{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:EHDTET3W2NLW3PISABXNZE5NYJ","short_pith_number":"pith:EHDTET3W","schema_version":"1.0","canonical_sha256":"21c7324f76d3576dbd12006edc93adc2515bbb82a0446e5dc7a0bb4204301fa8","source":{"kind":"arxiv","id":"1702.00087","version":1},"attestation_state":"computed","paper":{"title":"An Example in Complete Intersections and an Erratum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Satya Mandal","submitted_at":"2017-01-31T23:37:47Z","abstract_excerpt":"This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A=k[X_1, X_2, \\ldots, X_n]$ is a polynomial ring over a field $k$. The Complete Intersection conjecture states that, for any ideal $I$ in $A$, $\\mu(I)=\\mu(I/I^2)$, where $\\mu$ denotes the minimal number of generators. When $k$ is an infinite field, with $1/2\\in k$, a proof of this conjecture was claimed recently, which was a consequence of a stronger claim. A counter example of this stronger claim surfaced recently. This note discusses such examples and attempts to provide some clarity to the inconsistencie"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.00087","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-31T23:37:47Z","cross_cats_sorted":[],"title_canon_sha256":"0c172156d2386edd79dd2167075949dbbcffc07cb936ef0ea31df78e5c52d98e","abstract_canon_sha256":"9809198ea4b92463de335e01609f0bb8423b2e65906e5b4c74647562abc6e08c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:35.242096Z","signature_b64":"cC2EzaH9diLe0sYBSenOgxnWuv19VJE3lfhFN+ULMAjO8C3b531YpaumSpxmZNTHdXKVQW9VvBpv+8zVMw/MBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21c7324f76d3576dbd12006edc93adc2515bbb82a0446e5dc7a0bb4204301fa8","last_reissued_at":"2026-05-18T00:51:35.241699Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:35.241699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Example in Complete Intersections and an Erratum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Satya Mandal","submitted_at":"2017-01-31T23:37:47Z","abstract_excerpt":"This is essentially an erratum, with some example to indicate inconsistencies. Suppose $A=k[X_1, X_2, \\ldots, X_n]$ is a polynomial ring over a field $k$. The Complete Intersection conjecture states that, for any ideal $I$ in $A$, $\\mu(I)=\\mu(I/I^2)$, where $\\mu$ denotes the minimal number of generators. When $k$ is an infinite field, with $1/2\\in k$, a proof of this conjecture was claimed recently, which was a consequence of a stronger claim. A counter example of this stronger claim surfaced recently. This note discusses such examples and attempts to provide some clarity to the inconsistencie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00087","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.00087","created_at":"2026-05-18T00:51:35.241764+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.00087v1","created_at":"2026-05-18T00:51:35.241764+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00087","created_at":"2026-05-18T00:51:35.241764+00:00"},{"alias_kind":"pith_short_12","alias_value":"EHDTET3W2NLW","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"EHDTET3W2NLW3PIS","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"EHDTET3W","created_at":"2026-05-18T12:31:12.930513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ","json":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ.json","graph_json":"https://pith.science/api/pith-number/EHDTET3W2NLW3PISABXNZE5NYJ/graph.json","events_json":"https://pith.science/api/pith-number/EHDTET3W2NLW3PISABXNZE5NYJ/events.json","paper":"https://pith.science/paper/EHDTET3W"},"agent_actions":{"view_html":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ","download_json":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ.json","view_paper":"https://pith.science/paper/EHDTET3W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.00087&json=true","fetch_graph":"https://pith.science/api/pith-number/EHDTET3W2NLW3PISABXNZE5NYJ/graph.json","fetch_events":"https://pith.science/api/pith-number/EHDTET3W2NLW3PISABXNZE5NYJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ/action/storage_attestation","attest_author":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ/action/author_attestation","sign_citation":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ/action/citation_signature","submit_replication":"https://pith.science/pith/EHDTET3W2NLW3PISABXNZE5NYJ/action/replication_record"}},"created_at":"2026-05-18T00:51:35.241764+00:00","updated_at":"2026-05-18T00:51:35.241764+00:00"}