{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:AF3ZWOJO2VMAQMANHY32HOVU2W","short_pith_number":"pith:AF3ZWOJO","schema_version":"1.0","canonical_sha256":"01779b392ed55808300d3e37a3bab4d599a234699f486dcd8877f3180e62e579","source":{"kind":"arxiv","id":"1210.2658","version":1},"attestation_state":"computed","paper":{"title":"Singularities on the base of a Fano type fibration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caucher Birkar","submitted_at":"2012-10-09T16:30:54Z","abstract_excerpt":"Let $f\\colon X\\to Z$ be a Mori fibre space. McKernan conjectured that the singularities of $Z$ are bounded in terms of the singularities of $X$. Shokurov generalised this to pairs: let $(X,B)$ be a klt pair and $f\\colon X\\to Z$ a contraction such that $K_X+B\\sim_\\R 0/Z$ and that the general fibres of $f$ are Fano type varieties; adjunction for fibre spaces produces a discriminant divisor $B_Z$ and a moduli divisor $M_Z$ on $Z$. it is then conjectured that the singularities of $(Z,B_Z+M_Z)$ are bounded in terms of the singularities of $(X,B)$. We prove Shokurov conjecture when $(F,\\Supp B_F)$ b"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.2658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-10-09T16:30:54Z","cross_cats_sorted":[],"title_canon_sha256":"c7db4ae05414c47baf633925fca44a0a4889cc68e19d3ed5b4f6ed25c8306f7c","abstract_canon_sha256":"47e8c974906dea03f0d0cbd4721f2e98da66977da7a0efc176d6595c71a55a30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:41.013857Z","signature_b64":"Qb8dISB7OqxKnCgSqtWwADQU9N3qmJs0adAqAYuMtL2vfSQU2wUTDxjIcg3Gft2LnGnCpgIe8K1EBI2AfAMfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01779b392ed55808300d3e37a3bab4d599a234699f486dcd8877f3180e62e579","last_reissued_at":"2026-05-18T03:43:41.013250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:41.013250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Singularities on the base of a Fano type fibration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caucher Birkar","submitted_at":"2012-10-09T16:30:54Z","abstract_excerpt":"Let $f\\colon X\\to Z$ be a Mori fibre space. McKernan conjectured that the singularities of $Z$ are bounded in terms of the singularities of $X$. Shokurov generalised this to pairs: let $(X,B)$ be a klt pair and $f\\colon X\\to Z$ a contraction such that $K_X+B\\sim_\\R 0/Z$ and that the general fibres of $f$ are Fano type varieties; adjunction for fibre spaces produces a discriminant divisor $B_Z$ and a moduli divisor $M_Z$ on $Z$. it is then conjectured that the singularities of $(Z,B_Z+M_Z)$ are bounded in terms of the singularities of $(X,B)$. We prove Shokurov conjecture when $(F,\\Supp B_F)$ b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2658","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.2658","created_at":"2026-05-18T03:43:41.013350+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2658v1","created_at":"2026-05-18T03:43:41.013350+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2658","created_at":"2026-05-18T03:43:41.013350+00:00"},{"alias_kind":"pith_short_12","alias_value":"AF3ZWOJO2VMA","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"AF3ZWOJO2VMAQMAN","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"AF3ZWOJO","created_at":"2026-05-18T12:26:58.693483+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W","json":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W.json","graph_json":"https://pith.science/api/pith-number/AF3ZWOJO2VMAQMANHY32HOVU2W/graph.json","events_json":"https://pith.science/api/pith-number/AF3ZWOJO2VMAQMANHY32HOVU2W/events.json","paper":"https://pith.science/paper/AF3ZWOJO"},"agent_actions":{"view_html":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W","download_json":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W.json","view_paper":"https://pith.science/paper/AF3ZWOJO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2658&json=true","fetch_graph":"https://pith.science/api/pith-number/AF3ZWOJO2VMAQMANHY32HOVU2W/graph.json","fetch_events":"https://pith.science/api/pith-number/AF3ZWOJO2VMAQMANHY32HOVU2W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W/action/storage_attestation","attest_author":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W/action/author_attestation","sign_citation":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W/action/citation_signature","submit_replication":"https://pith.science/pith/AF3ZWOJO2VMAQMANHY32HOVU2W/action/replication_record"}},"created_at":"2026-05-18T03:43:41.013350+00:00","updated_at":"2026-05-18T03:43:41.013350+00:00"}