{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5JSIG2IR7WWFXVYQA7KSGUDIUL","short_pith_number":"pith:5JSIG2IR","schema_version":"1.0","canonical_sha256":"ea64836911fdac5bd71007d5235068a2ec3ed970bd0bfeac870458360708a39e","source":{"kind":"arxiv","id":"1507.02497","version":2},"attestation_state":"computed","paper":{"title":"Corrigendum to \"Maps between non-commutative spaces\" [Trans. Amer. Math. Soc., 356(7) (2004) 2927-2944]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"S.Paul Smith","submitted_at":"2015-07-09T13:22:54Z","abstract_excerpt":"The statement of Lemma 3.1 in the published paper is not correct. Lemma 3.1 is needed for the proof of Theorem 3.2. Theorem 3.2 as originally stated is true but its \"proof\" is not correct. Here we change the statements and proofs of Lemma 3.1 and Theorem 3.2. We also prove a new result. Let $k$ be a field, $A$ a left and right noetherian $\\mathbb{N}$-graded $k$-algebra such that ${\\rm dim}_k(A_n)< \\infty$ for all $n$, and $J$ a graded two-sided ideal of $A$. If the non-commutative scheme ${\\sf Proj}_{nc}(A)$ is isomorphic to a projective scheme $X$, then there is a closed subscheme $Z \\subsete"},"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":"1507.02497","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-09T13:22:54Z","cross_cats_sorted":[],"title_canon_sha256":"f6aa126e154e119f4bfd6faaa781f3ef5bd83557834440ea3744daaca53b8556","abstract_canon_sha256":"2d0f22ede3130029b252727144e4e1452e1e6e7f2675c99dd588316f04ed355f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:47.289256Z","signature_b64":"MrHNMEAbqx6CQqmZJQ34ZzbyR0SYn43SISIJYmRKqGeSXocYtqoSFcY19LbH5Im+it7EtwGSNvCcYwpcmon+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea64836911fdac5bd71007d5235068a2ec3ed970bd0bfeac870458360708a39e","last_reissued_at":"2026-05-18T01:21:47.288575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:47.288575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Corrigendum to \"Maps between non-commutative spaces\" [Trans. Amer. Math. Soc., 356(7) (2004) 2927-2944]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"S.Paul Smith","submitted_at":"2015-07-09T13:22:54Z","abstract_excerpt":"The statement of Lemma 3.1 in the published paper is not correct. Lemma 3.1 is needed for the proof of Theorem 3.2. Theorem 3.2 as originally stated is true but its \"proof\" is not correct. Here we change the statements and proofs of Lemma 3.1 and Theorem 3.2. We also prove a new result. Let $k$ be a field, $A$ a left and right noetherian $\\mathbb{N}$-graded $k$-algebra such that ${\\rm dim}_k(A_n)< \\infty$ for all $n$, and $J$ a graded two-sided ideal of $A$. If the non-commutative scheme ${\\sf Proj}_{nc}(A)$ is isomorphic to a projective scheme $X$, then there is a closed subscheme $Z \\subsete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02497","kind":"arxiv","version":2},"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":"1507.02497","created_at":"2026-05-18T01:21:47.288701+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.02497v2","created_at":"2026-05-18T01:21:47.288701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02497","created_at":"2026-05-18T01:21:47.288701+00:00"},{"alias_kind":"pith_short_12","alias_value":"5JSIG2IR7WWF","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"5JSIG2IR7WWFXVYQ","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"5JSIG2IR","created_at":"2026-05-18T12:29:05.191682+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/5JSIG2IR7WWFXVYQA7KSGUDIUL","json":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL.json","graph_json":"https://pith.science/api/pith-number/5JSIG2IR7WWFXVYQA7KSGUDIUL/graph.json","events_json":"https://pith.science/api/pith-number/5JSIG2IR7WWFXVYQA7KSGUDIUL/events.json","paper":"https://pith.science/paper/5JSIG2IR"},"agent_actions":{"view_html":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL","download_json":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL.json","view_paper":"https://pith.science/paper/5JSIG2IR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.02497&json=true","fetch_graph":"https://pith.science/api/pith-number/5JSIG2IR7WWFXVYQA7KSGUDIUL/graph.json","fetch_events":"https://pith.science/api/pith-number/5JSIG2IR7WWFXVYQA7KSGUDIUL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL/action/storage_attestation","attest_author":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL/action/author_attestation","sign_citation":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL/action/citation_signature","submit_replication":"https://pith.science/pith/5JSIG2IR7WWFXVYQA7KSGUDIUL/action/replication_record"}},"created_at":"2026-05-18T01:21:47.288701+00:00","updated_at":"2026-05-18T01:21:47.288701+00:00"}