{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:TYTJYOMPR3LHPYLKZX5YFQEXXM","short_pith_number":"pith:TYTJYOMP","canonical_record":{"source":{"id":"math/0206116","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2002-06-11T15:48:53Z","cross_cats_sorted":[],"title_canon_sha256":"5db269eba22255fe7a1c268805ff23f5c6facca396f52c4ad0e009c887c7dff1","abstract_canon_sha256":"88275b9b5374d12475e1d8d90873c3dcfa0d4f6a8b8a93bda6ce90e01a31b190"},"schema_version":"1.0"},"canonical_sha256":"9e269c398f8ed677e16acdfb82c097bb1517069cf26fd0ca625a8713b7c76d5c","source":{"kind":"arxiv","id":"math/0206116","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0206116","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0206116v2","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0206116","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"TYTJYOMPR3LH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"TYTJYOMPR3LHPYLK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"TYTJYOMP","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:TYTJYOMPR3LHPYLKZX5YFQEXXM","target":"record","payload":{"canonical_record":{"source":{"id":"math/0206116","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2002-06-11T15:48:53Z","cross_cats_sorted":[],"title_canon_sha256":"5db269eba22255fe7a1c268805ff23f5c6facca396f52c4ad0e009c887c7dff1","abstract_canon_sha256":"88275b9b5374d12475e1d8d90873c3dcfa0d4f6a8b8a93bda6ce90e01a31b190"},"schema_version":"1.0"},"canonical_sha256":"9e269c398f8ed677e16acdfb82c097bb1517069cf26fd0ca625a8713b7c76d5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:29.516471Z","signature_b64":"xR8z3E0Zock1MwleS9r/StCCrUwUSWBzj9gELAQvAWXgGMFHatnnHSHDmFrTCeWvYmouWX7Tsuu6QhtKru/OBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e269c398f8ed677e16acdfb82c097bb1517069cf26fd0ca625a8713b7c76d5c","last_reissued_at":"2026-05-18T01:05:29.515832Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:29.515832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0206116","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jDyrPYu7oT+ig0yCBE8oMl4xXCghzy/DQj+ErvC0IyFrPrWMv0CL/oNGLfuafLT6facni/9ig9gOEcC5kl5MDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:53:42.299909Z"},"content_sha256":"a77d708660444d9173f209d6f5da47b3890c97551122c08c833f24d24604c5e0","schema_version":"1.0","event_id":"sha256:a77d708660444d9173f209d6f5da47b3890c97551122c08c833f24d24604c5e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:TYTJYOMPR3LHPYLKZX5YFQEXXM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemann-Roch for quotients and Todd classes of simplicial toric varieties","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dan Edidin, William Graham","submitted_at":"2002-06-11T15:48:53Z","abstract_excerpt":"In this paper we give an explicit formula for the Riemann-Roch map for singular schemes which are quotients of smooth schemes by diagonalizable groups. As an application we obtain a simple proof of a formula for the Todd class of a simplicial toric variety. An equivariant version of this formula was previously obtained for complete simplicial toric varieties by Brion and Vergne using different techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206116","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLRRifpD+mrudNCdxQk/8S5FLW7CGctoqdO84p82TOsRN1AgcpP8RJZgak3rcqXg+gXY7VKdqePLXmNvRCTACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:53:42.300607Z"},"content_sha256":"4d83787989ede54730fbd61b4f78eb470013135908c7e292aaf14b032c8ba42f","schema_version":"1.0","event_id":"sha256:4d83787989ede54730fbd61b4f78eb470013135908c7e292aaf14b032c8ba42f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYTJYOMPR3LHPYLKZX5YFQEXXM/bundle.json","state_url":"https://pith.science/pith/TYTJYOMPR3LHPYLKZX5YFQEXXM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYTJYOMPR3LHPYLKZX5YFQEXXM/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":"2026-05-25T16:53:42Z","links":{"resolver":"https://pith.science/pith/TYTJYOMPR3LHPYLKZX5YFQEXXM","bundle":"https://pith.science/pith/TYTJYOMPR3LHPYLKZX5YFQEXXM/bundle.json","state":"https://pith.science/pith/TYTJYOMPR3LHPYLKZX5YFQEXXM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYTJYOMPR3LHPYLKZX5YFQEXXM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:TYTJYOMPR3LHPYLKZX5YFQEXXM","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":"88275b9b5374d12475e1d8d90873c3dcfa0d4f6a8b8a93bda6ce90e01a31b190","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2002-06-11T15:48:53Z","title_canon_sha256":"5db269eba22255fe7a1c268805ff23f5c6facca396f52c4ad0e009c887c7dff1"},"schema_version":"1.0","source":{"id":"math/0206116","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0206116","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"math/0206116v2","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0206116","created_at":"2026-05-18T01:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"TYTJYOMPR3LH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"TYTJYOMPR3LHPYLK","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"TYTJYOMP","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:4d83787989ede54730fbd61b4f78eb470013135908c7e292aaf14b032c8ba42f","target":"graph","created_at":"2026-05-18T01:05:29Z","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":"In this paper we give an explicit formula for the Riemann-Roch map for singular schemes which are quotients of smooth schemes by diagonalizable groups. As an application we obtain a simple proof of a formula for the Todd class of a simplicial toric variety. An equivariant version of this formula was previously obtained for complete simplicial toric varieties by Brion and Vergne using different techniques.","authors_text":"Dan Edidin, William Graham","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2002-06-11T15:48:53Z","title":"Riemann-Roch for quotients and Todd classes of simplicial toric varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206116","kind":"arxiv","version":2},"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:a77d708660444d9173f209d6f5da47b3890c97551122c08c833f24d24604c5e0","target":"record","created_at":"2026-05-18T01:05:29Z","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":"88275b9b5374d12475e1d8d90873c3dcfa0d4f6a8b8a93bda6ce90e01a31b190","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2002-06-11T15:48:53Z","title_canon_sha256":"5db269eba22255fe7a1c268805ff23f5c6facca396f52c4ad0e009c887c7dff1"},"schema_version":"1.0","source":{"id":"math/0206116","kind":"arxiv","version":2}},"canonical_sha256":"9e269c398f8ed677e16acdfb82c097bb1517069cf26fd0ca625a8713b7c76d5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e269c398f8ed677e16acdfb82c097bb1517069cf26fd0ca625a8713b7c76d5c","first_computed_at":"2026-05-18T01:05:29.515832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:29.515832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xR8z3E0Zock1MwleS9r/StCCrUwUSWBzj9gELAQvAWXgGMFHatnnHSHDmFrTCeWvYmouWX7Tsuu6QhtKru/OBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:29.516471Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0206116","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a77d708660444d9173f209d6f5da47b3890c97551122c08c833f24d24604c5e0","sha256:4d83787989ede54730fbd61b4f78eb470013135908c7e292aaf14b032c8ba42f"],"state_sha256":"fcb7b4acf56b46503782c39eaeed1343664eeda146f1435cd0a8092858a457f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"leB+avf+CQ1GCJqJC2EqxtrR4+J1ajyCNUwgIolwaQRyFZWt5GyNjcbPHN/PJ8cgknfFg4wbo3hcA1NLDmIXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:53:42.304605Z","bundle_sha256":"c617b76c99d45442ea172b0aa367f4a35d5cf0d8e465d5cd90a369ff0205ba8c"}}