{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:X7HDXGOB7ISTUZIKARMHWORPSK","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":"c47801b0621eaebff3674b453173b62f26660a5153e32861509abeb13f17e5a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-08-17T15:46:40Z","title_canon_sha256":"2ff9b2311ff41ce75e14e43c26b2a908e0ab2026df6bfd7dbd344bf4244c02af"},"schema_version":"1.0","source":{"id":"2408.09233","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.09233","created_at":"2026-07-05T09:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"2408.09233v3","created_at":"2026-07-05T09:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09233","created_at":"2026-07-05T09:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"X7HDXGOB7IST","created_at":"2026-07-05T09:54:46Z"},{"alias_kind":"pith_short_16","alias_value":"X7HDXGOB7ISTUZIK","created_at":"2026-07-05T09:54:46Z"},{"alias_kind":"pith_short_8","alias_value":"X7HDXGOB","created_at":"2026-07-05T09:54:46Z"}],"graph_snapshots":[{"event_id":"sha256:06ae7c8e1f3ca31d22decfaff66a838762df15f5df8189bc7832d053104e2ce0","target":"graph","created_at":"2026-07-05T09:54:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.09233/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a class of real algebraic varieties characterised by a simple rationality condition, which exhibit strong properties regarding approximation of continuous and smooth mappings by regular ones. They form a natural counterpart to the classes of malleable and quasi-malleable varieties. The approximation property studied here is stronger than those considered before and allows us to deduce non-trivial facts about extensions of regular mappings between varieties.","authors_text":"Juliusz Banecki","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-08-17T15:46:40Z","title":"Relative Stone-Weierstrass theorem for mappings between varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09233","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:df1c00cd60964b1118c006789609a332da59b550d29bbb921d2bd36ec9b31a8e","target":"record","created_at":"2026-07-05T09:54:46Z","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":"c47801b0621eaebff3674b453173b62f26660a5153e32861509abeb13f17e5a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-08-17T15:46:40Z","title_canon_sha256":"2ff9b2311ff41ce75e14e43c26b2a908e0ab2026df6bfd7dbd344bf4244c02af"},"schema_version":"1.0","source":{"id":"2408.09233","kind":"arxiv","version":3}},"canonical_sha256":"bfce3b99c1fa253a650a04587b3a2f9287f6b5531d0f89f6740d86ad7bdfd278","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfce3b99c1fa253a650a04587b3a2f9287f6b5531d0f89f6740d86ad7bdfd278","first_computed_at":"2026-07-05T09:54:46.294728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:46.294728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/1Tn1UJSptacpBMREThbVo0Qt9gRDZs82/mlMnxEkl09FFDMDmbowZdNBctNDpSk5kgoQIP/aieEB5y04CE4AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:46.295289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.09233","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df1c00cd60964b1118c006789609a332da59b550d29bbb921d2bd36ec9b31a8e","sha256:06ae7c8e1f3ca31d22decfaff66a838762df15f5df8189bc7832d053104e2ce0"],"state_sha256":"e62698254d3f2dae46e4846785d9e6c85109c63d8847d29bd13d90b515cf6839"}