{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:L7UDBOPQERJ7UHRPGX3OE5P6HD","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":"d5a810a4c23fb256626920cd3b4d4198e0cdbf7d71950b3612c482e32b8347f5","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-27T01:00:19Z","title_canon_sha256":"12134bc3a6cc2501f5e2a476c5d71404902b7b0ba194bdf6d2cd991a3913d1bd"},"schema_version":"1.0","source":{"id":"1202.5810","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.5810","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"arxiv_version","alias_value":"1202.5810v3","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.5810","created_at":"2026-05-18T03:07:41Z"},{"alias_kind":"pith_short_12","alias_value":"L7UDBOPQERJ7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L7UDBOPQERJ7UHRP","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L7UDBOPQ","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:a345c10d97338bc0a6bc698ac6975d41c1a2b2b97189d9b8c6b3a49f4fca047b","target":"graph","created_at":"2026-05-18T03:07:41Z","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":"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","authors_text":"Joachim von zur Gathen, Konstantin Ziegler, Raoul Blankertz","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-27T01:00:19Z","title":"Compositions and collisions at degree p^2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.5810","kind":"arxiv","version":3},"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":"sha256:3b377770940f7eeb23dec7ed394f9fb72231683db95d820b9c25a176c6cfdea5","target":"record","created_at":"2026-05-18T03:07:41Z","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":"d5a810a4c23fb256626920cd3b4d4198e0cdbf7d71950b3612c482e32b8347f5","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-02-27T01:00:19Z","title_canon_sha256":"12134bc3a6cc2501f5e2a476c5d71404902b7b0ba194bdf6d2cd991a3913d1bd"},"schema_version":"1.0","source":{"id":"1202.5810","kind":"arxiv","version":3}},"canonical_sha256":"5fe830b9f02453fa1e2f35f6e275fe38ca694670bff7dacfc1c4559bcf3ce1ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fe830b9f02453fa1e2f35f6e275fe38ca694670bff7dacfc1c4559bcf3ce1ce","first_computed_at":"2026-05-18T03:07:41.422852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:41.422852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U4yJaAFnmKUo8V4vto50xwhnRXtoQYhUOkwQ/RrwNg6SHp9hPvvamAfd3SkO4Gy1Jj7sfYQzREQ1FBsc3AdLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:41.423321Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.5810","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b377770940f7eeb23dec7ed394f9fb72231683db95d820b9c25a176c6cfdea5","sha256:a345c10d97338bc0a6bc698ac6975d41c1a2b2b97189d9b8c6b3a49f4fca047b"],"state_sha256":"2184f7aa87a54539368dd5e88d51a61d30141a8b60cac64f447ebc95b625fed5"}