{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PJQWOZ3DYF2PCVBEROGTJJ6GCC","short_pith_number":"pith:PJQWOZ3D","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"},"canonical_sha256":"7a61676763c174f154248b8d34a7c6108b4e0d41dd61579796d1787974b5ed83","source":{"kind":"arxiv","id":"1207.0123","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0123","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0123v4","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0123","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"PJQWOZ3DYF2P","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PJQWOZ3DYF2PCVBE","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PJQWOZ3D","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PJQWOZ3DYF2PCVBEROGTJJ6GCC","target":"record","payload":{"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"},"canonical_sha256":"7a61676763c174f154248b8d34a7c6108b4e0d41dd61579796d1787974b5ed83","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"},"source_kind":"arxiv","source_id":"1207.0123","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3/IB7PVT+52LzpysbrOLvPe0wGUJ01dsJLJ1OGv2g2j0Az0B5wEvNQ87+KWwrQIgWfiCc0yjWOwnH3ewIZo0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:36:51.082447Z"},"content_sha256":"5c7076fae63aff289621bb925b6234c5215375f0b5822432f86658d52f012138","schema_version":"1.0","event_id":"sha256:5c7076fae63aff289621bb925b6234c5215375f0b5822432f86658d52f012138"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PJQWOZ3DYF2PCVBEROGTJJ6GCC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:31:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4iMhE7ntZGh6mF9VLidctAs+J1nx9CfDQRan/qkp9j72bhiaobvXp/dKHF2VA1MBDfBVTU3rq2tXD//dt/6nAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T13:36:51.082791Z"},"content_sha256":"826e3be5979629405de74533b56be3a1f32c6b18002cd11bfcbbbc932a7a8fc4","schema_version":"1.0","event_id":"sha256:826e3be5979629405de74533b56be3a1f32c6b18002cd11bfcbbbc932a7a8fc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/bundle.json","state_url":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T13:36:51Z","links":{"resolver":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC","bundle":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/bundle.json","state":"https://pith.science/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJQWOZ3DYF2PCVBEROGTJJ6GCC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PJQWOZ3DYF2PCVBEROGTJJ6GCC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2db639a3eec8fdeefc38736bf85b952da8c06e9e820910aaafe933535c12ca1b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-06-30T18:17:13Z","title_canon_sha256":"02fcc4dcdeb3e36b2890799a224998a46ffef0a5a60cb81115dfea9e67b54ac3"},"schema_version":"1.0","source":{"id":"1207.0123","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.0123","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"arxiv_version","alias_value":"1207.0123v4","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.0123","created_at":"2026-05-18T03:31:30Z"},{"alias_kind":"pith_short_12","alias_value":"PJQWOZ3DYF2P","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PJQWOZ3DYF2PCVBE","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PJQWOZ3D","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:826e3be5979629405de74533b56be3a1f32c6b18002cd11bfcbbbc932a7a8fc4","target":"graph","created_at":"2026-05-18T03:31:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Adam Massey","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-06-30T18:17:13Z","title":"The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0123","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5c7076fae63aff289621bb925b6234c5215375f0b5822432f86658d52f012138","target":"record","created_at":"2026-05-18T03:31:30Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2db639a3eec8fdeefc38736bf85b952da8c06e9e820910aaafe933535c12ca1b","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2012-06-30T18:17:13Z","title_canon_sha256":"02fcc4dcdeb3e36b2890799a224998a46ffef0a5a60cb81115dfea9e67b54ac3"},"schema_version":"1.0","source":{"id":"1207.0123","kind":"arxiv","version":4}},"canonical_sha256":"7a61676763c174f154248b8d34a7c6108b4e0d41dd61579796d1787974b5ed83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a61676763c174f154248b8d34a7c6108b4e0d41dd61579796d1787974b5ed83","first_computed_at":"2026-05-18T03:31:30.648549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:30.648549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AD8zQ8bI3Vj3vevkKj/RM07GGQamA3IVu9bUEBdeOfuc0IEGMs+GGsUQ0niWdp8/9egKJ1xD6NfcNo/PG4DSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:30.649340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.0123","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c7076fae63aff289621bb925b6234c5215375f0b5822432f86658d52f012138","sha256:826e3be5979629405de74533b56be3a1f32c6b18002cd11bfcbbbc932a7a8fc4"],"state_sha256":"fbeac0d30ae62b2ffeb66a77535174be45e1a68e90421f23c79c2c6ca425b366"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LxVt6vOf5nHDXOT/bK2ZhQIKUSiWBAntbNfsCFU2WqSDNiogcdcl2aA5a9qdF3qWa3DVFdK9M1NieLji82nhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T13:36:51.084686Z","bundle_sha256":"b6f5a6ad05bf4c056b4c9be29aad1b1f61a1ec8326a3b3f3c1fb25bd0aa1dc8a"}}