{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WFZXIYXVKEHVJDK4YRDYXBP4FN","short_pith_number":"pith:WFZXIYXV","canonical_record":{"source":{"id":"1106.2172","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-10T20:45:51Z","cross_cats_sorted":[],"title_canon_sha256":"1c7a64b851bd07fa9bedc96521650be3c3af124ed11dd3e276f732fb8cacc851","abstract_canon_sha256":"60ea0553ac84a83d02e9e72377eac443eb0aad8cd0aa67e520a8e02b562346bd"},"schema_version":"1.0"},"canonical_sha256":"b1737462f5510f548d5cc4478b85fc2b6fc3768b37c0dd3597ed4010af6ee5d5","source":{"kind":"arxiv","id":"1106.2172","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2172","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2172v5","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2172","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"WFZXIYXVKEHV","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WFZXIYXVKEHVJDK4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WFZXIYXV","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WFZXIYXVKEHVJDK4YRDYXBP4FN","target":"record","payload":{"canonical_record":{"source":{"id":"1106.2172","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-10T20:45:51Z","cross_cats_sorted":[],"title_canon_sha256":"1c7a64b851bd07fa9bedc96521650be3c3af124ed11dd3e276f732fb8cacc851","abstract_canon_sha256":"60ea0553ac84a83d02e9e72377eac443eb0aad8cd0aa67e520a8e02b562346bd"},"schema_version":"1.0"},"canonical_sha256":"b1737462f5510f548d5cc4478b85fc2b6fc3768b37c0dd3597ed4010af6ee5d5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:49.609434Z","signature_b64":"IlUjiIG0QGjN4c0VIpKUDUpXqWsIcCgXbzUItMCV7kD5UHSpf0ZGor/cCeoc9OVtNOQyusf7Gh89z1EDWoiTDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1737462f5510f548d5cc4478b85fc2b6fc3768b37c0dd3597ed4010af6ee5d5","last_reissued_at":"2026-05-18T01:30:49.609032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:49.609032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.2172","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M21fj5/iOPIe4Um5QknP1tHSCRhn0AGippZZ8IFAW77AvaYMkKlmffKWX453BHSljoRFWh0jShvkkbeeJaEZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:50:36.565754Z"},"content_sha256":"1c22bdb59eeb5f0c65b98bed421d96cb434d60d05fdcd7c53bbf7bc871d13a23","schema_version":"1.0","event_id":"sha256:1c22bdb59eeb5f0c65b98bed421d96cb434d60d05fdcd7c53bbf7bc871d13a23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WFZXIYXVKEHVJDK4YRDYXBP4FN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jacobian discrepancies and rational singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Roi Docampo, Tommaso de Fernex","submitted_at":"2011-06-10T20:45:51Z","abstract_excerpt":"Inspired by several works on jet schemes and motivic integration, we consider an extension to singular varieties of the classical definition of discrepancy for morphisms of smooth varieties. The resulting invariant, which we call Jacobian discrepancy, is closely related to the jet schemes and the Nash blow-up of the variety. This notion leads to a framework in which adjunction and inversion of adjunction hold in full generality, and several consequences are drawn from these properties. The main result of the paper is a formula measuring the gap between the dualizing sheaf and the Grauert-Rieme"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2172","kind":"arxiv","version":5},"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":"2026-05-18T01:30:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7UzSc6zQxq3XH4yQ4rNEKXn0LXAHvfv2jgyz/VESk9UQcqD2g9a8NEXHogzeKtchjuf2Zvt0PR36cVq3xFsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:50:36.566105Z"},"content_sha256":"c298986ad5db8a74055471afd7a17db15e6a8feb762e77ae38bd54795f870b4c","schema_version":"1.0","event_id":"sha256:c298986ad5db8a74055471afd7a17db15e6a8feb762e77ae38bd54795f870b4c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFZXIYXVKEHVJDK4YRDYXBP4FN/bundle.json","state_url":"https://pith.science/pith/WFZXIYXVKEHVJDK4YRDYXBP4FN