{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LNILTKT47Z7T3WVSBMICOOJOAI","short_pith_number":"pith:LNILTKT4","canonical_record":{"source":{"id":"1805.10452","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T09:31:47Z","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"title_canon_sha256":"682bde8019605228c21a563d1fcf7b8fa9a3398a7d3d7737f54f08bdd3937ee3","abstract_canon_sha256":"b7055c78b4d61771df8260ebe7da42ef3446e2c67ba9a6e1533a5e3ab0b2ffb2"},"schema_version":"1.0"},"canonical_sha256":"5b50b9aa7cfe7f3ddab20b1027392e022fdc48e8b9c18cf50ba0949f5df0d79c","source":{"kind":"arxiv","id":"1805.10452","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10452","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10452v3","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10452","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"LNILTKT47Z7T","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LNILTKT47Z7T3WVS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LNILTKT4","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LNILTKT47Z7T3WVSBMICOOJOAI","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10452","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T09:31:47Z","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"title_canon_sha256":"682bde8019605228c21a563d1fcf7b8fa9a3398a7d3d7737f54f08bdd3937ee3","abstract_canon_sha256":"b7055c78b4d61771df8260ebe7da42ef3446e2c67ba9a6e1533a5e3ab0b2ffb2"},"schema_version":"1.0"},"canonical_sha256":"5b50b9aa7cfe7f3ddab20b1027392e022fdc48e8b9c18cf50ba0949f5df0d79c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:30.260138Z","signature_b64":"Jk3O5qS/CIvAE6N2rZQuIu+tXVESQx74RfE7NyVqKcXtD5xIOYsZt2pt5dwMRckfkWQEdCyuKwgjB7O5jSbqDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b50b9aa7cfe7f3ddab20b1027392e022fdc48e8b9c18cf50ba0949f5df0d79c","last_reissued_at":"2026-05-18T00:00:30.259576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:30.259576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10452","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":"2026-05-18T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Buk1/se68HD3cMfzNaZ+yZm1q5TWCjP7XCBJ7RsaooiTGl/7muQJh/++cX12X27AM7DDAzPdQQBrOPg2iPEJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:17:56.469022Z"},"content_sha256":"72f4b9f63f70f8511098a7b68632d4807eade803a7ea351bed3918c5e1f7f885","schema_version":"1.0","event_id":"sha256:72f4b9f63f70f8511098a7b68632d4807eade803a7ea351bed3918c5e1f7f885"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LNILTKT47Z7T3WVSBMICOOJOAI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weil sums of binomials: properties, applications, and open problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"math.NT","authors_text":"Daniel J. Katz","submitted_at":"2018-05-26T09:31:47Z","abstract_excerpt":"We present a survey on Weil sums in which an additive character of a finite field $F$ is applied to a binomial whose individual terms (monomials) become permutations of $F$ when regarded as functions. Then we indicate how these Weil sums are used in applications, especially how they characterize the nonlinearity of power permutations and the correlation of linear recursive sequences over finite fields. In these applications, one is interested in the spectrum of Weil sum values that are obtained as the coefficients in the binomial are varied. We review the basic properties of such spectra, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10452","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":"2026-05-18T00:00:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ak+nXaK4gOS9BdRu9+cHUgyj/gmDbwqQ+T18Zbr2O/escEJDEcmQNsstFvrEjaoy7KA9I+qzW5PKMs1picE3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:17:56.469384Z"},"content_sha256":"056faf866c937cad20c0b86289dccedb277eccb3d257522289c5e5065a12bd29","schema_version":"1.0","event_id":"sha256:056faf866c937cad20c0b86289dccedb277eccb3d257522289c5e5065a12bd29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LNILTKT47Z7T3WVSBMICOOJOAI/bundle.json","state_url":"https://pith.science/pith/LNILTKT47Z7T3WVSBMICOOJOAI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LNILTKT47Z7T3WVSBMICOOJOAI/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":"2026-06-21T13:17:56Z","links":{"resolver":"https://pith.science/pith/LNILTKT47Z7T3WVSBMICOOJOAI","bundle":"https://pith.science/pith/LNILTKT47Z7T3WVSBMICOOJOAI/bundle.json","state":"https://pith.science/pith/LNILTKT47Z7T3WVSBMICOOJOAI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LNILTKT47Z7T3WVSBMICOOJOAI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LNILTKT47Z7T3WVSBMICOOJOAI","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":"b7055c78b4d61771df8260ebe7da42ef3446e2c67ba9a6e1533a5e3ab0b2ffb2","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T09:31:47Z","title_canon_sha256":"682bde8019605228c21a563d1fcf7b8fa9a3398a7d3d7737f54f08bdd3937ee3"},"schema_version":"1.0","source":{"id":"1805.10452","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10452","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10452v3","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10452","created_at":"2026-05-18T00:00:30Z"},{"alias_kind":"pith_short_12","alias_value":"LNILTKT47Z7T","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LNILTKT47Z7T3WVS","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LNILTKT4","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:056faf866c937cad20c0b86289dccedb277eccb3d257522289c5e5065a12bd29","target":"graph","created_at":"2026-05-18T00:00:30Z","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 present a survey on Weil sums in which an additive character of a finite field $F$ is applied to a binomial whose individual terms (monomials) become permutations of $F$ when regarded as functions. Then we indicate how these Weil sums are used in applications, especially how they characterize the nonlinearity of power permutations and the correlation of linear recursive sequences over finite fields. In these applications, one is interested in the spectrum of Weil sum values that are obtained as the coefficients in the binomial are varied. We review the basic properties of such spectra, and ","authors_text":"Daniel J. Katz","cross_cats":["cs.IT","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T09:31:47Z","title":"Weil sums of binomials: properties, applications, and open problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10452","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":"sha256:72f4b9f63f70f8511098a7b68632d4807eade803a7ea351bed3918c5e1f7f885","target":"record","created_at":"2026-05-18T00:00:30Z","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":"b7055c78b4d61771df8260ebe7da42ef3446e2c67ba9a6e1533a5e3ab0b2ffb2","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T09:31:47Z","title_canon_sha256":"682bde8019605228c21a563d1fcf7b8fa9a3398a7d3d7737f54f08bdd3937ee3"},"schema_version":"1.0","source":{"id":"1805.10452","kind":"arxiv","version":3}},"canonical_sha256":"5b50b9aa7cfe7f3ddab20b1027392e022fdc48e8b9c18cf50ba0949f5df0d79c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b50b9aa7cfe7f3ddab20b1027392e022fdc48e8b9c18cf50ba0949f5df0d79c","first_computed_at":"2026-05-18T00:00:30.259576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:30.259576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jk3O5qS/CIvAE6N2rZQuIu+tXVESQx74RfE7NyVqKcXtD5xIOYsZt2pt5dwMRckfkWQEdCyuKwgjB7O5jSbqDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:30.260138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10452","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72f4b9f63f70f8511098a7b68632d4807eade803a7ea351bed3918c5e1f7f885","sha256:056faf866c937cad20c0b86289dccedb277eccb3d257522289c5e5065a12bd29"],"state_sha256":"f6fff0a9543655dd1566dbe4fd904728a06033bf9055d20c16fd32d675bdd5de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Y6UXVyu4KDTbPJ2hgYsDQNXpN1oqolcBCruRf82P48yZ2AXbuZUdZdcJBA75ndj//Yr1qPfNmb797PEVWNqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:17:56.471973Z","bundle_sha256":"4ec27bcd74838827de0e9e1cd648fce27398f827f897d1cfa525b99e5e7c3fac"}}