{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PJQWOZ3DYF2PCVBEROGTJJ6GCC","short_pith_number":"pith:PJQWOZ3D","schema_version":"1.0","canonical_sha256":"7a61676763c174f154248b8d34a7c6108b4e0d41dd61579796d1787974b5ed83","source":{"kind":"arxiv","id":"1207.0123","version":4},"attestation_state":"computed","paper":{"title":"The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.KT","authors_text":"Adam Massey","submitted_at":"2012-06-30T18:17:13Z","abstract_excerpt":"We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\\KH$-theory entirely in terms of the torus pieces of open sets forming an open cover of $X$. We then construct conditions under which, given two complete simplicial toric varieties, the two spectra $\\KH(X) \\otimes \\Q$ and $\\KH(Y) \\otimes \\Q$ are weakly equivalent. We apply this result to determine the rational $\\KH$-theory of weighted projective spaces. We next examine $\\K$-regularity for complete toric surfaces; in particular, we show that complete toric surfaces are $\\K_{0}$-regular. We then determine c"},"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":"1207.0123","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-06-30T18:17:13Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"02fcc4dcdeb3e36b2890799a224998a46ffef0a5a60cb81115dfea9e67b54ac3","abstract_canon_sha256":"2db639a3eec8fdeefc38736bf85b952da8c06e9e820910aaafe933535c12ca1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:30.649340Z","signature_b64":"AD8zQ8bI3Vj3vevkKj/RM07GGQamA3IVu9bUEBdeOfuc0IEGMs+GGsUQ0niWdp8/9egKJ1xD6NfcNo/PG4DSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a61676763c174f154248b8d34a7c6108b4e0d41dd61579796d1787974b5ed83","last_reissued_at":"2026-05-18T03:31:30.648549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:30.648549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.KT","authors_text":"Adam Massey","submitted_at":"2012-06-30T18:17:13Z","abstract_excerpt":"We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\\KH$-theory entirely in terms of the torus pieces of open sets forming an open cover of $X$. We then construct conditions under which, given two complete simplicial toric varieties, the two spectra $\\KH(X) \\otimes \\Q$ and $\\KH(Y) \\otimes \\Q$ are weakly equivalent. We apply this result to determine the rational $\\KH$-theory of weighted projective spaces. We next examine $\\K$-regularity for complete toric surfaces; in particular, we show that complete toric surfaces are $\\K_{0}$-regular. We then determine c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0123","kind":"arxiv","version":4},"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":"1207.0123","created_at":"2026-05-18T03:31:30.648672+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.0123v4","created_at":"2026-05-18T03:31:30.648672+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0123","created_at":"2026-05-18T03:31:30.648672+00:00"},{"alias_kind":"pith_short_12","alias_value":"PJQWOZ3DYF2P","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PJQWOZ3DYF2PCVBE","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PJQWOZ3D","created_at":"2026-05-18T12:27:18.751474+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/PJQWOZ3DYF2PCVBEROGTJJ6GCC","json":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC.json","graph_json":"https://pith.science/api/pith-number/PJQWOZ3DYF2PCVBEROGTJJ6GCC/graph.json","events_json":"https://pith.science/api/pith-number/PJQWOZ3DYF2PCVBEROGTJJ6GCC/events.json","paper":"https://pith.science/paper/PJQWOZ3D"},"agent_actions":{"view_html":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC","download_json":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC.json","view_paper":"https://pith.science/paper/PJQWOZ3D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.0123&json=true","fetch_graph":"https://pith.science/api/pith-number/PJQWOZ3DYF2PCVBEROGTJJ6GCC/graph.json","fetch_events":"https://pith.science/api/pith-number/PJQWOZ3DYF2PCVBEROGTJJ6GCC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/action/storage_attestation","attest_author":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/action/author_attestation","sign_citation":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/action/citation_signature","submit_replication":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/action/replication_record"}},"created_at":"2026-05-18T03:31:30.648672+00:00","updated_at":"2026-05-18T03:31:30.648672+00:00"}