{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7T576ZX45RI3LTPK5YC5LV47C7","short_pith_number":"pith:7T576ZX4","schema_version":"1.0","canonical_sha256":"fcfbff66fcec51b5cdeaee05d5d79f17e4f9ff27776713ab18759daf8798bd22","source":{"kind":"arxiv","id":"1708.00349","version":1},"attestation_state":"computed","paper":{"title":"Exceptional Scattered Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniele Bartoli, Yue Zhou","submitted_at":"2017-08-01T14:16:05Z","abstract_excerpt":"Let $f$ be an $\\mathbb{F}_q$-linear function over $\\mathbb{F}_{q^n}$. If the $\\mathbb{F}_q$-subspace $U= \\{ (x^{q^t}, f(x)) : x\\in \\mathbb{F}_{q^n} \\}$ defines a maximum scattered linear set, then we call $f$ a scattered polynomial of index $t$. As these polynomials appear to be very rare, it is natural to look for some classification of them. We say a function $f$ is an exceptional scattered polynomial of index $t$ if the subspace $U$ associated with $f$ defines a maximum scattered linear set in $\\mathrm{PG}(1, q^{mn})$ for infinitely many $m$. Our main results are the complete classification"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.00349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-01T14:16:05Z","cross_cats_sorted":[],"title_canon_sha256":"123a81c6032e6b9c54b7197a65a7f8f517a2d51c5e309d825c0dbfc4ae462e75","abstract_canon_sha256":"5085bcd138e7e01f98d96df4cb694d3e2d9c14e2f284e67dd0f53902d3f37a10"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:49.775392Z","signature_b64":"XIytmVVWka9c2Fw8wkb43TlxyfEZz0we7AgRxSq3cHN7SazLtvFRXhlLm7hUSMVRCvruWKkWK+Df42J8Yf+BDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcfbff66fcec51b5cdeaee05d5d79f17e4f9ff27776713ab18759daf8798bd22","last_reissued_at":"2026-05-18T00:38:49.774680Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:49.774680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exceptional Scattered Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniele Bartoli, Yue Zhou","submitted_at":"2017-08-01T14:16:05Z","abstract_excerpt":"Let $f$ be an $\\mathbb{F}_q$-linear function over $\\mathbb{F}_{q^n}$. If the $\\mathbb{F}_q$-subspace $U= \\{ (x^{q^t}, f(x)) : x\\in \\mathbb{F}_{q^n} \\}$ defines a maximum scattered linear set, then we call $f$ a scattered polynomial of index $t$. As these polynomials appear to be very rare, it is natural to look for some classification of them. We say a function $f$ is an exceptional scattered polynomial of index $t$ if the subspace $U$ associated with $f$ defines a maximum scattered linear set in $\\mathrm{PG}(1, q^{mn})$ for infinitely many $m$. Our main results are the complete classification"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00349","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.00349","created_at":"2026-05-18T00:38:49.774795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.00349v1","created_at":"2026-05-18T00:38:49.774795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00349","created_at":"2026-05-18T00:38:49.774795+00:00"},{"alias_kind":"pith_short_12","alias_value":"7T576ZX45RI3","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7T576ZX45RI3LTPK","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7T576ZX4","created_at":"2026-05-18T12:31:05.417338+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7","json":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7.json","graph_json":"https://pith.science/api/pith-number/7T576ZX45RI3LTPK5YC5LV47C7/graph.json","events_json":"https://pith.science/api/pith-number/7T576ZX45RI3LTPK5YC5LV47C7/events.json","paper":"https://pith.science/paper/7T576ZX4"},"agent_actions":{"view_html":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7","download_json":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7.json","view_paper":"https://pith.science/paper/7T576ZX4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.00349&json=true","fetch_graph":"https://pith.science/api/pith-number/7T576ZX45RI3LTPK5YC5LV47C7/graph.json","fetch_events":"https://pith.science/api/pith-number/7T576ZX45RI3LTPK5YC5LV47C7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7/action/storage_attestation","attest_author":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7/action/author_attestation","sign_citation":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7/action/citation_signature","submit_replication":"https://pith.science/pith/7T576ZX45RI3LTPK5YC5LV47C7/action/replication_record"}},"created_at":"2026-05-18T00:38:49.774795+00:00","updated_at":"2026-05-18T00:38:49.774795+00:00"}