{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GAZ5WXAVAHODRFQTDZR5SCHKDU","short_pith_number":"pith:GAZ5WXAV","canonical_record":{"source":{"id":"1410.6179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-22T20:23:19Z","cross_cats_sorted":[],"title_canon_sha256":"7a6e26d5878e5998c44c622be9fa5587f0b5cb8115a0bbbb468a33866bd131b8","abstract_canon_sha256":"3075ea871a19b7096ee8284bc8101414adfc2aaa74c61ad879ec6e2749119449"},"schema_version":"1.0"},"canonical_sha256":"3033db5c1501dc3896131e63d908ea1d29c91b6532385aa43aef0e081e8dd692","source":{"kind":"arxiv","id":"1410.6179","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6179","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6179v1","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6179","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"GAZ5WXAVAHOD","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GAZ5WXAVAHODRFQT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GAZ5WXAV","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GAZ5WXAVAHODRFQTDZR5SCHKDU","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6179","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-22T20:23:19Z","cross_cats_sorted":[],"title_canon_sha256":"7a6e26d5878e5998c44c622be9fa5587f0b5cb8115a0bbbb468a33866bd131b8","abstract_canon_sha256":"3075ea871a19b7096ee8284bc8101414adfc2aaa74c61ad879ec6e2749119449"},"schema_version":"1.0"},"canonical_sha256":"3033db5c1501dc3896131e63d908ea1d29c91b6532385aa43aef0e081e8dd692","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:31.440612Z","signature_b64":"qMQMn6ynsS+IbBYcZDExH380TNP5l8EVmpA0J+9oTERXktIut3S3tTy3nL/iEiOyBibRRwNBmTKEzvobYjEBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3033db5c1501dc3896131e63d908ea1d29c91b6532385aa43aef0e081e8dd692","last_reissued_at":"2026-05-18T02:39:31.440099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:31.440099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6179","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e5LRn0xAVZ1gPwe2OD/2WGLF49hbW6JtMPK3/8uZZdr2E8GYCvf0KcjP4xC3QZY2fnzGKfq5pc0yL40SUcPcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:26:06.981729Z"},"content_sha256":"aea93b81731307a907e0131de25f5e871287c3e28c6612b09627dacb586a45cd","schema_version":"1.0","event_id":"sha256:aea93b81731307a907e0131de25f5e871287c3e28c6612b09627dacb586a45cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GAZ5WXAVAHODRFQTDZR5SCHKDU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluating Prime Power Gauss and Jacobi Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christopher Pinner, Misty Long, Vincent Pigno","submitted_at":"2014-10-22T20:23:19Z","abstract_excerpt":"We show that for any mod $p^m$ characters, $\\chi_1, \\dots, \\chi_k,$ the Jacobi sum, $$ \\sum_{x_1=1}^{p^m}\\dots \\sum_{\\substack{x_k=1\\\\x_1+\\dots+x_k=B}}^{p^m}\\chi_1(x_1)\\dots \\chi_k(x_k), $$ has a simple evaluation when $m$ is sufficiently large (for $m\\geq 2$ if $p\\nmid B$). As part of the proof we give a simple evaluation of the mod $p^m$ Gauss sums when $m\\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6179","kind":"arxiv","version":1},"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":"2026-05-18T02:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nMIKUGdLdq8NzeEMiT0uVSpJYR74Po1Ona7nZDLfhxoF7A1RRMjX2MXZ5WHH+0hAtE2pgOZfALOYksznO7RCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:26:06.982074Z"},"content_sha256":"00aeec48a9e4fa113212db41719a4ed14024441fe98469362a23b1d4d607568b","schema_version":"1.0","event_id":"sha256:00aeec48a9e4fa113212db41719a4ed14024441fe98469362a23b1d4d607568b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAZ5WXAVAHODRFQTDZR5SCHKDU/bundle.json","state_url":"https://pith.science/pith/GAZ5WXAVAHODRFQTDZR5SCHKDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAZ5WXAVAHODRFQTDZR5SCHKDU/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":"2026-06-22T23:26:06Z","links":{"resolver":"https://pith.science/pith/GAZ5WXAVAHODRFQTDZR5SCHKDU","bundle":"https://pith.science/pith/GAZ5WXAVAHODRFQTDZR5SCHKDU/bundle.json","state":"https://pith.science/pith/GAZ5WXAVAHODRFQTDZR5SCHKDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAZ5WXAVAHODRFQTDZR5SCHKDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GAZ5WXAVAHODRFQTDZR5SCHKDU","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":"3075ea871a19b7096ee8284bc8101414adfc2aaa74c61ad879ec6e2749119449","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-22T20:23:19Z","title_canon_sha256":"7a6e26d5878e5998c44c622be9fa5587f0b5cb8115a0bbbb468a33866bd131b8"},"schema_version":"1.0","source":{"id":"1410.6179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6179","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6179v1","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6179","created_at":"2026-05-18T02:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"GAZ5WXAVAHOD","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GAZ5WXAVAHODRFQT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GAZ5WXAV","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:00aeec48a9e4fa113212db41719a4ed14024441fe98469362a23b1d4d607568b","target":"graph","created_at":"2026-05-18T02:39:31Z","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":"We show that for any mod $p^m$ characters, $\\chi_1, \\dots, \\chi_k,$ the Jacobi sum, $$ \\sum_{x_1=1}^{p^m}\\dots \\sum_{\\substack{x_k=1\\\\x_1+\\dots+x_k=B}}^{p^m}\\chi_1(x_1)\\dots \\chi_k(x_k), $$ has a simple evaluation when $m$ is sufficiently large (for $m\\geq 2$ if $p\\nmid B$). As part of the proof we give a simple evaluation of the mod $p^m$ Gauss sums when $m\\geq 2$.","authors_text":"Christopher Pinner, Misty Long, Vincent Pigno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-22T20:23:19Z","title":"Evaluating Prime Power Gauss and Jacobi Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6179","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:aea93b81731307a907e0131de25f5e871287c3e28c6612b09627dacb586a45cd","target":"record","created_at":"2026-05-18T02:39:31Z","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":"3075ea871a19b7096ee8284bc8101414adfc2aaa74c61ad879ec6e2749119449","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-10-22T20:23:19Z","title_canon_sha256":"7a6e26d5878e5998c44c622be9fa5587f0b5cb8115a0bbbb468a33866bd131b8"},"schema_version":"1.0","source":{"id":"1410.6179","kind":"arxiv","version":1}},"canonical_sha256":"3033db5c1501dc3896131e63d908ea1d29c91b6532385aa43aef0e081e8dd692","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3033db5c1501dc3896131e63d908ea1d29c91b6532385aa43aef0e081e8dd692","first_computed_at":"2026-05-18T02:39:31.440099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:31.440099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qMQMn6ynsS+IbBYcZDExH380TNP5l8EVmpA0J+9oTERXktIut3S3tTy3nL/iEiOyBibRRwNBmTKEzvobYjEBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:31.440612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aea93b81731307a907e0131de25f5e871287c3e28c6612b09627dacb586a45cd","sha256:00aeec48a9e4fa113212db41719a4ed14024441fe98469362a23b1d4d607568b"],"state_sha256":"aef785e87d8f5e29858b14bb2209c92e613852329881e1cedbc7d3a5cc074945"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uTOkDjoDkl8Zwp6kjY9yI7QsJ2hc6mgMA5JvXeOne1CMpQHSQIBAPBUaCGNeCHMwV8A9/T5y7RgrWQExZDMBBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:26:06.983975Z","bundle_sha256":"f6df9702f212ea291f5c0ef2eb3f15c783f0dbc06dbd4d970567eabff8de8852"}}