{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PU5YVALJV5HXLL6NAIF5FNDUDV","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":"af4fc412f2b7392841d98b5029109d7e01e85d99c807478df8aee23f50b4ffac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-28T23:09:32Z","title_canon_sha256":"fd4e9b5c5dd36da3ec24eea721b7da9340842385851d190c2cbebb780cb2b0e6"},"schema_version":"1.0","source":{"id":"1509.08534","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08534","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08534v2","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08534","created_at":"2026-05-18T01:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"PU5YVALJV5HX","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PU5YVALJV5HXLL6N","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PU5YVALJ","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:97f05f97b5a8faad311fe599f3962227758d2e1976c698cd2ecaa19cb20dc928","target":"graph","created_at":"2026-05-18T01:30:42Z","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":"Suppose $A=k[X_1, X_2, \\ldots, X_n]$ is a polynomial ring over a field $k$ and $I$ is an ideal in $A$. Then M. P. Murthy conjectured that $\\mu(I)=\\mu(I/I^2)$, where $\\mu$ denotes the minimal number of generators. Recently, Fasel \\cite{F} settled this conjecture, affirmatively, when $k$ is an infinite perfect field, with $1/2\\in k$ {\\rm (always)}. We are able to do the same, when $k$ is an infinite field. In fact, we prove similar results for ideals $I$ in a polynomial ring $A=R[X]$, that contains a monic polynomial and $R$ is essentially finite type smooth algebra over an infinite field $k$, o","authors_text":"Satya Mandal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-28T23:09:32Z","title":"On the complete intersection conjecture of Murthy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08534","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":"sha256:31bd5e36d1d874e9fc8802f37101509136ebe6065d5c1c0bf76dc7f6b9158c57","target":"record","created_at":"2026-05-18T01:30:42Z","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":"af4fc412f2b7392841d98b5029109d7e01e85d99c807478df8aee23f50b4ffac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-28T23:09:32Z","title_canon_sha256":"fd4e9b5c5dd36da3ec24eea721b7da9340842385851d190c2cbebb780cb2b0e6"},"schema_version":"1.0","source":{"id":"1509.08534","kind":"arxiv","version":2}},"canonical_sha256":"7d3b8a8169af4f75afcd020bd2b4741d4dc8f6f4e9789d201fecab6102fd1258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d3b8a8169af4f75afcd020bd2b4741d4dc8f6f4e9789d201fecab6102fd1258","first_computed_at":"2026-05-18T01:30:42.481105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:42.481105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oNJBCNBnBy5G61Vtvkd7UBquuvF4t2XiZYqRW7PLu2af7L4NKTQfbJ9PIZJ+29jKkvh39hQzNDPlNFdXh9kjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:42.481764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08534","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31bd5e36d1d874e9fc8802f37101509136ebe6065d5c1c0bf76dc7f6b9158c57","sha256:97f05f97b5a8faad311fe599f3962227758d2e1976c698cd2ecaa19cb20dc928"],"state_sha256":"6e5b77723be5a856d5637aeb40cbe95ef647b046dd978a604a8b103c86d01a91"}