{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:475JZGBTHMHHFE6MUENPCJ2E5K","short_pith_number":"pith:475JZGBT","schema_version":"1.0","canonical_sha256":"e7fa9c98333b0e7293cca11af12744ea8f257fe919a3aab9fce856721017125a","source":{"kind":"arxiv","id":"2602.06668","version":3},"attestation_state":"computed","paper":{"title":"Almost All Vectorial Functions Have Trivial Extended-Affine Stabilizers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Keita Ishizuka","submitted_at":"2026-02-06T12:53:38Z","abstract_excerpt":"We prove that asymptotically almost all vectorial functions over finite fields have trivial extended-affine stabilizers. As a consequence, the number of EA-equivalence classes is asymptotically equal to the naive estimate, namely the total number of functions divided by the size of the EA-group, with vanishing relative error. Furthermore, we derive upper bounds on collision probabilities for both extended-affine and CCZ equivalences. For EA-equivalence, we leverage the trivial-stabilizer result to establish a matching lower bound, yielding a tight asymptotic formula that shows two independentl"},"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":"2602.06668","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-02-06T12:53:38Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"fa30692f1fad2ff96c3131aaf5a7425be6362a3f9a769539b55cbb0a067ebcbf","abstract_canon_sha256":"d0d3a7d77c7f6b20bb1fea5715739a88c60483bf0f353ee25fd93ef3cbea05a6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:01:14.477535Z","signature_b64":"StDiT1K+IABLxstXgoqvUCej2Viv+qd925jgBIxyQbTLjkQbBjf8Z1ya5BYXgGehUY4dIIswo4CZ/s56IR+JDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7fa9c98333b0e7293cca11af12744ea8f257fe919a3aab9fce856721017125a","last_reissued_at":"2026-05-25T02:01:14.476670Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:01:14.476670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost All Vectorial Functions Have Trivial Extended-Affine Stabilizers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Keita Ishizuka","submitted_at":"2026-02-06T12:53:38Z","abstract_excerpt":"We prove that asymptotically almost all vectorial functions over finite fields have trivial extended-affine stabilizers. As a consequence, the number of EA-equivalence classes is asymptotically equal to the naive estimate, namely the total number of functions divided by the size of the EA-group, with vanishing relative error. Furthermore, we derive upper bounds on collision probabilities for both extended-affine and CCZ equivalences. For EA-equivalence, we leverage the trivial-stabilizer result to establish a matching lower bound, yielding a tight asymptotic formula that shows two independentl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.06668","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.06668/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2602.06668","created_at":"2026-05-25T02:01:14.476775+00:00"},{"alias_kind":"arxiv_version","alias_value":"2602.06668v3","created_at":"2026-05-25T02:01:14.476775+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.06668","created_at":"2026-05-25T02:01:14.476775+00:00"},{"alias_kind":"pith_short_12","alias_value":"475JZGBTHMHH","created_at":"2026-05-25T02:01:14.476775+00:00"},{"alias_kind":"pith_short_16","alias_value":"475JZGBTHMHHFE6M","created_at":"2026-05-25T02:01:14.476775+00:00"},{"alias_kind":"pith_short_8","alias_value":"475JZGBT","created_at":"2026-05-25T02:01:14.476775+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/475JZGBTHMHHFE6MUENPCJ2E5K","json":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K.json","graph_json":"https://pith.science/api/pith-number/475JZGBTHMHHFE6MUENPCJ2E5K/graph.json","events_json":"https://pith.science/api/pith-number/475JZGBTHMHHFE6MUENPCJ2E5K/events.json","paper":"https://pith.science/paper/475JZGBT"},"agent_actions":{"view_html":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K","download_json":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K.json","view_paper":"https://pith.science/paper/475JZGBT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2602.06668&json=true","fetch_graph":"https://pith.science/api/pith-number/475JZGBTHMHHFE6MUENPCJ2E5K/graph.json","fetch_events":"https://pith.science/api/pith-number/475JZGBTHMHHFE6MUENPCJ2E5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K/action/storage_attestation","attest_author":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K/action/author_attestation","sign_citation":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K/action/citation_signature","submit_replication":"https://pith.science/pith/475JZGBTHMHHFE6MUENPCJ2E5K/action/replication_record"}},"created_at":"2026-05-25T02:01:14.476775+00:00","updated_at":"2026-05-25T02:01:14.476775+00:00"}