{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VSHSZMIGWD2TK3YCFZAIO6WNE7","short_pith_number":"pith:VSHSZMIG","schema_version":"1.0","canonical_sha256":"ac8f2cb106b0f5356f022e40877acd27fcbc7a6c019351f9846dc032923302b8","source":{"kind":"arxiv","id":"1505.04967","version":1},"attestation_state":"computed","paper":{"title":"Real Jacobian mates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Janusz Gwo\\'zdziewicz","submitted_at":"2015-05-19T12:36:23Z","abstract_excerpt":"Let $p$ be a real polynomial in two variables. We say that a polynomial $q$ is a real Jacobian mate of $p$ if the Jacobian determinant of the mapping $(p,q):\\mathbb{R}^2\\to\\mathbb{R}^2$ is everywhere positive. We present a class of polynomials that do not have real Jacobian mates."},"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":"1505.04967","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-05-19T12:36:23Z","cross_cats_sorted":[],"title_canon_sha256":"7f3684cf9388fa343a5ea414f5e8ea4d77ed69b57307bd65c47ec6f242310928","abstract_canon_sha256":"3c31c42d5652243e9a71e41f33826eead5a5ff091881b5c4235837575855785c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:57.909878Z","signature_b64":"v4alqRSkzjjANHz3Zb0AjUJpw2PtgAyP4I+sy8FZV8ehtLt27nyTjhtd3QqZ+h1qmdi/AgiQJ2fumZN9GT8PDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac8f2cb106b0f5356f022e40877acd27fcbc7a6c019351f9846dc032923302b8","last_reissued_at":"2026-05-18T01:04:57.909245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:57.909245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real Jacobian mates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Janusz Gwo\\'zdziewicz","submitted_at":"2015-05-19T12:36:23Z","abstract_excerpt":"Let $p$ be a real polynomial in two variables. We say that a polynomial $q$ is a real Jacobian mate of $p$ if the Jacobian determinant of the mapping $(p,q):\\mathbb{R}^2\\to\\mathbb{R}^2$ is everywhere positive. We present a class of polynomials that do not have real Jacobian mates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04967","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1505.04967","created_at":"2026-05-18T01:04:57.909368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.04967v1","created_at":"2026-05-18T01:04:57.909368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04967","created_at":"2026-05-18T01:04:57.909368+00:00"},{"alias_kind":"pith_short_12","alias_value":"VSHSZMIGWD2T","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"VSHSZMIGWD2TK3YC","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"VSHSZMIG","created_at":"2026-05-18T12:29:47.479230+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7","json":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7.json","graph_json":"https://pith.science/api/pith-number/VSHSZMIGWD2TK3YCFZAIO6WNE7/graph.json","events_json":"https://pith.science/api/pith-number/VSHSZMIGWD2TK3YCFZAIO6WNE7/events.json","paper":"https://pith.science/paper/VSHSZMIG"},"agent_actions":{"view_html":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7","download_json":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7.json","view_paper":"https://pith.science/paper/VSHSZMIG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.04967&json=true","fetch_graph":"https://pith.science/api/pith-number/VSHSZMIGWD2TK3YCFZAIO6WNE7/graph.json","fetch_events":"https://pith.science/api/pith-number/VSHSZMIGWD2TK3YCFZAIO6WNE7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7/action/storage_attestation","attest_author":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7/action/author_attestation","sign_citation":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7/action/citation_signature","submit_replication":"https://pith.science/pith/VSHSZMIGWD2TK3YCFZAIO6WNE7/action/replication_record"}},"created_at":"2026-05-18T01:04:57.909368+00:00","updated_at":"2026-05-18T01:04:57.909368+00:00"}