{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YKT7JOFBQB6E6VYNIA2YGL27XM","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":"58e53140d98817576a775fb1e5068e09ea6ca5ea614e61dbca4373f4e58ff0fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-02T08:26:30Z","title_canon_sha256":"ef494ce50e356399e231d917e695d33916e6ac1d6ee0c7d44f1755b5789b657b"},"schema_version":"1.0","source":{"id":"1512.00609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00609","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00609v1","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00609","created_at":"2026-05-18T01:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"YKT7JOFBQB6E","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YKT7JOFBQB6E6VYN","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YKT7JOFB","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:f217a73a9b00ef89d5dff8d5bd0f74708c2f43faf2a06cf4ca74b35b52f4b83f","target":"graph","created_at":"2026-05-18T01:25:25Z","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 continous map $f: \\mathbb{C}^n \\rightarrow \\mathbb{C}^N$ is $k$-regular if the image of any $k$ points spans a $k$-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev, to construct $k$-regular maps with small $N$ and only a few nontrivial examples are known so far. Applying tools from algebraic geometry we construct a 4-regular polynomial map $\\mathbb{C}^3\\rightarrow \\mathbb{C}^{11}$ and a 5-regular polynomial map $\\mathbb{C}^3\\rightarrow \\mathbb{C}^{14}$.","authors_text":"Christopher Miller, Mateusz Micha{\\l}ek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-02T08:26:30Z","title":"Examples of $k$-regular maps and interpolation spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00609","kind":"arxiv","version":1},"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":"sha256:0b9697678c9dd6c6f5ca754580c539e204c54265c89ff856fa9f72db50c4f411","target":"record","created_at":"2026-05-18T01:25:25Z","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":"58e53140d98817576a775fb1e5068e09ea6ca5ea614e61dbca4373f4e58ff0fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-12-02T08:26:30Z","title_canon_sha256":"ef494ce50e356399e231d917e695d33916e6ac1d6ee0c7d44f1755b5789b657b"},"schema_version":"1.0","source":{"id":"1512.00609","kind":"arxiv","version":1}},"canonical_sha256":"c2a7f4b8a1807c4f570d4035832f5fbb237b653f2fa61b76a24c66fd9046ace3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2a7f4b8a1807c4f570d4035832f5fbb237b653f2fa61b76a24c66fd9046ace3","first_computed_at":"2026-05-18T01:25:25.562952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:25.562952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hGsK7mS4oxveIqKDklcjjtrhhWm0xCi+9gVTuylykUNCxPos6o398vKswMSA4YMIs57eQacgxNZw/rPFV8DrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:25.563417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b9697678c9dd6c6f5ca754580c539e204c54265c89ff856fa9f72db50c4f411","sha256:f217a73a9b00ef89d5dff8d5bd0f74708c2f43faf2a06cf4ca74b35b52f4b83f"],"state_sha256":"c40c7017dc8602c4fcfb3ff7c548c670afa4bae0acbff8679c870c2e9b0af042"}