{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:J6HV7VXOZEP3VS3FIN4AANRBFO","short_pith_number":"pith:J6HV7VXO","canonical_record":{"source":{"id":"1205.3843","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-17T03:26:50Z","cross_cats_sorted":[],"title_canon_sha256":"0e14770ccc27128950b63f720d5ad9941cdf6f4ae31525a0274a77b137a84a6a","abstract_canon_sha256":"77f56ea14a0b8305504932a5d8b353a1ce080b209838811746588d77477b6505"},"schema_version":"1.0"},"canonical_sha256":"4f8f5fd6eec91fbacb6543780036212b84ffd73a5e61a35c7fadb98837156c52","source":{"kind":"arxiv","id":"1205.3843","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3843","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3843v4","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3843","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"J6HV7VXOZEP3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"J6HV7VXOZEP3VS3F","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"J6HV7VXO","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:J6HV7VXOZEP3VS3FIN4AANRBFO","target":"record","payload":{"canonical_record":{"source":{"id":"1205.3843","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-17T03:26:50Z","cross_cats_sorted":[],"title_canon_sha256":"0e14770ccc27128950b63f720d5ad9941cdf6f4ae31525a0274a77b137a84a6a","abstract_canon_sha256":"77f56ea14a0b8305504932a5d8b353a1ce080b209838811746588d77477b6505"},"schema_version":"1.0"},"canonical_sha256":"4f8f5fd6eec91fbacb6543780036212b84ffd73a5e61a35c7fadb98837156c52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:10.378988Z","signature_b64":"ZCVO5co1LuNX1tV1bBavDyUnee/7Eoe4VpsLGV99dNn4YrLgqtMlGOJZpAXZ3ozJF/q25XO9vIfGTqtsC5pmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f8f5fd6eec91fbacb6543780036212b84ffd73a5e61a35c7fadb98837156c52","last_reissued_at":"2026-05-18T00:36:10.378313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:10.378313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.3843","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":"2026-05-18T00:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5U4J5oC/pP6Y/W2GDgnwHAwfJzH4moLlYdlgNKLKROlqktnP6q+rbBa1SxWelKZzVnnqCXrAeVrE/BUYkmKZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:05:00.242131Z"},"content_sha256":"e1c88000acf4527a88eed0a1ed6b0c5fc7c9362003ced0446d41d0d01eb981f2","schema_version":"1.0","event_id":"sha256:e1c88000acf4527a88eed0a1ed6b0c5fc7c9362003ced0446d41d0d01eb981f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:J6HV7VXOZEP3VS3FIN4AANRBFO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free Divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Xia Liao","submitted_at":"2012-05-17T03:26:50Z","abstract_excerpt":"Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on $X$ with respect to $D$, and the Chern-Schwartz-MacPherson class of the complement of $D$ in $X$. Our result confirms a conjectural formula for these classes, at least after push-forward to projective space; it proves the full form of the conjecture for locally quasi-homogeneous free divisors in $\\mathbb P^n$. The result generalizes several previously known results. For example"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3843","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":"2026-05-18T00:36:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i51QrUnAhs7vkK+MMYv347QF8yfYrDTpdJgdVScteUEDMqNl2x13HKdlHn7ewJZbekyc4fV1uqDly4v/1MD8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:05:00.242692Z"},"content_sha256":"de30bf5023d9bdecc833e87649515ac892bd18e7eefa54512dd0ce7d82537012","schema_version":"1.0","event_id":"sha256:de30bf5023d9bdecc833e87649515ac892bd18e7eefa54512dd0ce7d82537012"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J6HV7VXOZEP3VS3FIN4AANRBFO/bundle.json","state_url":"https://pith.science/pith/J6HV7VXOZEP3VS3FIN4AANRBFO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J6HV7VXOZEP3VS3FIN4AANRBFO/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":"2026-06-04T22:05:00Z","links":{"resolver":"https://pith.science/pith/J6HV7VXOZEP3VS3FIN4AANRBFO","bundle":"https://pith.science/pith/J6HV7VXOZEP3VS3FIN4AANRBFO/bundle.json","state":"https://pith.science/pith/J6HV7VXOZEP3VS3FIN4AANRBFO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J6HV7VXOZEP3VS3FIN4AANRBFO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:J6HV7VXOZEP3VS3FIN4AANRBFO","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":"77f56ea14a0b8305504932a5d8b353a1ce080b209838811746588d77477b6505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-17T03:26:50Z","title_canon_sha256":"0e14770ccc27128950b63f720d5ad9941cdf6f4ae31525a0274a77b137a84a6a"},"schema_version":"1.0","source":{"id":"1205.3843","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.3843","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"arxiv_version","alias_value":"1205.3843v4","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.3843","created_at":"2026-05-18T00:36:10Z"},{"alias_kind":"pith_short_12","alias_value":"J6HV7VXOZEP3","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"J6HV7VXOZEP3VS3F","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"J6HV7VXO","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:de30bf5023d9bdecc833e87649515ac892bd18e7eefa54512dd0ce7d82537012","target":"graph","created_at":"2026-05-18T00:36:10Z","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":"Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on $X$ with respect to $D$, and the Chern-Schwartz-MacPherson class of the complement of $D$ in $X$. Our result confirms a conjectural formula for these classes, at least after push-forward to projective space; it proves the full form of the conjecture for locally quasi-homogeneous free divisors in $\\mathbb P^n$. The result generalizes several previously known results. For example","authors_text":"Xia Liao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-17T03:26:50Z","title":"Chern Classes Of Logarithmic Vector Fields For Locally-Homogenous Free Divisors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3843","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:e1c88000acf4527a88eed0a1ed6b0c5fc7c9362003ced0446d41d0d01eb981f2","target":"record","created_at":"2026-05-18T00:36:10Z","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":"77f56ea14a0b8305504932a5d8b353a1ce080b209838811746588d77477b6505","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-05-17T03:26:50Z","title_canon_sha256":"0e14770ccc27128950b63f720d5ad9941cdf6f4ae31525a0274a77b137a84a6a"},"schema_version":"1.0","source":{"id":"1205.3843","kind":"arxiv","version":4}},"canonical_sha256":"4f8f5fd6eec91fbacb6543780036212b84ffd73a5e61a35c7fadb98837156c52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f8f5fd6eec91fbacb6543780036212b84ffd73a5e61a35c7fadb98837156c52","first_computed_at":"2026-05-18T00:36:10.378313Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:10.378313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZCVO5co1LuNX1tV1bBavDyUnee/7Eoe4VpsLGV99dNn4YrLgqtMlGOJZpAXZ3ozJF/q25XO9vIfGTqtsC5pmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:10.378988Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.3843","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1c88000acf4527a88eed0a1ed6b0c5fc7c9362003ced0446d41d0d01eb981f2","sha256:de30bf5023d9bdecc833e87649515ac892bd18e7eefa54512dd0ce7d82537012"],"state_sha256":"8c8b9ee23a0ce4da8b878b3f78d354e5b5128799b32844b40effb6235b9eb1ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T/8/IllBDjofN+DPvkt2YEJbPdRnA/GcxBw8iZu0t/oA1O5UvoYI4/qhC6PjsNadOrByptzfb79GeLXgBBB2AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:05:00.245314Z","bundle_sha256":"ae1ba4bc6d4cdcfeccbd606a11f61cd525dd2cd135bf40cc274bca988ee3d953"}}