{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:ZJRKDPXLV4MC5AEAKKMVJCA4GQ","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":"39c56e7f8bf587a2345815096aed693ffbaa47510c37567fb4434211f2a28f4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-09-03T14:45:12Z","title_canon_sha256":"d4de957dc7ebccf04d61b2cd40b8863ec47eec8b3ce0f8fa365099198e902c59"},"schema_version":"1.0","source":{"id":"0909.0672","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0672","created_at":"2026-05-18T04:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0672v2","created_at":"2026-05-18T04:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0672","created_at":"2026-05-18T04:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"ZJRKDPXLV4MC","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"ZJRKDPXLV4MC5AEA","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"ZJRKDPXL","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:43078ed0c5e5c0195a2148e49a39baa7969d5d3066930009144e95bbd3377f4b","target":"graph","created_at":"2026-05-18T04:38:17Z","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 classify the minimal surfaces of general type with $K^2 \\leq 4\\chi-8$ whose canonical map is composed with a pencil, up to a finite number of families.\n  More precisely we prove that there is exactly one irreducible family for each value of $\\chi \\gg 0$, $4\\chi-10 \\leq K^2 \\leq 4\\chi-8$. All these surfaces are complete intersections in a toric $4-$fold and bidouble covers of Hirzebruch surfaces. The surfaces with $K^2=4\\chi-8$ were previously constructed by Catanese as bidouble covers of $\\PP^1 \\times \\PP^1$.","authors_text":"Roberto Pignatelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-09-03T14:45:12Z","title":"On surfaces with a canonical pencil"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0672","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":"sha256:43706a3d4729639cf9f0f976b3b386d6aeda34ac9cae4af09d734adf154ffd89","target":"record","created_at":"2026-05-18T04:38:17Z","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":"39c56e7f8bf587a2345815096aed693ffbaa47510c37567fb4434211f2a28f4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-09-03T14:45:12Z","title_canon_sha256":"d4de957dc7ebccf04d61b2cd40b8863ec47eec8b3ce0f8fa365099198e902c59"},"schema_version":"1.0","source":{"id":"0909.0672","kind":"arxiv","version":2}},"canonical_sha256":"ca62a1beebaf182e8080529954881c343baefe2c6ed7c6df619f799c08ec2b24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca62a1beebaf182e8080529954881c343baefe2c6ed7c6df619f799c08ec2b24","first_computed_at":"2026-05-18T04:38:17.420963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:17.420963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Vb62M54gsAY6Px8U+chA92TGt9LZ9BnebFQt25awEH9MFOLxnYO8VhW3/ctcMTNmPKZoj2UaqhLExctK1FXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:17.421640Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0672","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43706a3d4729639cf9f0f976b3b386d6aeda34ac9cae4af09d734adf154ffd89","sha256:43078ed0c5e5c0195a2148e49a39baa7969d5d3066930009144e95bbd3377f4b"],"state_sha256":"05c90e1c17fc16e9e6ea7ff05c747d5e4af12ddc2ccb78b178f165178ba59f82"}