{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z3O5V2FSFYTNYTNKKCRONDARPN","short_pith_number":"pith:Z3O5V2FS","canonical_record":{"source":{"id":"1409.6593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-23T15:24:22Z","cross_cats_sorted":[],"title_canon_sha256":"e883b2c99ef1720296cc8e534d6426eb9c75dd882165cfb9318604150700dbc6","abstract_canon_sha256":"054e7698ce335f93543c2a30760b93c2382b782a1894256868b378745daf0b2c"},"schema_version":"1.0"},"canonical_sha256":"cedddae8b22e26dc4daa50a2e68c117b6756767a8caa77e5178e9982e4717757","source":{"kind":"arxiv","id":"1409.6593","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6593","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6593v1","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6593","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"Z3O5V2FSFYTN","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3O5V2FSFYTNYTNK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3O5V2FS","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z3O5V2FSFYTNYTNKKCRONDARPN","target":"record","payload":{"canonical_record":{"source":{"id":"1409.6593","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-23T15:24:22Z","cross_cats_sorted":[],"title_canon_sha256":"e883b2c99ef1720296cc8e534d6426eb9c75dd882165cfb9318604150700dbc6","abstract_canon_sha256":"054e7698ce335f93543c2a30760b93c2382b782a1894256868b378745daf0b2c"},"schema_version":"1.0"},"canonical_sha256":"cedddae8b22e26dc4daa50a2e68c117b6756767a8caa77e5178e9982e4717757","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:44.268215Z","signature_b64":"c22eBH6h57Ez7KQxWIn8lgGtYoggin+IrES8ZhAPQ0iylHgcMii7V4aiJlVTEdU7mW2omSyK8Ve3tt6uArU+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cedddae8b22e26dc4daa50a2e68c117b6756767a8caa77e5178e9982e4717757","last_reissued_at":"2026-05-18T01:17:44.267607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:44.267607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.6593","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbmfbXG4i42FRHBGYHn2+K5ULNM30DUpSxjkx+v5yfEE16IzX0sBoXyihHge7tkp9k/L0UvY03gKL8tLbpK/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:48:00.860366Z"},"content_sha256":"499a3e9c26fde78eb563354d090bf5cb0fc6addd75492741732d783949920e89","schema_version":"1.0","event_id":"sha256:499a3e9c26fde78eb563354d090bf5cb0fc6addd75492741732d783949920e89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z3O5V2FSFYTNYTNKKCRONDARPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the minimal number of singular fibers with non-compact Jacobians for families of curves over $\\mathbb P^1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kang Zuo, Sheng-Li Tan, Wan-Yuan Xu, Xin Lu","submitted_at":"2014-09-23T15:24:22Z","abstract_excerpt":"Let $f:X \\to \\mathbb{P}^1$ be a non-isotrivial family of semi-stable curves of genus $g\\geq 1$ defined over an algebraically closed field $k$ with $s_{nc}$ singular fibers whose Jacobians are non-compact. We prove that $s_{nc}\\geq 5$ if $k=\\mathbb C$ and $g\\geq 5$; we also prove that $s_{nc}\\geq 4$ if ${\\rm char}~k>0$ and the relative Jacobian of $f$ is non-smooth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6593","kind":"arxiv","version":1},"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":"2026-05-18T01:17:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cC2rtiQDDgUfxcnJTytcQvqU9j29fDT972mE+kxYZVSQE7ToJ3peU+9JSpl5qqdV9ckvfyF3quIqCl5mna4yDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:48:00.861100Z"},"content_sha256":"c57d3c700b48d92eaa1db21beeea91d8767019f7961b26d40fb4c16ad4709d65","schema_version":"1.0","event_id":"sha256:c57d3c700b48d92eaa1db21beeea91d8767019f7961b26d40fb4c16ad4709d65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3O5V2FSFYTNYTNKKCRONDARPN/bundle.json","state_url":"https://pith.science/pith/Z3O5V2FSFYTNYTNKKCRONDARPