{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:22CSUQKFWDVHAZUWDMAUAMVMAA","short_pith_number":"pith:22CSUQKF","canonical_record":{"source":{"id":"1210.0881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-02T19:04:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cacfd131eb7c450bc79af7783ca37b818e83b7d37c7131ee5ffb765203503789","abstract_canon_sha256":"0cc17197a3b9c08151f923949aeea0cac49835bcefb0fad7678cd510303e66f3"},"schema_version":"1.0"},"canonical_sha256":"d6852a4145b0ea7066961b014032ac00045f1f045d9eae3c10d50aea077aa314","source":{"kind":"arxiv","id":"1210.0881","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0881","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0881v1","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0881","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"22CSUQKFWDVH","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"22CSUQKFWDVHAZUW","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"22CSUQKF","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:22CSUQKFWDVHAZUWDMAUAMVMAA","target":"record","payload":{"canonical_record":{"source":{"id":"1210.0881","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-02T19:04:22Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cacfd131eb7c450bc79af7783ca37b818e83b7d37c7131ee5ffb765203503789","abstract_canon_sha256":"0cc17197a3b9c08151f923949aeea0cac49835bcefb0fad7678cd510303e66f3"},"schema_version":"1.0"},"canonical_sha256":"d6852a4145b0ea7066961b014032ac00045f1f045d9eae3c10d50aea077aa314","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:14.042526Z","signature_b64":"X51t0KyCBeNw5tZTYhnUZc0tpT93yFXOElLRIrt2EMjEw4oyvSJWapo51THvMiFM7e1XnaRJloHBCdPJCAYBDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6852a4145b0ea7066961b014032ac00045f1f045d9eae3c10d50aea077aa314","last_reissued_at":"2026-05-18T03:44:14.042099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:14.042099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.0881","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":"2026-05-18T03:44:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OONHTg/rud8/irF3zl3fay281ruq2z4+8qgpb8vdPjgE0z2YwbcNBH02wTWCb3oMl/U0EM8+p9WVpHfmibObAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:51:49.869300Z"},"content_sha256":"d20132dbd0b10f5aa762ebf7ce87493a8aebaafe6fb4f61e2d07260eb216f99d","schema_version":"1.0","event_id":"sha256:d20132dbd0b10f5aa762ebf7ce87493a8aebaafe6fb4f61e2d07260eb216f99d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:22CSUQKFWDVHAZUWDMAUAMVMAA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Class of Permutation Binomials over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Xiang-dong Hou","submitted_at":"2012-10-02T19:04:22Z","abstract_excerpt":"Let $q>2$ be a prime power and $f={\\tt x}^{q-2}+t{\\tt x}^{q^2-q-1}$, where $t\\in\\Bbb F_q^*$. It was recently conjectured that $f$ is a permutation polynomial of $\\Bbb F_{q^2}$ if and only if one of the following holds: (i) $t=1$, $q\\equiv 1\\pmod 4$; (ii) $t=-3$, $q\\equiv \\pm1\\pmod{12}$; (iii) $t=3$, $q\\equiv -1\\pmod 6$. We confirm this conjecture in the present paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0881","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":"2026-05-18T03:44:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrR5KKgXbHy3eTr5WWddpn2S1wKQugEFti5tsahgavN2k/QFI22xnUXGBdWUmnLYEsSJiRU1Gi8Bj4FoufQJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:51:49.869903Z"},"content_sha256":"85ea73d4d7eea7161e968936cba6108244c9e58be9fe75f03244111dc1aa3f88","schema_version":"1.0","event_id":"sha256:85ea73d4d7eea7161e968936cba6108244c9e58be9fe75f03244111dc1aa3f88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/22CSUQKFWDVHAZUWDMAUAMVMAA/bundle.json","state_url":"https://pith.science/pith/22CSUQKFWDVHAZUWDMAUAMVMAA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/22CSUQKFWDVHAZUWDMAUAMVMAA/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":"2026-05-31T13:51:49Z","links":{"resolver":"https://pith.science/pith/22CSUQKFWDVHAZUWDMAUAMVMAA","bundle":"https://pith.science/pith/22CSUQKFWDVHAZUWDMAUAMVMAA/bundle.json","state":"https://pith.science/pith/22CSUQKFWDVHAZUWDMAUAMVMAA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/22CSUQKFWDVHAZUWDMAUAMVMAA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:22CSUQKFWDVHAZUWDMAUAMVMAA","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":"0cc17197a3b9c08151f923949aeea0cac49835bcefb0fad7678cd510303e66f3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-02T19:04:22Z","title_canon_sha256":"cacfd131eb7c450bc79af7783ca37b818e83b7d37c7131ee5ffb765203503789"},"schema_version":"1.0","source":{"id":"1210.0881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.0881","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"arxiv_version","alias_value":"1210.0881v1","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0881","created_at":"2026-05-18T03:44:14Z"},{"alias_kind":"pith_short_12","alias_value":"22CSUQKFWDVH","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"22CSUQKFWDVHAZUW","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"22CSUQKF","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:85ea73d4d7eea7161e968936cba6108244c9e58be9fe75f03244111dc1aa3f88","target":"graph","created_at":"2026-05-18T03:44:14Z","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 $q>2$ be a prime power and $f={\\tt x}^{q-2}+t{\\tt x}^{q^2-q-1}$, where $t\\in\\Bbb F_q^*$. It was recently conjectured that $f$ is a permutation polynomial of $\\Bbb F_{q^2}$ if and only if one of the following holds: (i) $t=1$, $q\\equiv 1\\pmod 4$; (ii) $t=-3$, $q\\equiv \\pm1\\pmod{12}$; (iii) $t=3$, $q\\equiv -1\\pmod 6$. We confirm this conjecture in the present paper.","authors_text":"Xiang-dong Hou","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-02T19:04:22Z","title":"A Class of Permutation Binomials over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0881","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:d20132dbd0b10f5aa762ebf7ce87493a8aebaafe6fb4f61e2d07260eb216f99d","target":"record","created_at":"2026-05-18T03:44:14Z","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":"0cc17197a3b9c08151f923949aeea0cac49835bcefb0fad7678cd510303e66f3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-02T19:04:22Z","title_canon_sha256":"cacfd131eb7c450bc79af7783ca37b818e83b7d37c7131ee5ffb765203503789"},"schema_version":"1.0","source":{"id":"1210.0881","kind":"arxiv","version":1}},"canonical_sha256":"d6852a4145b0ea7066961b014032ac00045f1f045d9eae3c10d50aea077aa314","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6852a4145b0ea7066961b014032ac00045f1f045d9eae3c10d50aea077aa314","first_computed_at":"2026-05-18T03:44:14.042099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:14.042099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X51t0KyCBeNw5tZTYhnUZc0tpT93yFXOElLRIrt2EMjEw4oyvSJWapo51THvMiFM7e1XnaRJloHBCdPJCAYBDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:14.042526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.0881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d20132dbd0b10f5aa762ebf7ce87493a8aebaafe6fb4f61e2d07260eb216f99d","sha256:85ea73d4d7eea7161e968936cba6108244c9e58be9fe75f03244111dc1aa3f88"],"state_sha256":"944d320bac1c289001d26246c209176b2222ef1352505ac7ecb35b23c1f147a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hJv5A5pRp0YND4EymCdl9wUgLusdsie5uQ97xh8KbYaY4pV4e4o9cKYWSgdlxhKBzfuYlWblGo1wm6UqE0uEBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:51:49.872397Z","bundle_sha256":"46a44d62e33194de9686f52ee0a0a858bc0188a7d2a1fc1dbb210b3a5a24287d"}}