{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:CW6CO6E3MZER2ZF3KXJUOWAMCL","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":"9569f7144f45aeba22570cf9aeb55a194fd6c02d241ce44a645961bd28501dfb","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:43:35Z","title_canon_sha256":"7425b783bbbfdf7820cf46a1e3cc3b002177183ccb7ee7bfeaa3241add56e0b4"},"schema_version":"1.0","source":{"id":"alg-geom/9305008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9305008","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9305008v1","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9305008","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"CW6CO6E3MZER","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"CW6CO6E3MZER2ZF3","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"CW6CO6E3","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:64c5631912a0173217ef92636d5d415db5199a35bfac734772176153b93dcd81","target":"graph","created_at":"2026-05-18T01:09:21Z","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":"Let $k$ be an algebraically closed field of characteristic zero. Let $H:k^2\\to k^2$ be a polynomial mapping such that the Jacobian $\\text{Jac}\\,H$ is a non-zero constant. In this note we prove, that if there is a line $l \\subset k^2$ such that $H|_l:l\\to k^2$ is an injection, then $H$ is a polynomial automorphism.","authors_text":"Janusz Gwo\\'zdziewicz","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:43:35Z","title":"Injectivity on one line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9305008","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:f22b41a7f6db19c39a88a2fb0e3b5266e7b32ef808c56b4473805c9e30612a9b","target":"record","created_at":"2026-05-18T01:09:21Z","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":"9569f7144f45aeba22570cf9aeb55a194fd6c02d241ce44a645961bd28501dfb","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:43:35Z","title_canon_sha256":"7425b783bbbfdf7820cf46a1e3cc3b002177183ccb7ee7bfeaa3241add56e0b4"},"schema_version":"1.0","source":{"id":"alg-geom/9305008","kind":"arxiv","version":1}},"canonical_sha256":"15bc27789b66491d64bb55d347580c12f5f66fc8203325a6564b1a2b2782e0dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15bc27789b66491d64bb55d347580c12f5f66fc8203325a6564b1a2b2782e0dc","first_computed_at":"2026-05-18T01:09:21.811197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:21.811197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nwjklsJo0gOWwxSj1mFEJaiNZxN4/TDIiJcRb/XNGSmA7YXbYMWD9GxSVpyD0YNBi6vfPKefLS42/ZdIz1RXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:21.811586Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9305008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f22b41a7f6db19c39a88a2fb0e3b5266e7b32ef808c56b4473805c9e30612a9b","sha256:64c5631912a0173217ef92636d5d415db5199a35bfac734772176153b93dcd81"],"state_sha256":"156884de4b1a0d6431c3e46317dbb10e976fc82f66b43d4d7c441ef6314dab97"}