{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LC3G2EEBOJVARXP6IZGLCVILHZ","short_pith_number":"pith:LC3G2EEB","canonical_record":{"source":{"id":"1610.08458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-26T18:50:58Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"9d00577948ab02ead224093a51985008ed6c6eb21d9757ae674e805393f1410e","abstract_canon_sha256":"845ff23da42261e9964138d34851cd79f387f21fc4d050c5f2858aa7aa38c614"},"schema_version":"1.0"},"canonical_sha256":"58b66d1081726a08ddfe464cb1550b3e59a975091d4318154bb2affcfb9a0b2e","source":{"kind":"arxiv","id":"1610.08458","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08458","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08458v2","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08458","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"LC3G2EEBOJVA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LC3G2EEBOJVARXP6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LC3G2EEB","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LC3G2EEBOJVARXP6IZGLCVILHZ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08458","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-26T18:50:58Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"9d00577948ab02ead224093a51985008ed6c6eb21d9757ae674e805393f1410e","abstract_canon_sha256":"845ff23da42261e9964138d34851cd79f387f21fc4d050c5f2858aa7aa38c614"},"schema_version":"1.0"},"canonical_sha256":"58b66d1081726a08ddfe464cb1550b3e59a975091d4318154bb2affcfb9a0b2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:44.035413Z","signature_b64":"OUJa3Q59VR1n3PlkMDFUAiYogrCAhhd4lvpW4zqPeelqpbdx3OXoOaiuRT85d9GkbbJeqP426ID7O9vnCtmKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58b66d1081726a08ddfe464cb1550b3e59a975091d4318154bb2affcfb9a0b2e","last_reissued_at":"2026-05-18T00:52:44.034911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:44.034911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08458","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSoB5HC9T5l95QxMBb5jB01S/QJ4s5qL3WnXV9mhvX89XmEzidPKlzXI9j+w4+yiG2qskDDGSzVvuVKJMj3wCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:28:20.735104Z"},"content_sha256":"e1b3941c4d08bede128f6d7fed5de8579832b1362c2052d3f03d10db42a3cda5","schema_version":"1.0","event_id":"sha256:e1b3941c4d08bede128f6d7fed5de8579832b1362c2052d3f03d10db42a3cda5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LC3G2EEBOJVARXP6IZGLCVILHZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sections of the Matsumoto-Cadavid-Korkmaz Lefschetz fibration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Noriyuki Hamada","submitted_at":"2016-10-26T18:50:58Z","abstract_excerpt":"We give a maximal set of disjoint $(-1)$-sections of the well-known Lefschetz fibration constructed by Matsumoto, Cadavid and Korkmaz. In fact, we obtain several such sets for a fixed genus, which implies that the Matsumoto-Cadavid-Korkmaz Lefschetz fibration has more than one supporting minimal Lefschetz pencils. We also determine the diffeomorphism types of the obtained supporting minimal Lefschetz pencils."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08458","kind":"arxiv","version":2},"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":"2026-05-18T00:52:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PCpAjVGh1l6B1I9cHelwnurHJRP236CzsFKPWxe57scYVjd/dv0jI3n1b779h891rUFqiwJBIRTTqeH6AbLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:28:20.735464Z"},"content_sha256":"5ed90db235d9b4e485634738dd96166f07aea6f8287efb179fc3096a14d1a0ec","schema_version":"1.0","event_id":"sha256:5ed90db235d9b4e485634738dd96166f07aea6f8287efb179fc3096a14d1a0ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LC3G2EEBOJVARXP6IZGLCVILHZ/bundle.json","state_url":"https://pith.science/pith/LC3G2EEBOJVARXP6IZGLCVILHZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LC3G2EEBOJVARXP6IZGLCVILHZ/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":"2026-06-26T13:28:20Z","links":{"resolver":"https://pith.science/pith/LC3G2EEBOJVARXP6IZGLCVILHZ","bundle":"https://pith.science/pith/LC3G2EEBOJVARXP6IZGLCVILHZ/bundle.json","state":"https://pith.science/pith/LC3G2EEBOJVARXP6IZGLCVILHZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LC3G2EEBOJVARXP6IZGLCVILHZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LC3G2EEBOJVARXP6IZGLCVILHZ","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":"845ff23da42261e9964138d34851cd79f387f21fc4d050c5f2858aa7aa38c614","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-26T18:50:58Z","title_canon_sha256":"9d00577948ab02ead224093a51985008ed6c6eb21d9757ae674e805393f1410e"},"schema_version":"1.0","source":{"id":"1610.08458","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08458","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08458v2","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08458","created_at":"2026-05-18T00:52:44Z"},{"alias_kind":"pith_short_12","alias_value":"LC3G2EEBOJVA","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LC3G2EEBOJVARXP6","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LC3G2EEB","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:5ed90db235d9b4e485634738dd96166f07aea6f8287efb179fc3096a14d1a0ec","target":"graph","created_at":"2026-05-18T00:52:44Z","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 give a maximal set of disjoint $(-1)$-sections of the well-known Lefschetz fibration constructed by Matsumoto, Cadavid and Korkmaz. In fact, we obtain several such sets for a fixed genus, which implies that the Matsumoto-Cadavid-Korkmaz Lefschetz fibration has more than one supporting minimal Lefschetz pencils. We also determine the diffeomorphism types of the obtained supporting minimal Lefschetz pencils.","authors_text":"Noriyuki Hamada","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-26T18:50:58Z","title":"Sections of the Matsumoto-Cadavid-Korkmaz Lefschetz fibration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08458","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:e1b3941c4d08bede128f6d7fed5de8579832b1362c2052d3f03d10db42a3cda5","target":"record","created_at":"2026-05-18T00:52:44Z","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":"845ff23da42261e9964138d34851cd79f387f21fc4d050c5f2858aa7aa38c614","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-10-26T18:50:58Z","title_canon_sha256":"9d00577948ab02ead224093a51985008ed6c6eb21d9757ae674e805393f1410e"},"schema_version":"1.0","source":{"id":"1610.08458","kind":"arxiv","version":2}},"canonical_sha256":"58b66d1081726a08ddfe464cb1550b3e59a975091d4318154bb2affcfb9a0b2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58b66d1081726a08ddfe464cb1550b3e59a975091d4318154bb2affcfb9a0b2e","first_computed_at":"2026-05-18T00:52:44.034911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:44.034911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OUJa3Q59VR1n3PlkMDFUAiYogrCAhhd4lvpW4zqPeelqpbdx3OXoOaiuRT85d9GkbbJeqP426ID7O9vnCtmKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:44.035413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08458","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1b3941c4d08bede128f6d7fed5de8579832b1362c2052d3f03d10db42a3cda5","sha256:5ed90db235d9b4e485634738dd96166f07aea6f8287efb179fc3096a14d1a0ec"],"state_sha256":"4633646734f49ab8e18f5a7d573ac8f9bded6ad0614e37d614381fc8fdeacc8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rn16jBLGMavXy6eoyO/Bq0HW5Zno8OXKm1OtPquvIWNFUxk/P20rdMf56tKGGXsQXMEic8zgfFpi8sP/A4W1CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:28:20.737427Z","bundle_sha256":"ef00b8d9f5ad6683b58e10e28edfc0c44a6e4bd3908a4cabda50d326171984a8"}}