{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:Y3H5BNPBUIRGJZBKASFJL6TLJU","short_pith_number":"pith:Y3H5BNPB","schema_version":"1.0","canonical_sha256":"c6cfd0b5e1a22264e42a048a95fa6b4d1edda73d6571bdc74d5eda9802314b85","source":{"kind":"arxiv","id":"2303.10723","version":8},"attestation_state":"computed","paper":{"title":"Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GT"],"primary_cat":"math.AG","authors_text":"Naoki Kitazawa","submitted_at":"2023-03-19T17:40:33Z","abstract_excerpt":"We present new real algebraic maps of non-positive codimensions with prescribed images whose boundaries consist of explicit non-singular real algebraic hypersurfaces satisfying so-called \"transversality\" as follows. Explicit information on important real polynomials is given. Preimages are one-point sets or products of spheres. They are locally like so-called moment maps.\n  Celebrated theory of Nash and Tognoli says that smooth closed manifolds are {\\it non-singular} real algebraic manifolds and the zero sets of some real polynomial maps. In general, we can approximate smooth functions or more"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2303.10723","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-03-19T17:40:33Z","cross_cats_sorted":["math.GN","math.GT"],"title_canon_sha256":"50a85d590d7b9b689fc64d63c954a23aaa4c3f4749c34f5ea0d0e67e28727411","abstract_canon_sha256":"0e63c8bbe047118b881878883e675372cc357a90c2a6a76d70ec8b7acaaac0d9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:06:53.382949Z","signature_b64":"tlSWUV0lMkq2E9P/W/NDSL5exkKixRzZOG43DZgad23/NdmuoRSmHZz5xUK21C5oVcnt23neprzKquSdXXhqCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6cfd0b5e1a22264e42a048a95fa6b4d1edda73d6571bdc74d5eda9802314b85","last_reissued_at":"2026-07-05T09:06:53.382540Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:06:53.382540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.GT"],"primary_cat":"math.AG","authors_text":"Naoki Kitazawa","submitted_at":"2023-03-19T17:40:33Z","abstract_excerpt":"We present new real algebraic maps of non-positive codimensions with prescribed images whose boundaries consist of explicit non-singular real algebraic hypersurfaces satisfying so-called \"transversality\" as follows. Explicit information on important real polynomials is given. Preimages are one-point sets or products of spheres. They are locally like so-called moment maps.\n  Celebrated theory of Nash and Tognoli says that smooth closed manifolds are {\\it non-singular} real algebraic manifolds and the zero sets of some real polynomial maps. In general, we can approximate smooth functions or more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.10723","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.10723/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2303.10723","created_at":"2026-07-05T09:06:53.382592+00:00"},{"alias_kind":"arxiv_version","alias_value":"2303.10723v8","created_at":"2026-07-05T09:06:53.382592+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.10723","created_at":"2026-07-05T09:06:53.382592+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y3H5BNPBUIRG","created_at":"2026-07-05T09:06:53.382592+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y3H5BNPBUIRGJZBK","created_at":"2026-07-05T09:06:53.382592+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y3H5BNPB","created_at":"2026-07-05T09:06:53.382592+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.12219","citing_title":"Representations of Reeb spaces via simplified graphs and examples","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2605.12219","citing_title":"Representations of Reeb spaces via simplified graphs and examples","ref_index":11,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU","json":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU.json","graph_json":"https://pith.science/api/pith-number/Y3H5BNPBUIRGJZBKASFJL6TLJU/graph.json","events_json":"https://pith.science/api/pith-number/Y3H5BNPBUIRGJZBKASFJL6TLJU/events.json","paper":"https://pith.science/paper/Y3H5BNPB"},"agent_actions":{"view_html":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU","download_json":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU.json","view_paper":"https://pith.science/paper/Y3H5BNPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2303.10723&json=true","fetch_graph":"https://pith.science/api/pith-number/Y3H5BNPBUIRGJZBKASFJL6TLJU/graph.json","fetch_events":"https://pith.science/api/pith-number/Y3H5BNPBUIRGJZBKASFJL6TLJU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU/action/storage_attestation","attest_author":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU/action/author_attestation","sign_citation":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU/action/citation_signature","submit_replication":"https://pith.science/pith/Y3H5BNPBUIRGJZBKASFJL6TLJU/action/replication_record"}},"created_at":"2026-07-05T09:06:53.382592+00:00","updated_at":"2026-07-05T09:06:53.382592+00:00"}