{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:L7UDBOPQERJ7UHRPGX3OE5P6HD","short_pith_number":"pith:L7UDBOPQ","schema_version":"1.0","canonical_sha256":"5fe830b9f02453fa1e2f35f6e275fe38ca694670bff7dacfc1c4559bcf3ce1ce","source":{"kind":"arxiv","id":"1202.5810","version":3},"attestation_state":"computed","paper":{"title":"Compositions and collisions at degree p^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Joachim von zur Gathen, Konstantin Ziegler, Raoul Blankertz","submitted_at":"2012-02-27T01:00:19Z","abstract_excerpt":"A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. In order to count the decomposables, one wants to know, under a suitable normalization, the number of equal-degree collisions of the form f = g o h = g^* o h^* with (g, h) = (g^*, h^*) and deg g = deg g^*. Such collisions only occur in the wild case, where the field characteristic p divides deg f. Reasonable bounds on the number of decomposables over a finite field are known, but they are less sharp in the wild case, in particular for degree p^2.\n  We provide a classification of all po"},"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":"1202.5810","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-27T01:00:19Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"12134bc3a6cc2501f5e2a476c5d71404902b7b0ba194bdf6d2cd991a3913d1bd","abstract_canon_sha256":"d5a810a4c23fb256626920cd3b4d4198e0cdbf7d71950b3612c482e32b8347f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:41.423321Z","signature_b64":"U4yJaAFnmKUo8V4vto50xwhnRXtoQYhUOkwQ/RrwNg6SHp9hPvvamAfd3SkO4Gy1Jj7sfYQzREQ1FBsc3AdLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fe830b9f02453fa1e2f35f6e275fe38ca694670bff7dacfc1c4559bcf3ce1ce","last_reissued_at":"2026-05-18T03:07:41.422852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:41.422852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compositions and collisions at degree p^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Joachim von zur Gathen, Konstantin Ziegler, Raoul Blankertz","submitted_at":"2012-02-27T01:00:19Z","abstract_excerpt":"A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. In order to count the decomposables, one wants to know, under a suitable normalization, the number of equal-degree collisions of the form f = g o h = g^* o h^* with (g, h) = (g^*, h^*) and deg g = deg g^*. Such collisions only occur in the wild case, where the field characteristic p divides deg f. Reasonable bounds on the number of decomposables over a finite field are known, but they are less sharp in the wild case, in particular for degree p^2.\n  We provide a classification of all po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5810","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":"1202.5810","created_at":"2026-05-18T03:07:41.422920+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.5810v3","created_at":"2026-05-18T03:07:41.422920+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5810","created_at":"2026-05-18T03:07:41.422920+00:00"},{"alias_kind":"pith_short_12","alias_value":"L7UDBOPQERJ7","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"L7UDBOPQERJ7UHRP","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"L7UDBOPQ","created_at":"2026-05-18T12:27:14.488303+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/L7UDBOPQERJ7UHRPGX3OE5P6HD","json":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD.json","graph_json":"https://pith.science/api/pith-number/L7UDBOPQERJ7UHRPGX3OE5P6HD/graph.json","events_json":"https://pith.science/api/pith-number/L7UDBOPQERJ7UHRPGX3OE5P6HD/events.json","paper":"https://pith.science/paper/L7UDBOPQ"},"agent_actions":{"view_html":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD","download_json":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD.json","view_paper":"https://pith.science/paper/L7UDBOPQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.5810&json=true","fetch_graph":"https://pith.science/api/pith-number/L7UDBOPQERJ7UHRPGX3OE5P6HD/graph.json","fetch_events":"https://pith.science/api/pith-number/L7UDBOPQERJ7UHRPGX3OE5P6HD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD/action/storage_attestation","attest_author":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD/action/author_attestation","sign_citation":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD/action/citation_signature","submit_replication":"https://pith.science/pith/L7UDBOPQERJ7UHRPGX3OE5P6HD/action/replication_record"}},"created_at":"2026-05-18T03:07:41.422920+00:00","updated_at":"2026-05-18T03:07:41.422920+00:00"}