{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:KNNM77LPHU4CPTSHR4FMOCTAS4","short_pith_number":"pith:KNNM77LP","canonical_record":{"source":{"id":"math/0207108","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2002-07-12T14:44:12Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"638da8f3fd160693fec7ff7adee48fa8879793a86083decabbe73cf8afd551b7","abstract_canon_sha256":"eb96b10c881d2e6c26bdb8104e7a326b7bedc1d7c22e293c05bcbf2385d44bff"},"schema_version":"1.0"},"canonical_sha256":"535acffd6f3d3827ce478f0ac70a60973a9edca5d9b64cf8a4ea1a260e6529d2","source":{"kind":"arxiv","id":"math/0207108","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0207108","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0207108v4","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0207108","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"KNNM77LPHU4C","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"KNNM77LPHU4CPTSH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"KNNM77LP","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:KNNM77LPHU4CPTSHR4FMOCTAS4","target":"record","payload":{"canonical_record":{"source":{"id":"math/0207108","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2002-07-12T14:44:12Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"638da8f3fd160693fec7ff7adee48fa8879793a86083decabbe73cf8afd551b7","abstract_canon_sha256":"eb96b10c881d2e6c26bdb8104e7a326b7bedc1d7c22e293c05bcbf2385d44bff"},"schema_version":"1.0"},"canonical_sha256":"535acffd6f3d3827ce478f0ac70a60973a9edca5d9b64cf8a4ea1a260e6529d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:55.988563Z","signature_b64":"fNmiF/Kc2CAzTaEMNjlbVH5fsUyk+4WoFfLko0UyhMkA+hw9hEbv/75mxFzNIFrxrU0hH92kMaLeoqo05H5nBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"535acffd6f3d3827ce478f0ac70a60973a9edca5d9b64cf8a4ea1a260e6529d2","last_reissued_at":"2026-05-18T01:19:55.988040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:55.988040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0207108","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":"2026-05-18T01:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vs+tkQLBv6sJVCRlEx+kbD5qhcQ85sthQCRCCxYFKcO8EyE1yy6Y+LKzyHBIc/y5+vLQ18CV7ZpLH7xhQPpwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:13:16.874049Z"},"content_sha256":"1ae26b489fca40c2e62166ce9abf6589e508bb9fb55eefec4fa933a8c67b6a80","schema_version":"1.0","event_id":"sha256:1ae26b489fca40c2e62166ce9abf6589e508bb9fb55eefec4fa933a8c67b6a80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:KNNM77LPHU4CPTSHR4FMOCTAS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils","license":"","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Mihai Tibar","submitted_at":"2002-07-12T14:44:12Z","abstract_excerpt":"We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0207108","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":"2026-05-18T01:19:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bmb+/ALGL2gmmvBepO3LVbGWfOHKG3A8rup6yY5jP6ENqo8cXQPor035DmI0NFSEKut9T3Nm7zMLhC7JPBtfCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:13:16.874723Z"},"content_sha256":"f3cb83c6a9fc5e9ef4b1286fb34e6d18675a36f77d05e74edf59a1614692ab68","schema_version":"1.0","event_id":"sha256:f3cb83c6a9fc5e9ef4b1286fb34e6d18675a36f77d05e74edf59a1614692ab68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNNM77LPHU4CPTSHR4FMOCTAS4/bundle.json","state_url":"https://pith.science/pith/KNNM77LPHU4CPTSHR4FMOCTAS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNNM77LPHU4CPTSHR4FMOCTAS4/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":"2026-05-31T06:13:16Z","links":{"resolver":"https://pith.science/pith/KNNM77LPHU4CPTSHR4FMOCTAS4","bundle":"https://pith.science/pith/KNNM77LPHU4CPTSHR4FMOCTAS4/bundle.json","state":"https://pith.science/pith/KNNM77LPHU4CPTSHR4FMOCTAS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNNM77LPHU4CPTSHR4FMOCTAS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:KNNM77LPHU4CPTSHR4FMOCTAS4","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":"eb96b10c881d2e6c26bdb8104e7a326b7bedc1d7c22e293c05bcbf2385d44bff","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2002-07-12T14:44:12Z","title_canon_sha256":"638da8f3fd160693fec7ff7adee48fa8879793a86083decabbe73cf8afd551b7"},"schema_version":"1.0","source":{"id":"math/0207108","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0207108","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"math/0207108v4","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0207108","created_at":"2026-05-18T01:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"KNNM77LPHU4C","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"KNNM77LPHU4CPTSH","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"KNNM77LP","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:f3cb83c6a9fc5e9ef4b1286fb34e6d18675a36f77d05e74edf59a1614692ab68","target":"graph","created_at":"2026-05-18T01:19:55Z","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 prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.","authors_text":"Mihai Tibar","cross_cats":["math.CV"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2002-07-12T14:44:12Z","title":"The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0207108","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":"sha256:1ae26b489fca40c2e62166ce9abf6589e508bb9fb55eefec4fa933a8c67b6a80","target":"record","created_at":"2026-05-18T01:19:55Z","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":"eb96b10c881d2e6c26bdb8104e7a326b7bedc1d7c22e293c05bcbf2385d44bff","cross_cats_sorted":["math.CV"],"license":"","primary_cat":"math.AG","submitted_at":"2002-07-12T14:44:12Z","title_canon_sha256":"638da8f3fd160693fec7ff7adee48fa8879793a86083decabbe73cf8afd551b7"},"schema_version":"1.0","source":{"id":"math/0207108","kind":"arxiv","version":4}},"canonical_sha256":"535acffd6f3d3827ce478f0ac70a60973a9edca5d9b64cf8a4ea1a260e6529d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"535acffd6f3d3827ce478f0ac70a60973a9edca5d9b64cf8a4ea1a260e6529d2","first_computed_at":"2026-05-18T01:19:55.988040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:55.988040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fNmiF/Kc2CAzTaEMNjlbVH5fsUyk+4WoFfLko0UyhMkA+hw9hEbv/75mxFzNIFrxrU0hH92kMaLeoqo05H5nBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:55.988563Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0207108","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ae26b489fca40c2e62166ce9abf6589e508bb9fb55eefec4fa933a8c67b6a80","sha256:f3cb83c6a9fc5e9ef4b1286fb34e6d18675a36f77d05e74edf59a1614692ab68"],"state_sha256":"e417c4150a02125353eb775b99ab100c57c96862c3aabab854df0c70031bd226"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kuwPUqLyhK9m52Al+2SLQE5uCii/HBgNs2/56wfNZX2DokBuAbzTRWF7qKZf/sHvn6jHXALPdgCsUiWh4G/dDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:13:16.878170Z","bundle_sha256":"4edf5f893c7fcdc79ea9df58a34a0de15614c83193bdd3526355da0210bd48ba"}}