{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KTNKYS723DQVOOLQEQY5OMIIL4","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":"d792fd55072715608bc64fb93eee2ba64b899b9bbb9abaced367e039a7b51825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-30T14:33:38Z","title_canon_sha256":"4ccc786e4c5ae0f664526d5592c7c27ec985d9ba4484efeb52a4b654efb0dd76"},"schema_version":"1.0","source":{"id":"1609.09753","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.09753","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1609.09753v3","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.09753","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"KTNKYS723DQV","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KTNKYS723DQVOOLQ","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KTNKYS72","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:8298906448dd51f959c79c14614c5f3be15917d2fdcce62f00667145f36be559","target":"graph","created_at":"2026-05-18T00:31:29Z","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":"We classify Keller maps $x + H$ in dimension $n$ over fields with $\\tfrac16$, for which $H$ is homogeneous, and\n  (1) deg $H = 3$ and rk $JH \\le 2$;\n  (2) deg $H = 3$ and $n \\le 4$;\n  (3) deg $H = 4$ and $n \\le 3$;\n  (4) deg $H = 4 = n$ and $H_1, H_2, H_3, H_4$ are linearly dependent over $K$.\n  In our proof of these classifications, we formulate (and prove) several results which are more general than needed for these classifications. One of these results is the classification of all homogeneous polynomial maps $H$ as in (1) over fields with $\\tfrac16$.","authors_text":"Michiel de Bondt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-30T14:33:38Z","title":"Computations of Keller maps over fields with $\\tfrac16$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09753","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":"sha256:6f70e05cb32f17cbac62737287dc34f750b9c9fee1f6a3f33709193007fcb7cf","target":"record","created_at":"2026-05-18T00:31:29Z","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":"d792fd55072715608bc64fb93eee2ba64b899b9bbb9abaced367e039a7b51825","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-30T14:33:38Z","title_canon_sha256":"4ccc786e4c5ae0f664526d5592c7c27ec985d9ba4484efeb52a4b654efb0dd76"},"schema_version":"1.0","source":{"id":"1609.09753","kind":"arxiv","version":3}},"canonical_sha256":"54daac4bfad8e15739702431d731085f37bb7c2d331d35a535cc3173416a1068","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54daac4bfad8e15739702431d731085f37bb7c2d331d35a535cc3173416a1068","first_computed_at":"2026-05-18T00:31:29.023250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:29.023250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b46TGPJrowZLlekHEumyO4HICJQY3Ti2sAuDKN0SxhHlBB+QrVrLxwrc3gu3QHq6aJ4HUYyNr5yqGwYYHpY/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:29.023946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.09753","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f70e05cb32f17cbac62737287dc34f750b9c9fee1f6a3f33709193007fcb7cf","sha256:8298906448dd51f959c79c14614c5f3be15917d2fdcce62f00667145f36be559"],"state_sha256":"3959333e2ef1a4a735f6315b7ce75323d3a14baa9c7ed160ea8a71f5bf6b6471"}