{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CUKQQOFKKALBCBOGUSE4SYT5TT","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":"8fe259a83bcde6431c7e8d1973ef3102e1ae4f67adb7bb8c03feb3e41f242cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-11T08:56:19Z","title_canon_sha256":"63b47f9bcbcebcf83e1bc4368c78799fd94af71cc5063faf08271b3b93feeeb5"},"schema_version":"1.0","source":{"id":"1107.1968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1968","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1968v1","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1968","created_at":"2026-05-18T04:18:33Z"},{"alias_kind":"pith_short_12","alias_value":"CUKQQOFKKALB","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CUKQQOFKKALBCBOG","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CUKQQOFK","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:61398786e7c2d17deb23e49fbde03424ba3f1b98b48fab32a7677afcac58cc34","target":"graph","created_at":"2026-05-18T04:18:33Z","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":"We give families of examples of principal open subsets of the affine space \\mathbb{A}^{3} which do not have the cancellation property. We show as a by-product that the cylinders over Koras-Russell threefolds of the first kind have a trivial Makar-Limanov invariant.","authors_text":"Adrien Dubouloz (IMB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-11T08:56:19Z","title":"Affine open subsets in A^3 without the cancellation property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1968","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":"sha256:3a0ba8d37d0007e3d46116f015498cda3f9ade2626ea4be8500fa6da83a01051","target":"record","created_at":"2026-05-18T04:18:33Z","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":"8fe259a83bcde6431c7e8d1973ef3102e1ae4f67adb7bb8c03feb3e41f242cac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-11T08:56:19Z","title_canon_sha256":"63b47f9bcbcebcf83e1bc4368c78799fd94af71cc5063faf08271b3b93feeeb5"},"schema_version":"1.0","source":{"id":"1107.1968","kind":"arxiv","version":1}},"canonical_sha256":"15150838aa50161105c6a489c9627d9cf9675035c303ec7084bfc5ac665a1603","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15150838aa50161105c6a489c9627d9cf9675035c303ec7084bfc5ac665a1603","first_computed_at":"2026-05-18T04:18:33.733716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:33.733716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yU52gM4oG8cCWOorUrg1rVFyvKLigvXGlsmTOay5qkuGI2f89qfGEO8bFP7CudxNfxCfbYfLUGnjVX5InKAfAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:33.734296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a0ba8d37d0007e3d46116f015498cda3f9ade2626ea4be8500fa6da83a01051","sha256:61398786e7c2d17deb23e49fbde03424ba3f1b98b48fab32a7677afcac58cc34"],"state_sha256":"7dbc46ba59c0ff780f95455e435c82ed1e444e6a6b02d24831935f68c84fc38d"}