{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6CSKRJ5Y5ABXT6XUBNFFMX7O4S","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":"92775d941a6de3f7c9bcdb949177537108214e2bc32e5a5a8b138b06bec70a31","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-08T13:34:33Z","title_canon_sha256":"a1e80a29ec1e5692181ef17230ba1cce14b97e98fa59cf5b0df2ddec165a76dc"},"schema_version":"1.0","source":{"id":"1609.02420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.02420","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1609.02420v2","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.02420","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"6CSKRJ5Y5ABX","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6CSKRJ5Y5ABXT6XU","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6CSKRJ5Y","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:1b08d071d543c8eefba159e9026aa69df495a769ceecddf686a900d9d46a7402","target":"graph","created_at":"2026-05-17T23:49:06Z","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 construct two types of non-holomorphic Lefschetz fibrations over $S^2$ with $(-1)$-sections ---hence, they are fiber sum indecomposable--- by giving the corresponding positive relators. One type of the two does not satisfy the slope inequality (a necessary condition for a fibration to be holomorphic) and has a simply-connected total space, and the other has a total space that cannot admit any complex structure in the first place. These give an alternative existence proof for non-holomorphic Lefschetz pencils without Donaldson's theorem.","authors_text":"Naoyuki Monden, Noriyuki Hamada, Ryoma Kobayashi","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-08T13:34:33Z","title":"Non-holomorphic Lefschetz fibrations with $(-1)$-sections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02420","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":"sha256:218e6b171a308d6292f681555d812d2f2a9e3ad5446f35d42f32f35711eeeb84","target":"record","created_at":"2026-05-17T23:49:06Z","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":"92775d941a6de3f7c9bcdb949177537108214e2bc32e5a5a8b138b06bec70a31","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-09-08T13:34:33Z","title_canon_sha256":"a1e80a29ec1e5692181ef17230ba1cce14b97e98fa59cf5b0df2ddec165a76dc"},"schema_version":"1.0","source":{"id":"1609.02420","kind":"arxiv","version":2}},"canonical_sha256":"f0a4a8a7b8e80379faf40b4a565feee490a0d89e52658ba038d9d19e556316ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0a4a8a7b8e80379faf40b4a565feee490a0d89e52658ba038d9d19e556316ad","first_computed_at":"2026-05-17T23:49:06.474892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:06.474892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LF3Omjx8c+fhF7eRUIkTjrqYNcWHRcm3Qioibje37hKIPooF9R0YcbVujqc7GeQfwPOsOkGxdNgDOu8bXNitDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:06.475592Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:218e6b171a308d6292f681555d812d2f2a9e3ad5446f35d42f32f35711eeeb84","sha256:1b08d071d543c8eefba159e9026aa69df495a769ceecddf686a900d9d46a7402"],"state_sha256":"749129f25d57c728ac27ef553eadd16e05ee3b10ebc69583d8e016eed05ea02e"}