{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ALY4CU6FKA3T42SDZ2QJD2RBWN","short_pith_number":"pith:ALY4CU6F","canonical_record":{"source":{"id":"1205.4742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-21T20:37:44Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"ff50162e08e6058c7c9228b7f0e963729ea3b197cb90ff053d69242ae5714d5f","abstract_canon_sha256":"335736becee807221c6a67dbe8d0d7a99020be6db11a279fb850d941cc30c41f"},"schema_version":"1.0"},"canonical_sha256":"02f1c153c550373e6a43cea091ea21b3695eecf119a91f5cfd9f5eee9d59df7f","source":{"kind":"arxiv","id":"1205.4742","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4742","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4742v2","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4742","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"ALY4CU6FKA3T","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ALY4CU6FKA3T42SD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ALY4CU6F","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ALY4CU6FKA3T42SDZ2QJD2RBWN","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4742","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-21T20:37:44Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"ff50162e08e6058c7c9228b7f0e963729ea3b197cb90ff053d69242ae5714d5f","abstract_canon_sha256":"335736becee807221c6a67dbe8d0d7a99020be6db11a279fb850d941cc30c41f"},"schema_version":"1.0"},"canonical_sha256":"02f1c153c550373e6a43cea091ea21b3695eecf119a91f5cfd9f5eee9d59df7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:02.406629Z","signature_b64":"vgbBwaH/SJzTAZfQLXTXsG/Q7HDOyqgnuE8amasTUg5xuDGsMjT8jYdZZl+5wYF+myLJHbJ4yWlEXKpn9WkRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02f1c153c550373e6a43cea091ea21b3695eecf119a91f5cfd9f5eee9d59df7f","last_reissued_at":"2026-05-18T03:41:02.405924Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:02.405924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4742","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":"2026-05-18T03:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oYlKwOiNs2hJ2PM/MPSdm213cUXShUOVu+XP0xSqLyp4Nzav9JQpKEB4jKKQzZ/61JIoTIWjckEz2Wjox/2qDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:18:18.712818Z"},"content_sha256":"6364e4c8bc83a7b7bf4373c84ed4f50b13e11ae29290e015492d288b947e80e2","schema_version":"1.0","event_id":"sha256:6364e4c8bc83a7b7bf4373c84ed4f50b13e11ae29290e015492d288b947e80e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ALY4CU6FKA3T42SDZ2QJD2RBWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemann-Roch for Deligne-Mumford stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AG","authors_text":"Dan Edidin","submitted_at":"2012-05-21T20:37:44Z","abstract_excerpt":"We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory together with some basic commutative algebra of Artin rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4742","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":"2026-05-18T03:41:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HpQoRpLi/n4Os1pg6HjSQfWbJdaoSsp5zYTu0Tz2nzTvV2i0sia7LpYl7ppwU+iV6y7Qi0+r7/RGJIxqf3+9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:18:18.713165Z"},"content_sha256":"f91bfbc8e3f523acee86e44f7e7f951825d9af77b54e76d06fc7e4faed3b3f56","schema_version":"1.0","event_id":"sha256:f91bfbc8e3f523acee86e44f7e7f951825d9af77b54e76d06fc7e4faed3b3f56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ALY4CU6FKA3T42SDZ2QJD2RBWN/bundle.json","state_url":"https://pith.science/pith/ALY4CU6FKA3T42SDZ2QJD2RBWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ALY4CU6FKA3T42SDZ2QJD2RBWN/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":"2026-06-05T16:18:18Z","links":{"resolver":"https://pith.science/pith/ALY4CU6FKA3T42SDZ2QJD2RBWN","bundle":"https://pith.science/pith/ALY4CU6FKA3T42SDZ2QJD2RBWN/bundle.json","state":"https://pith.science/pith/ALY4CU6FKA3T42SDZ2QJD2RBWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ALY4CU6FKA3T42SDZ2QJD2RBWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ALY4CU6FKA3T42SDZ2QJD2RBWN","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":"335736becee807221c6a67dbe8d0d7a99020be6db11a279fb850d941cc30c41f","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-21T20:37:44Z","title_canon_sha256":"ff50162e08e6058c7c9228b7f0e963729ea3b197cb90ff053d69242ae5714d5f"},"schema_version":"1.0","source":{"id":"1205.4742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4742","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4742v2","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4742","created_at":"2026-05-18T03:41:02Z"},{"alias_kind":"pith_short_12","alias_value":"ALY4CU6FKA3T","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ALY4CU6FKA3T42SD","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ALY4CU6F","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:f91bfbc8e3f523acee86e44f7e7f951825d9af77b54e76d06fc7e4faed3b3f56","target":"graph","created_at":"2026-05-18T03:41:02Z","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 give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory together with some basic commutative algebra of Artin rings.","authors_text":"Dan Edidin","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-21T20:37:44Z","title":"Riemann-Roch for Deligne-Mumford stacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4742","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":"sha256:6364e4c8bc83a7b7bf4373c84ed4f50b13e11ae29290e015492d288b947e80e2","target":"record","created_at":"2026-05-18T03:41:02Z","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":"335736becee807221c6a67dbe8d0d7a99020be6db11a279fb850d941cc30c41f","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-21T20:37:44Z","title_canon_sha256":"ff50162e08e6058c7c9228b7f0e963729ea3b197cb90ff053d69242ae5714d5f"},"schema_version":"1.0","source":{"id":"1205.4742","kind":"arxiv","version":2}},"canonical_sha256":"02f1c153c550373e6a43cea091ea21b3695eecf119a91f5cfd9f5eee9d59df7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02f1c153c550373e6a43cea091ea21b3695eecf119a91f5cfd9f5eee9d59df7f","first_computed_at":"2026-05-18T03:41:02.405924Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:02.405924Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgbBwaH/SJzTAZfQLXTXsG/Q7HDOyqgnuE8amasTUg5xuDGsMjT8jYdZZl+5wYF+myLJHbJ4yWlEXKpn9WkRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:02.406629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6364e4c8bc83a7b7bf4373c84ed4f50b13e11ae29290e015492d288b947e80e2","sha256:f91bfbc8e3f523acee86e44f7e7f951825d9af77b54e76d06fc7e4faed3b3f56"],"state_sha256":"c52e8710230e30ee119d10e0834d35ffbf89b02d80ec8ffe774fb1b44ad8dae4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7qQ7lLapjlXfKgHidglkTsB4KxGsG3f1WM4atX3vUuM8pEyleJYMW7PE3GhOchLgLAQY/cnl8gwUr2ngeDpfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:18:18.715352Z","bundle_sha256":"212a29e1f27264bb33b0d1148ee5c2935e6d4d282d1ac748c487bebaa8ab41f7"}}