{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1996:BFTCDGHCPDHZDFONBGE5BR2RJM","short_pith_number":"pith:BFTCDGHC","schema_version":"1.0","canonical_sha256":"09662198e278cf9195cd0989d0c7514b2a485edd1ee9a3ebef378f1584c591c9","source":{"kind":"arxiv","id":"alg-geom/9605012","version":1},"attestation_state":"computed","paper":{"title":"Complete Intersections K-Theory and Chern Classes","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Institute of Mathematical Sciences, Kansas, Lawrence, Madras), Satya Mandal (University of Kansas","submitted_at":"1996-05-23T09:25:26Z","abstract_excerpt":"Throughout this abstruct $A$ will denote a noetherian commutative ring of dimension $n$. The paper has two parts. Among the interesting results in Part-1 are the following: 1) {\\it suppose that $f_1, f_2, ..., f_r$ (with $r \\leq n$) is a regular sequence in $A$ and suppose $Q$ is a projective $A$-module of rank $r$ that maps onto the ideal $(f_1, f_2, ..., f_{r-1},f_r^{(r-1)!})$. Then $[Q]=[Q_0 \\oplus A]$ in $K_0(A)$ for some projective $A-module~Q_0$ of rank $r-1$.} 2) The set $$F_0K_0(A) = \\{[A/I] \\in K_0(A): I~ is~ a~ locally~ complete ~intersection~ ideal~ in~ A~ of~ height~n \\}$$ is a {\\i"},"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":"alg-geom/9605012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1996-05-23T09:25:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"a761f0b4d44e09fbfa509922d6c2576a7ddcfac58543f51cc5a098ff29557ee4","abstract_canon_sha256":"9be5e2e63ba6df1fd4a150b8c5995e60afa3dbc102569795f6af31fc0c9f2a64"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:06.041469Z","signature_b64":"FvgpiJXTvdChRKcRIQE07UYL69/s4VT3BmOPKPEf9jtn46SgfkvBW8OOEBo0UxJlGgSARUgYwn6FBiTk16R1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09662198e278cf9195cd0989d0c7514b2a485edd1ee9a3ebef378f1584c591c9","last_reissued_at":"2026-07-04T15:08:06.041089Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:06.041089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete Intersections K-Theory and Chern Classes","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Institute of Mathematical Sciences, Kansas, Lawrence, Madras), Satya Mandal (University of Kansas","submitted_at":"1996-05-23T09:25:26Z","abstract_excerpt":"Throughout this abstruct $A$ will denote a noetherian commutative ring of dimension $n$. The paper has two parts. Among the interesting results in Part-1 are the following: 1) {\\it suppose that $f_1, f_2, ..., f_r$ (with $r \\leq n$) is a regular sequence in $A$ and suppose $Q$ is a projective $A$-module of rank $r$ that maps onto the ideal $(f_1, f_2, ..., f_{r-1},f_r^{(r-1)!})$. Then $[Q]=[Q_0 \\oplus A]$ in $K_0(A)$ for some projective $A-module~Q_0$ of rank $r-1$.} 2) The set $$F_0K_0(A) = \\{[A/I] \\in K_0(A): I~ is~ a~ locally~ complete ~intersection~ ideal~ in~ A~ of~ height~n \\}$$ is a {\\i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9605012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/alg-geom/9605012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"alg-geom/9605012","created_at":"2026-07-04T15:08:06.041151+00:00"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9605012v1","created_at":"2026-07-04T15:08:06.041151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9605012","created_at":"2026-07-04T15:08:06.041151+00:00"},{"alias_kind":"pith_short_12","alias_value":"BFTCDGHCPDHZ","created_at":"2026-07-04T15:08:06.041151+00:00"},{"alias_kind":"pith_short_16","alias_value":"BFTCDGHCPDHZDFON","created_at":"2026-07-04T15:08:06.041151+00:00"},{"alias_kind":"pith_short_8","alias_value":"BFTCDGHC","created_at":"2026-07-04T15:08:06.041151+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/BFTCDGHCPDHZDFONBGE5BR2RJM","json":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM.json","graph_json":"https://pith.science/api/pith-number/BFTCDGHCPDHZDFONBGE5BR2RJM/graph.json","events_json":"https://pith.science/api/pith-number/BFTCDGHCPDHZDFONBGE5BR2RJM/events.json","paper":"https://pith.science/paper/BFTCDGHC"},"agent_actions":{"view_html":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM","download_json":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM.json","view_paper":"https://pith.science/paper/BFTCDGHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=alg-geom/9605012&json=true","fetch_graph":"https://pith.science/api/pith-number/BFTCDGHCPDHZDFONBGE5BR2RJM/graph.json","fetch_events":"https://pith.science/api/pith-number/BFTCDGHCPDHZDFONBGE5BR2RJM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM/action/storage_attestation","attest_author":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM/action/author_attestation","sign_citation":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM/action/citation_signature","submit_replication":"https://pith.science/pith/BFTCDGHCPDHZDFONBGE5BR2RJM/action/replication_record"}},"created_at":"2026-07-04T15:08:06.041151+00:00","updated_at":"2026-07-04T15:08:06.041151+00:00"}