{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:U5TGQBKRL754FPFEQJDFLLMNZ5","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":"69039c5b58a97fbf70b59271e9d1e3af92300c84c7640c8aaa8ee6c46441a997","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-12T17:31:40Z","title_canon_sha256":"fa23368db620ab380e6318c64bcb6e260b7a8d86e38cd8c4c96d25ff743fee7a"},"schema_version":"1.0","source":{"id":"0910.2142","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2142","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2142v2","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2142","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"U5TGQBKRL754","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"U5TGQBKRL754FPFE","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"U5TGQBKR","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:dfe6bb3f41f6b051b7cb85fcdfe2dd12718917007d90e9819365a09b5a6db467","target":"graph","created_at":"2026-05-18T02:38:18Z","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":"Bidouble covers $\\pi : S \\mapsto Q$ of the quadric Q are parametrized by connected families depending on four positive integers a,b,c,d. In the special case where b=d we call them abc-surfaces.\n  Such a Galois covering $\\pi$ admits a small perturbation yielding a general 4-tuple covering of Q with branch curve $\\De$, and a natural Lefschetz fibration obtained from a small perturbation of the composition of $ \\pi$ with the first projection.\n  We prove a more general result implying that the braid monodromy factorization corresponding to $\\De$ determines the three integers a,b,c in the case of a","authors_text":"Bronislaw Wajnryb (Technical University of Rzeszow), Fabrizio Catanese (Universitaet Bayreuth), Michael L\\\"onne (Universitaet Goettingen)","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-12T17:31:40Z","title":"Moduli spaces and braid monodromy types of bidouble covers of the quadric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2142","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":"sha256:02ba7a5c61b600d71036d698e31977f237ecc7da12093592ae37f42c96f46a20","target":"record","created_at":"2026-05-18T02:38:18Z","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":"69039c5b58a97fbf70b59271e9d1e3af92300c84c7640c8aaa8ee6c46441a997","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-12T17:31:40Z","title_canon_sha256":"fa23368db620ab380e6318c64bcb6e260b7a8d86e38cd8c4c96d25ff743fee7a"},"schema_version":"1.0","source":{"id":"0910.2142","kind":"arxiv","version":2}},"canonical_sha256":"a7666805515ffbc2bca4824655ad8dcf6b2cbfad760bb16d159e74e0aceffc87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7666805515ffbc2bca4824655ad8dcf6b2cbfad760bb16d159e74e0aceffc87","first_computed_at":"2026-05-18T02:38:18.766690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.766690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mRpE8tgLO5uOuO7o2T1ScRJqHf4qD7fFPQPCGn+mm8fKKEerrUyiWymWkL26hKuJ1WdxEvW7uEUcgjJ9juO1Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.767173Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2142","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02ba7a5c61b600d71036d698e31977f237ecc7da12093592ae37f42c96f46a20","sha256:dfe6bb3f41f6b051b7cb85fcdfe2dd12718917007d90e9819365a09b5a6db467"],"state_sha256":"d51b71197df36d14a8e4283126569de86e1de844c98a71854837258ef60e7ec3"}