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFZXIYXVKEHVJDK4YRDYXBP4FN/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":"2026-06-01T07:50:36Z","links":{"resolver":"https://pith.science/pith/WFZXIYXVKEHVJDK4YRDYXBP4FN","bundle":"https://pith.science/pith/WFZXIYXVKEHVJDK4YRDYXBP4FN/bundle.json","state":"https://pith.science/pith/WFZXIYXVKEHVJDK4YRDYXBP4FN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFZXIYXVKEHVJDK4YRDYXBP4FN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WFZXIYXVKEHVJDK4YRDYXBP4FN","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":"60ea0553ac84a83d02e9e72377eac443eb0aad8cd0aa67e520a8e02b562346bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-10T20:45:51Z","title_canon_sha256":"1c7a64b851bd07fa9bedc96521650be3c3af124ed11dd3e276f732fb8cacc851"},"schema_version":"1.0","source":{"id":"1106.2172","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2172","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2172v5","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2172","created_at":"2026-05-18T01:30:49Z"},{"alias_kind":"pith_short_12","alias_value":"WFZXIYXVKEHV","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WFZXIYXVKEHVJDK4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WFZXIYXV","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:c298986ad5db8a74055471afd7a17db15e6a8feb762e77ae38bd54795f870b4c","target":"graph","created_at":"2026-05-18T01:30:49Z","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":"Inspired by several works on jet schemes and motivic integration, we consider an extension to singular varieties of the classical definition of discrepancy for morphisms of smooth varieties. The resulting invariant, which we call Jacobian discrepancy, is closely related to the jet schemes and the Nash blow-up of the variety. This notion leads to a framework in which adjunction and inversion of adjunction hold in full generality, and several consequences are drawn from these properties. The main result of the paper is a formula measuring the gap between the dualizing sheaf and the Grauert-Rieme","authors_text":"Roi Docampo, Tommaso de Fernex","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-10T20:45:51Z","title":"Jacobian discrepancies and rational singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2172","kind":"arxiv","version":5},"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":"sha256:1c22bdb59eeb5f0c65b98bed421d96cb434d60d05fdcd7c53bbf7bc871d13a23","target":"record","created_at":"2026-05-18T01:30:49Z","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":"60ea0553ac84a83d02e9e72377eac443eb0aad8cd0aa67e520a8e02b562346bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-10T20:45:51Z","title_canon_sha256":"1c7a64b851bd07fa9bedc96521650be3c3af124ed11dd3e276f732fb8cacc851"},"schema_version":"1.0","source":{"id":"1106.2172","kind":"arxiv","version":5}},"canonical_sha256":"b1737462f5510f548d5cc4478b85fc2b6fc3768b37c0dd3597ed4010af6ee5d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1737462f5510f548d5cc4478b85fc2b6fc3768b37c0dd3597ed4010af6ee5d5","first_computed_at":"2026-05-18T01:30:49.609032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:49.609032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IlUjiIG0QGjN4c0VIpKUDUpXqWsIcCgXbzUItMCV7kD5UHSpf0ZGor/cCeoc9OVtNOQyusf7Gh89z1EDWoiTDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:49.609434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2172","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c22bdb59eeb5f0c65b98bed421d96cb434d60d05fdcd7c53bbf7bc871d13a23","sha256:c298986ad5db8a74055471afd7a17db15e6a8feb762e77ae38bd54795f870b4c"],"state_sha256":"0f76c0962296ceea3c91476cb083b27c8671b2cdd43dbce5be2e14c85a9af584"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FoYLI2fhLeF7l5sl587BBvLwTMxPff+x0awDXNRBgzlJKULDuiGcjNWDykfdNYfpRJLlk3r0G0Rk0kk0uLcAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:50:36.568113Z","bundle_sha256":"b5696b0488894e6f393539b7f9d10176b2ce1961e003023945afbb26c81b7482"}}