Qing Lu, Weizhe Zheng, Zhiyong Zheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-15T09:52:33Z","title":"On the distribution of Jacobi sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3405","kind":"arxiv","version":3},"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":"sha256:7fb793ece316cecbfa57d41114eb3fad570df8c0b8dc69d9a9537b1aa1ecc6f4","target":"record","created_at":"2026-05-18T00:09:10Z","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":"95c5c61693bd61828c405c848719063ce293bdc0c950af827f467f08054e7186","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-15T09:52:33Z","title_canon_sha256":"c0512fcf485d04bf89895bf2260065d32ecd27138068349177fb9f8d2a6eaa16"},"schema_version":"1.0","source":{"id":"1305.3405","kind":"arxiv","version":3}},"canonical_sha256":"463c22d488d670b476f111bf2a971e0bd40bb932dc5c1b18af753de10ed72962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"463c22d488d670b476f111bf2a971e0bd40bb932dc5c1b18af753de10ed72962","first_computed_at":"2026-05-18T00:09:10.594894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:10.594894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nxVNpTeRsgZdEPPRXyt63cIN0vCH0iHYnj4tN2BveJFWZw4H22YhQz3HPjN1ykPELF4NNLuPCyAjwD0EsrWKCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:10.595509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3405","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fb793ece316cecbfa57d41114eb3fad570df8c0b8dc69d9a9537b1aa1ecc6f4","sha256:93957b4868e3074d604d310cd29ffd8c5b18e7727e26559850fd8ff6bde8c72a"],"state_sha256":"b21882ffe92b65dccdbcea295ddb66efb2beedaf061c5eadb24d1033f469e1ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uuhmS8+K2xdWotTNODxUj+BIjsxr3iN+goyE1hSs7FjTUJnOxDwzvtUvEqTgYZhM4ctx3UWLlmyGrO9eFscSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:54:09.010227Z","bundle_sha256":"e7a66b94c3c4930a5bf14c32a1cc5f3a3769b70e4ea3e9cbf93da0140475f4b8"}}