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3O5V2FSFYTNYTNKKCRONDARPN/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":"2026-05-27T14:48:00Z","links":{"resolver":"https://pith.science/pith/Z3O5V2FSFYTNYTNKKCRONDARPN","bundle":"https://pith.science/pith/Z3O5V2FSFYTNYTNKKCRONDARPN/bundle.json","state":"https://pith.science/pith/Z3O5V2FSFYTNYTNKKCRONDARPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3O5V2FSFYTNYTNKKCRONDARPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z3O5V2FSFYTNYTNKKCRONDARPN","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":"054e7698ce335f93543c2a30760b93c2382b782a1894256868b378745daf0b2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-23T15:24:22Z","title_canon_sha256":"e883b2c99ef1720296cc8e534d6426eb9c75dd882165cfb9318604150700dbc6"},"schema_version":"1.0","source":{"id":"1409.6593","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.6593","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"1409.6593v1","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.6593","created_at":"2026-05-18T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"Z3O5V2FSFYTN","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z3O5V2FSFYTNYTNK","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z3O5V2FS","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:c57d3c700b48d92eaa1db21beeea91d8767019f7961b26d40fb4c16ad4709d65","target":"graph","created_at":"2026-05-18T01:17:44Z","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":"Let $f:X \\to \\mathbb{P}^1$ be a non-isotrivial family of semi-stable curves of genus $g\\geq 1$ defined over an algebraically closed field $k$ with $s_{nc}$ singular fibers whose Jacobians are non-compact. We prove that $s_{nc}\\geq 5$ if $k=\\mathbb C$ and $g\\geq 5$; we also prove that $s_{nc}\\geq 4$ if ${\\rm char}~k>0$ and the relative Jacobian of $f$ is non-smooth.","authors_text":"Kang Zuo, Sheng-Li Tan, Wan-Yuan Xu, Xin Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-23T15:24:22Z","title":"On the minimal number of singular fibers with non-compact Jacobians for families of curves over $\\mathbb P^1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6593","kind":"arxiv","version":1},"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":"sha256:499a3e9c26fde78eb563354d090bf5cb0fc6addd75492741732d783949920e89","target":"record","created_at":"2026-05-18T01:17:44Z","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":"054e7698ce335f93543c2a30760b93c2382b782a1894256868b378745daf0b2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-23T15:24:22Z","title_canon_sha256":"e883b2c99ef1720296cc8e534d6426eb9c75dd882165cfb9318604150700dbc6"},"schema_version":"1.0","source":{"id":"1409.6593","kind":"arxiv","version":1}},"canonical_sha256":"cedddae8b22e26dc4daa50a2e68c117b6756767a8caa77e5178e9982e4717757","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cedddae8b22e26dc4daa50a2e68c117b6756767a8caa77e5178e9982e4717757","first_computed_at":"2026-05-18T01:17:44.267607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:44.267607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c22eBH6h57Ez7KQxWIn8lgGtYoggin+IrES8ZhAPQ0iylHgcMii7V4aiJlVTEdU7mW2omSyK8Ve3tt6uArU+AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:44.268215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.6593","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:499a3e9c26fde78eb563354d090bf5cb0fc6addd75492741732d783949920e89","sha256:c57d3c700b48d92eaa1db21beeea91d8767019f7961b26d40fb4c16ad4709d65"],"state_sha256":"e1cf66143648014b52f7e4666ed9720c1e7991f65cf42fd034afb6b1d56097e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+O7bxwZGJhuW7zw3nVOf5VwWG4pZvhU/xgNH6ANDpqcQ9hIo5Cp4K8/+dnBeQSRWpCUnaCBxPEmyOmJksVujCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:48:00.864982Z","bundle_sha256":"b071ffdd73dc7e35b60ef6322675f4d73c2ac0a3cd321ec3cacfad932e11ccec"}}