{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:I2SABCKIE5D64HE2N2PKUIQMGY","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":"154eded3d5ab2ceacfd1c59e43437b650bd1cd18d2ad6c0b83b0dc9f635fa1f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-12T02:45:42Z","title_canon_sha256":"03f684a99ca9d2ed416687b19f459bada63b20549d82aab0ebdee1d89dd40184"},"schema_version":"1.0","source":{"id":"1709.03664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03664","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03664v2","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03664","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"I2SABCKIE5D6","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"I2SABCKIE5D64HE2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"I2SABCKI","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:0532882385670a3771a4d6b8949a1db73b09f62db69e7ee46d21440e4c98b80d","target":"graph","created_at":"2026-05-18T00:34:28Z","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 a number field and $O_K$ the ring of integers of $K$. In the spirit of Siegel's theorem on integral points on affine algebraic curves, the plane Jacobian conjecture over $K$ is equivalent to the following statement: if $P,Q\\in O_K[x,y]$ and $P_xQ_y-P_yQ_x\\equiv 1$, then the curve $P=0$ has more than one integral point.","authors_text":"Nguyen van Chau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-12T02:45:42Z","title":"Integral points on plane curves and Plane Jacobian Conjecture over number fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03664","kind":"arxiv","version":2},"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":"sha256:8cdb826431e2bbfef083dcb09b8d9acd2611b528759e7066a78eb96f7f8d132c","target":"record","created_at":"2026-05-18T00:34:28Z","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":"154eded3d5ab2ceacfd1c59e43437b650bd1cd18d2ad6c0b83b0dc9f635fa1f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-09-12T02:45:42Z","title_canon_sha256":"03f684a99ca9d2ed416687b19f459bada63b20549d82aab0ebdee1d89dd40184"},"schema_version":"1.0","source":{"id":"1709.03664","kind":"arxiv","version":2}},"canonical_sha256":"46a40089482747ee1c9a6e9eaa220c3630fcc628f77b8c52354dcd693e702751","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46a40089482747ee1c9a6e9eaa220c3630fcc628f77b8c52354dcd693e702751","first_computed_at":"2026-05-18T00:34:28.788290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:28.788290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mek+eYMcbghOqbuY0/c3ZIGqIO0m/yxQlYRQcFNP7Wri4ShAhpdeQ/6jIaiOIDZq2Do1nSHpxvP8zz59ozGGBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:28.788705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cdb826431e2bbfef083dcb09b8d9acd2611b528759e7066a78eb96f7f8d132c","sha256:0532882385670a3771a4d6b8949a1db73b09f62db69e7ee46d21440e4c98b80d"],"state_sha256":"980fa6196c2fc353eb1a0dc243fc0c2eddf2e082aac84e8bc1c49a9f1adb96e4"}