{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ROR5TBDOGSPHDTAHVTUAHEW2R4","short_pith_number":"pith:ROR5TBDO","canonical_record":{"source":{"id":"0709.2087","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.KT","submitted_at":"2007-09-13T14:40:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"77881867260d6dcf01d87afd3cc8a6e4c9f55e906f8e806b38d63f2ef8ebe770","abstract_canon_sha256":"e30229b7a9337f334999a630f56518ed0e8506926acf8df04b75f61947a912ee"},"schema_version":"1.0"},"canonical_sha256":"8ba3d9846e349e71cc07ace80392da8f3f7725d4e7f9d85d423f8db5b9086a5b","source":{"kind":"arxiv","id":"0709.2087","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.2087","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"0709.2087v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2087","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"ROR5TBDOGSPH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ROR5TBDOGSPHDTAH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ROR5TBDO","created_at":"2026-05-18T12:25:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ROR5TBDOGSPHDTAHVTUAHEW2R4","target":"record","payload":{"canonical_record":{"source":{"id":"0709.2087","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.KT","submitted_at":"2007-09-13T14:40:03Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"77881867260d6dcf01d87afd3cc8a6e4c9f55e906f8e806b38d63f2ef8ebe770","abstract_canon_sha256":"e30229b7a9337f334999a630f56518ed0e8506926acf8df04b75f61947a912ee"},"schema_version":"1.0"},"canonical_sha256":"8ba3d9846e349e71cc07ace80392da8f3f7725d4e7f9d85d423f8db5b9086a5b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:31.101341Z","signature_b64":"oXQo7oyQ2B2QK7XhMIiWWRci8iQqDG92Y9UQtObVkz13qCIhgnefcLisTjnIls1Q9JXYLaKd08HXJHQVN+e5Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ba3d9846e349e71cc07ace80392da8f3f7725d4e7f9d85d423f8db5b9086a5b","last_reissued_at":"2026-05-18T04:16:31.100919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:31.100919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0709.2087","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SOMG8uBehEBaJAibUTZtVIWa0fBqT1lepmXaEHgzWF1H4l8pgxayudJarAAK3tGMrynSw/oAxf8nhI907u+oBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:22:07.610922Z"},"content_sha256":"2206825040b220ba2f193e5d01ba7b6bc9058f5314d76f76c18994e7118f0a8d","schema_version":"1.0","event_id":"sha256:2206825040b220ba2f193e5d01ba7b6bc9058f5314d76f76c18994e7118f0a8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ROR5TBDOGSPHDTAHVTUAHEW2R4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $K$-theory of toric varieties","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.KT","authors_text":"Charles Weibel, Christian Haesemeyer, Guillermo Corti\\~nas, Mark E. Walker","submitted_at":"2007-09-13T14:40:03Z","abstract_excerpt":"Recent advances in computational techniques for $K$-theory allow us to describe the $K$-theory of toric varieties in terms of the $K$-theory of fields and simple cohomological data."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2087","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OuER+kEau0X+oXwDURN/p7OFV0JK/48KkTP05gAlKg+3Juqe9GX3G3gHRAvydHU03TuDmASwd2zo6o0vXkjaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:22:07.611595Z"},"content_sha256":"cf20419ebb4bbd3b8f809709c5348b300bb050d106099125247151b68e594b8d","schema_version":"1.0","event_id":"sha256:cf20419ebb4bbd3b8f809709c5348b300bb050d106099125247151b68e594b8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ROR5TBDOGSPHDTAHVTUAHEW2R4/bundle.json","state_url":"https://pith.science/pith/ROR5TBDOGSPHDTAHVTUAHEW2R4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ROR5TBDOGSPHDTAHVTUAHEW2R4/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":"2026-06-06T17:22:07Z","links":{"resolver":"https://pith.science/pith/ROR5TBDOGSPHDTAHVTUAHEW2R4","bundle":"https://pith.science/pith/ROR5TBDOGSPHDTAHVTUAHEW2R4/bundle.json","state":"https://pith.science/pith/ROR5TBDOGSPHDTAHVTUAHEW2R4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ROR5TBDOGSPHDTAHVTUAHEW2R4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ROR5TBDOGSPHDTAHVTUAHEW2R4","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":"e30229b7a9337f334999a630f56518ed0e8506926acf8df04b75f61947a912ee","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.KT","submitted_at":"2007-09-13T14:40:03Z","title_canon_sha256":"77881867260d6dcf01d87afd3cc8a6e4c9f55e906f8e806b38d63f2ef8ebe770"},"schema_version":"1.0","source":{"id":"0709.2087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0709.2087","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"0709.2087v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2087","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"ROR5TBDOGSPH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ROR5TBDOGSPHDTAH","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ROR5TBDO","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:cf20419ebb4bbd3b8f809709c5348b300bb050d106099125247151b68e594b8d","target":"graph","created_at":"2026-05-18T04:16:31Z","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":"Recent advances in computational techniques for $K$-theory allow us to describe the $K$-theory of toric varieties in terms of the $K$-theory of fields and simple cohomological data.","authors_text":"Charles Weibel, Christian Haesemeyer, Guillermo Corti\\~nas, Mark E. Walker","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.KT","submitted_at":"2007-09-13T14:40:03Z","title":"The $K$-theory of toric varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2087","kind":"arxiv","version":1},"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":"sha256:2206825040b220ba2f193e5d01ba7b6bc9058f5314d76f76c18994e7118f0a8d","target":"record","created_at":"2026-05-18T04:16:31Z","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":"e30229b7a9337f334999a630f56518ed0e8506926acf8df04b75f61947a912ee","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.KT","submitted_at":"2007-09-13T14:40:03Z","title_canon_sha256":"77881867260d6dcf01d87afd3cc8a6e4c9f55e906f8e806b38d63f2ef8ebe770"},"schema_version":"1.0","source":{"id":"0709.2087","kind":"arxiv","version":1}},"canonical_sha256":"8ba3d9846e349e71cc07ace80392da8f3f7725d4e7f9d85d423f8db5b9086a5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ba3d9846e349e71cc07ace80392da8f3f7725d4e7f9d85d423f8db5b9086a5b","first_computed_at":"2026-05-18T04:16:31.100919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.100919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oXQo7oyQ2B2QK7XhMIiWWRci8iQqDG92Y9UQtObVkz13qCIhgnefcLisTjnIls1Q9JXYLaKd08HXJHQVN+e5Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.101341Z","signed_message":"canonical_sha256_bytes"},"source_id":"0709.2087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2206825040b220ba2f193e5d01ba7b6bc9058f5314d76f76c18994e7118f0a8d","sha256:cf20419ebb4bbd3b8f809709c5348b300bb050d106099125247151b68e594b8d"],"state_sha256":"a4ee02babc7a81d43084187ee0232f0a242df0482e50f9d0b5e5bfef21c8a220"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZYWRTV4Vqyu9M8wQKu87HvFSgaksatfm4OTGoPAFIy4lIx5aqirc1CToXBzHH3dKKzU3gEdCblqevjVuviIuBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:22:07.615298Z","bundle_sha256":"aa833431eb0a90d538e7d95a3b74a86c1e57b065a95d7790ed865f09683a6511"}}