{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z33FL7B4WVS56DUXHDDD2AGRIB","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":"8f738b84c41a3e2aa4b6534d449232fdef6da467a598dba9c52a6230006932af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-07T10:52:11Z","title_canon_sha256":"ec6adf7f50a45b4248b00324c95f2954218ffe7e34ec0961b8114e0d8f003020"},"schema_version":"1.0","source":{"id":"1501.01438","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01438","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01438v1","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01438","created_at":"2026-05-18T02:29:54Z"},{"alias_kind":"pith_short_12","alias_value":"Z33FL7B4WVS5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z33FL7B4WVS56DUX","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z33FL7B4","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:b04fc4803e7f472405a9f9d7919f84105b08295588168fb0af1e57494ad6b8cd","target":"graph","created_at":"2026-05-18T02:29:54Z","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, D a locally nilpotent derivation on the polynomial ring k[X_1, X_2,X_3,X_4] and A the kernel of D. A question of M. Miyanishi asks whether projective modules over A are necessarily free. Implicit is a subquestion: whether the Grothendieck group K_0(A) is trivial.\n  In this paper we shall demonstrate an explicit k[X_1]-linear fixed point free locally nilpotent derivation D of k[X_1,X_2, X_3, X_4] whose kernel A has an isolated singularity and whose Grothendieck group K_0(A) is not finitely generated; in particular, there exists an i","authors_text":"Neena Gupta, S. M. Bhatwadekar, Swapnil A. Lokhande","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-07T10:52:11Z","title":"Some K-theoretic properties of the kernel of a locally nilpotent derivation on k[X_1, \\dots, X_4]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01438","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:a94c5cfa7f7fc5a13412dd09bda172372c77b777f725c38adef4e4a32517a153","target":"record","created_at":"2026-05-18T02:29:54Z","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":"8f738b84c41a3e2aa4b6534d449232fdef6da467a598dba9c52a6230006932af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-01-07T10:52:11Z","title_canon_sha256":"ec6adf7f50a45b4248b00324c95f2954218ffe7e34ec0961b8114e0d8f003020"},"schema_version":"1.0","source":{"id":"1501.01438","kind":"arxiv","version":1}},"canonical_sha256":"cef655fc3cb565df0e9738c63d00d14071cbbdc9ad89cd80270e6ef455e7a01a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cef655fc3cb565df0e9738c63d00d14071cbbdc9ad89cd80270e6ef455e7a01a","first_computed_at":"2026-05-18T02:29:54.238839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:54.238839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C3cNfsaSc1Sf3OZgzesy598QEcYLT/PoU2+BO8Nqggk1/JsE7LRUw2bG/Pq53Pae1LMu8cJMHd1AMHFW43ekCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:54.239253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01438","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a94c5cfa7f7fc5a13412dd09bda172372c77b777f725c38adef4e4a32517a153","sha256:b04fc4803e7f472405a9f9d7919f84105b08295588168fb0af1e57494ad6b8cd"],"state_sha256":"271c88a7fb14fcb2b3dfd7e46bfa97833706cbd5540b7073c634aa04c67cc7f6"}