{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2WYP3B6VR3BWLGZCNGYNLPNHYF","short_pith_number":"pith:2WYP3B6V","canonical_record":{"source":{"id":"1412.2213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-06T09:15:54Z","cross_cats_sorted":[],"title_canon_sha256":"c59da55cb14885c7e03e8b24fab47362864bc6f572a09a2fab9d163ce2711f24","abstract_canon_sha256":"042db39dcbad2b4b224e4f0abaefd9c0658fd031cb188ae895b71a0a64293918"},"schema_version":"1.0"},"canonical_sha256":"d5b0fd87d58ec3659b2269b0d5bda7c14b8f5f87fed3ed810cea405c53c01438","source":{"kind":"arxiv","id":"1412.2213","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2213","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2213v1","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2213","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"2WYP3B6VR3BW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2WYP3B6VR3BWLGZC","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2WYP3B6V","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2WYP3B6VR3BWLGZCNGYNLPNHYF","target":"record","payload":{"canonical_record":{"source":{"id":"1412.2213","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-06T09:15:54Z","cross_cats_sorted":[],"title_canon_sha256":"c59da55cb14885c7e03e8b24fab47362864bc6f572a09a2fab9d163ce2711f24","abstract_canon_sha256":"042db39dcbad2b4b224e4f0abaefd9c0658fd031cb188ae895b71a0a64293918"},"schema_version":"1.0"},"canonical_sha256":"d5b0fd87d58ec3659b2269b0d5bda7c14b8f5f87fed3ed810cea405c53c01438","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:58.612063Z","signature_b64":"owigYr7H1FcRn6EM8S+5SFEGzbDcGaN/hWIZgNUiA65KVUcO/S3YJAOZ933AT+cUC0EWU2c4RbkrUd2XhIWlBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5b0fd87d58ec3659b2269b0d5bda7c14b8f5f87fed3ed810cea405c53c01438","last_reissued_at":"2026-05-18T02:31:58.611290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:58.611290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.2213","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WGFbPHwlEFAopkdtidT+Kmw6eys2OSMZ8ATH+ctDWrK092SmsNYHZSqTGoWuN4IBf8ASnlJoGzJhW7w1vP2nDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:47:59.075728Z"},"content_sha256":"fbf0b1efcfcf7cc37d850d96039e2d2734f656f6e0eb6a2cc7106f746527f3d5","schema_version":"1.0","event_id":"sha256:fbf0b1efcfcf7cc37d850d96039e2d2734f656f6e0eb6a2cc7106f746527f3d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2WYP3B6VR3BWLGZCNGYNLPNHYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the cancellation problem for algebraic tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB)","submitted_at":"2014-12-06T09:15:54Z","abstract_excerpt":"We address a variant of Zariski Cancellation Problem, asking whether two varieties which become isomorphic after taking their product with an algebraic torus are isomorphic themselves. Such cancellation property is easily checked for curves, is known to hold for smooth varieties of log-general type by virtue of a result of Iitaka-Fujita, and more generally for varieties which are not dominantly covered by images of the punctured affine line.  We show in contrast that cancellation fails in general in every dimension bigger or equal to two."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2213","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YxZHPxJjHYYZLk3sf1buZk3R8IxTKXJP4f9DjAO9jpPVCvJYQL9CuN+7mpdmUTQjrUS5xmF9CZxzW5ZMZcv7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:47:59.076134Z"},"content_sha256":"dcc037ebf3441f44885d784b90907a55434f007a3ca90c5e05d813e560d1c43a","schema_version":"1.0","event_id":"sha256:dcc037ebf3441f44885d784b90907a55434f007a3ca90c5e05d813e560d1c43a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2WYP3B6VR3BWLGZCNGYNLPNHYF/bundle.json","state_url":"https://pith.science/pith/2WYP3B6VR3BWLGZCNGYNLPNHYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2WYP3B6VR3BWLGZCNGYNLPNHYF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T01:47:59Z","links":{"resolver":"https://pith.science/pith/2WYP3B6VR3BWLGZCNGYNLPNHYF","bundle":"https://pith.science/pith/2WYP3B6VR3BWLGZCNGYNLPNHYF/bundle.json","state":"https://pith.science/pith/2WYP3B6VR3BWLGZCNGYNLPNHYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2WYP3B6VR3BWLGZCNGYNLPNHYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2WYP3B6VR3BWLGZCNGYNLPNHYF","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":"042db39dcbad2b4b224e4f0abaefd9c0658fd031cb188ae895b71a0a64293918","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-06T09:15:54Z","title_canon_sha256":"c59da55cb14885c7e03e8b24fab47362864bc6f572a09a2fab9d163ce2711f24"},"schema_version":"1.0","source":{"id":"1412.2213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2213","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2213v1","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2213","created_at":"2026-05-18T02:31:58Z"},{"alias_kind":"pith_short_12","alias_value":"2WYP3B6VR3BW","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2WYP3B6VR3BWLGZC","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2WYP3B6V","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:dcc037ebf3441f44885d784b90907a55434f007a3ca90c5e05d813e560d1c43a","target":"graph","created_at":"2026-05-18T02:31:58Z","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 address a variant of Zariski Cancellation Problem, asking whether two varieties which become isomorphic after taking their product with an algebraic torus are isomorphic themselves. Such cancellation property is easily checked for curves, is known to hold for smooth varieties of log-general type by virtue of a result of Iitaka-Fujita, and more generally for varieties which are not dominantly covered by images of the punctured affine line.  We show in contrast that cancellation fails in general in every dimension bigger or equal to two.","authors_text":"Adrien Dubouloz (IMB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-06T09:15:54Z","title":"On the cancellation problem for algebraic tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2213","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:fbf0b1efcfcf7cc37d850d96039e2d2734f656f6e0eb6a2cc7106f746527f3d5","target":"record","created_at":"2026-05-18T02:31:58Z","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":"042db39dcbad2b4b224e4f0abaefd9c0658fd031cb188ae895b71a0a64293918","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-06T09:15:54Z","title_canon_sha256":"c59da55cb14885c7e03e8b24fab47362864bc6f572a09a2fab9d163ce2711f24"},"schema_version":"1.0","source":{"id":"1412.2213","kind":"arxiv","version":1}},"canonical_sha256":"d5b0fd87d58ec3659b2269b0d5bda7c14b8f5f87fed3ed810cea405c53c01438","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5b0fd87d58ec3659b2269b0d5bda7c14b8f5f87fed3ed810cea405c53c01438","first_computed_at":"2026-05-18T02:31:58.611290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:58.611290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"owigYr7H1FcRn6EM8S+5SFEGzbDcGaN/hWIZgNUiA65KVUcO/S3YJAOZ933AT+cUC0EWU2c4RbkrUd2XhIWlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:58.612063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbf0b1efcfcf7cc37d850d96039e2d2734f656f6e0eb6a2cc7106f746527f3d5","sha256:dcc037ebf3441f44885d784b90907a55434f007a3ca90c5e05d813e560d1c43a"],"state_sha256":"f2c3c8274b3ffdec803a11494edbf5f0da573a82c26395fb0b603fdd129e5fef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4CMZZJFI5La6KWas+VVV2JASZM3n6YH/2yzcwVaQwbGlvOS20KSBqozIVQF/2wjH7YHPd5cbje9UTTXGJWJCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:47:59.078426Z","bundle_sha256":"b7b5ecb6bab3173d76296749892e8af85740d645deb720bbd8976ca72a22c032"}}