{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7H4F5GKEXGZ7MWGBD5XYYUQ5JT","short_pith_number":"pith:7H4F5GKE","schema_version":"1.0","canonical_sha256":"f9f85e9944b9b3f658c11f6f8c521d4cd3a50c156a4fbd1619576b9f3f4c0c69","source":{"kind":"arxiv","id":"1809.03551","version":3},"attestation_state":"computed","paper":{"title":"Unicyclic Strong Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CR","authors_text":"Claude Gravel, Daniel Panario, David Thomson","submitted_at":"2018-09-10T19:03:59Z","abstract_excerpt":"In this paper, we study some properties of a certain kind of permutation $\\sigma$ over $\\mathbb{F}_{2}^{n}$, where $n$ is a positive integer. The desired properties for $\\sigma$ are: (1) the algebraic degree of each component function is $n-1$; (2) the permutation is unicyclic; (3) the number of terms of the algebraic normal form of each component is at least $2^{n-1}$. We call permutations that satisfy these three properties simultaneously unicyclic strong permutations. We prove that our permutations $\\sigma$ always have high algebraic degree and that the average number of terms of each compo"},"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":"1809.03551","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2018-09-10T19:03:59Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"d94d0a27b645a1df9ce7f84db0e03688074fec2d49f9bae51f043dd6a64dbfbf","abstract_canon_sha256":"29b347bcfe0792a99bc67321d3dfc38b4270957d2d6965c59e3c6a594379bbfa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:55.880371Z","signature_b64":"27N8rEEHOj5rN/ZNhDw6NKbW2pVqWHN3Wq7o3BHhh+mP15NGHaKq021ImPl19aAfUwaR7GOeOhZiI0PMp206BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9f85e9944b9b3f658c11f6f8c521d4cd3a50c156a4fbd1619576b9f3f4c0c69","last_reissued_at":"2026-05-17T23:40:55.879670Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:55.879670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unicyclic Strong Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CR","authors_text":"Claude Gravel, Daniel Panario, David Thomson","submitted_at":"2018-09-10T19:03:59Z","abstract_excerpt":"In this paper, we study some properties of a certain kind of permutation $\\sigma$ over $\\mathbb{F}_{2}^{n}$, where $n$ is a positive integer. The desired properties for $\\sigma$ are: (1) the algebraic degree of each component function is $n-1$; (2) the permutation is unicyclic; (3) the number of terms of the algebraic normal form of each component is at least $2^{n-1}$. We call permutations that satisfy these three properties simultaneously unicyclic strong permutations. We prove that our permutations $\\sigma$ always have high algebraic degree and that the average number of terms of each compo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03551","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1809.03551","created_at":"2026-05-17T23:40:55.879763+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.03551v3","created_at":"2026-05-17T23:40:55.879763+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03551","created_at":"2026-05-17T23:40:55.879763+00:00"},{"alias_kind":"pith_short_12","alias_value":"7H4F5GKEXGZ7","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7H4F5GKEXGZ7MWGB","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7H4F5GKE","created_at":"2026-05-18T12:32:11.075285+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/7H4F5GKEXGZ7MWGBD5XYYUQ5JT","json":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT.json","graph_json":"https://pith.science/api/pith-number/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/graph.json","events_json":"https://pith.science/api/pith-number/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/events.json","paper":"https://pith.science/paper/7H4F5GKE"},"agent_actions":{"view_html":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT","download_json":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT.json","view_paper":"https://pith.science/paper/7H4F5GKE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.03551&json=true","fetch_graph":"https://pith.science/api/pith-number/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/graph.json","fetch_events":"https://pith.science/api/pith-number/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/action/storage_attestation","attest_author":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/action/author_attestation","sign_citation":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/action/citation_signature","submit_replication":"https://pith.science/pith/7H4F5GKEXGZ7MWGBD5XYYUQ5JT/action/replication_record"}},"created_at":"2026-05-17T23:40:55.879763+00:00","updated_at":"2026-05-17T23:40:55.879763+00:00"}