{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OBP42ZVEE33BDHYBF5ICVMVSOH","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":"6cc481503efd6f93728697e6bb523df8a4da2e82b7f6469b40b925fb6d256f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T10:59:46Z","title_canon_sha256":"550b32eb08659db28e037db029b04e0b3299f4ab264ee6c3651a8b3ce3069f60"},"schema_version":"1.0","source":{"id":"1503.05706","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05706","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05706v8","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05706","created_at":"2026-05-18T00:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"OBP42ZVEE33B","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OBP42ZVEE33BDHYB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OBP42ZVE","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:77441cde9077df023defd4a4cba72e2b75551abb47a189a36aabb8b6436baea0","target":"graph","created_at":"2026-05-18T00:19:09Z","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":"In this work we characterize the subsets of ${\\mathbb R}^n$ that are images of Nash maps $f:{\\mathbb R}^m\\to{\\mathbb R}^n$. We prove Shiota's conjecture and show that a subset ${\\mathcal S}\\subset{\\mathbb R}^n$ is the image of a Nash map $f:{\\mathbb R}^m\\to{\\mathbb R}^n$ if and only if ${\\mathcal S}$ is semialgebraic, pure dimensional of dimension $d\\leq m$ and there exists an analytic path $\\alpha:[0,1]\\to{\\mathcal S}$ whose image meets all the connected components of the set of regular points of ${\\mathcal S}$. Some remarkable consequences are the following: (1) pure dimensional irreducible ","authors_text":"Jos\\'e F. Fernando","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T10:59:46Z","title":"On Nash images of Euclidean spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05706","kind":"arxiv","version":8},"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":"sha256:9380a3b4304be5d1493ad613a391218dce2f6da2abd3ff71134fdce82d24d07d","target":"record","created_at":"2026-05-18T00:19:09Z","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":"6cc481503efd6f93728697e6bb523df8a4da2e82b7f6469b40b925fb6d256f51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-19T10:59:46Z","title_canon_sha256":"550b32eb08659db28e037db029b04e0b3299f4ab264ee6c3651a8b3ce3069f60"},"schema_version":"1.0","source":{"id":"1503.05706","kind":"arxiv","version":8}},"canonical_sha256":"705fcd66a426f6119f012f502ab2b271e828af4416f65d149f878e2be05b1101","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"705fcd66a426f6119f012f502ab2b271e828af4416f65d149f878e2be05b1101","first_computed_at":"2026-05-18T00:19:09.217606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:09.217606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"32Y2jcKuw6bQWFZ2hp7CXuOsiLOeH4yDj+xKwnoDk0CUdrjQ44vvpXGF8Mae1RDLCUDclQE5cixKUoB9rhjFBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:09.218077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05706","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9380a3b4304be5d1493ad613a391218dce2f6da2abd3ff71134fdce82d24d07d","sha256:77441cde9077df023defd4a4cba72e2b75551abb47a189a36aabb8b6436baea0"],"state_sha256":"f21505c095c491d1fd3ae6bb77aac0da6dedb5151a4b72aee5cc7c8d34203687"}