{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:AMLLF3KGSKBOAHXVOFOP5VKYWB","short_pith_number":"pith:AMLLF3KG","schema_version":"1.0","canonical_sha256":"0316b2ed469282e01ef5715cfed558b0722b699d0349fe4fc136d0bbfef04849","source":{"kind":"arxiv","id":"1010.5880","version":1},"attestation_state":"computed","paper":{"title":"K_0 of hypersurfaces defined by x_1^2+ ... + x_n^2 = \\pm 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Manoj K Keshari, Satya Mandal","submitted_at":"2010-10-28T07:39:54Z","abstract_excerpt":"Let $k$ be a field of characteristic $\\ne 2$ and let $Q_{n,m}(x_1, ...,x_n,y_1, ...,y_m)=x_1^2+ ... +x_n^2-(y_1^2+ ... +y_m^2)$ be a quadratic form over $k$. Let $R(Q_{n,m})=R_{n,m}=k[x_1, ...,x_n,y_1, ...,y_m]/(Q_{n,m}-1)$. In this note we will calculate $\\wt K_0(R_{n,m})$ for every $n,m \\geq 0$."},"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":"1010.5880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2010-10-28T07:39:54Z","cross_cats_sorted":[],"title_canon_sha256":"187965f3ce456d765c00ea50f7f34c948fe8be1f4457c3d237b1ea81e1fdb71a","abstract_canon_sha256":"f17117d6bd406fd498698d0bfe4917e5f4ceb147c13da84f7c43d8ea367fbff2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:29.164247Z","signature_b64":"bcqV14rqM3L62wawRK6yDSPTjWmGHhsf3BJXHZiCkNGWWg8fCacuhJGnp5YxYdls4XeWKIQbNRFFoCD0uNO/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0316b2ed469282e01ef5715cfed558b0722b699d0349fe4fc136d0bbfef04849","last_reissued_at":"2026-05-18T02:45:29.163689Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:29.163689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"K_0 of hypersurfaces defined by x_1^2+ ... + x_n^2 = \\pm 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Manoj K Keshari, Satya Mandal","submitted_at":"2010-10-28T07:39:54Z","abstract_excerpt":"Let $k$ be a field of characteristic $\\ne 2$ and let $Q_{n,m}(x_1, ...,x_n,y_1, ...,y_m)=x_1^2+ ... +x_n^2-(y_1^2+ ... +y_m^2)$ be a quadratic form over $k$. Let $R(Q_{n,m})=R_{n,m}=k[x_1, ...,x_n,y_1, ...,y_m]/(Q_{n,m}-1)$. In this note we will calculate $\\wt K_0(R_{n,m})$ for every $n,m \\geq 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5880","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":"1010.5880","created_at":"2026-05-18T02:45:29.163773+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.5880v1","created_at":"2026-05-18T02:45:29.163773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5880","created_at":"2026-05-18T02:45:29.163773+00:00"},{"alias_kind":"pith_short_12","alias_value":"AMLLF3KGSKBO","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AMLLF3KGSKBOAHXV","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AMLLF3KG","created_at":"2026-05-18T12:26:05.355336+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/AMLLF3KGSKBOAHXVOFOP5VKYWB","json":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB.json","graph_json":"https://pith.science/api/pith-number/AMLLF3KGSKBOAHXVOFOP5VKYWB/graph.json","events_json":"https://pith.science/api/pith-number/AMLLF3KGSKBOAHXVOFOP5VKYWB/events.json","paper":"https://pith.science/paper/AMLLF3KG"},"agent_actions":{"view_html":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB","download_json":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB.json","view_paper":"https://pith.science/paper/AMLLF3KG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.5880&json=true","fetch_graph":"https://pith.science/api/pith-number/AMLLF3KGSKBOAHXVOFOP5VKYWB/graph.json","fetch_events":"https://pith.science/api/pith-number/AMLLF3KGSKBOAHXVOFOP5VKYWB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB/action/storage_attestation","attest_author":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB/action/author_attestation","sign_citation":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB/action/citation_signature","submit_replication":"https://pith.science/pith/AMLLF3KGSKBOAHXVOFOP5VKYWB/action/replication_record"}},"created_at":"2026-05-18T02:45:29.163773+00:00","updated_at":"2026-05-18T02:45:29.163773+00:00"}