{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:PP2Z4HY74HCS734LGTXTUSGS5X","short_pith_number":"pith:PP2Z4HY7","schema_version":"1.0","canonical_sha256":"7bf59e1f1fe1c52fef8b34ef3a48d2edf4eae9998578a2e91857df08ec3037a5","source":{"kind":"arxiv","id":"1011.4646","version":3},"attestation_state":"computed","paper":{"title":"On the dual of the mobile cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sung Rak Choi","submitted_at":"2010-11-21T10:07:03Z","abstract_excerpt":"We prove that the cone of mobile divisors and the cone of curves birationally movable in codimension 1 are dual in the $(K+B)$-negative part for a klt pair $(X/Z,B)$. We also prove the structure theorem and the contraction theorem for the expanded cone of curves birationally movable in codimension 1. The duality of the cones gives a partial answer to the problem posed by Sam Payne."},"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":"1011.4646","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-21T10:07:03Z","cross_cats_sorted":[],"title_canon_sha256":"c59661810586facc895a985472852504a9c806a22425962feeeae65f223e219e","abstract_canon_sha256":"af1ea2492a7605e573e5d6f8c57a5b2c7384254817da851fc149bb67f138746b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:40.060764Z","signature_b64":"sz4j4n1Xv9vH7+ccMFqVA1po1BU0rkPHtqPx60iy4AFnY8xfp/SXxMs9QdI/auMjkqsubTJge2SMmUFDdCMqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bf59e1f1fe1c52fef8b34ef3a48d2edf4eae9998578a2e91857df08ec3037a5","last_reissued_at":"2026-05-18T04:22:40.060288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:40.060288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the dual of the mobile cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sung Rak Choi","submitted_at":"2010-11-21T10:07:03Z","abstract_excerpt":"We prove that the cone of mobile divisors and the cone of curves birationally movable in codimension 1 are dual in the $(K+B)$-negative part for a klt pair $(X/Z,B)$. We also prove the structure theorem and the contraction theorem for the expanded cone of curves birationally movable in codimension 1. The duality of the cones gives a partial answer to the problem posed by Sam Payne."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4646","kind":"arxiv","version":3},"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":"1011.4646","created_at":"2026-05-18T04:22:40.060364+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.4646v3","created_at":"2026-05-18T04:22:40.060364+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4646","created_at":"2026-05-18T04:22:40.060364+00:00"},{"alias_kind":"pith_short_12","alias_value":"PP2Z4HY74HCS","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"PP2Z4HY74HCS734L","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"PP2Z4HY7","created_at":"2026-05-18T12:26:12.377268+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/PP2Z4HY74HCS734LGTXTUSGS5X","json":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X.json","graph_json":"https://pith.science/api/pith-number/PP2Z4HY74HCS734LGTXTUSGS5X/graph.json","events_json":"https://pith.science/api/pith-number/PP2Z4HY74HCS734LGTXTUSGS5X/events.json","paper":"https://pith.science/paper/PP2Z4HY7"},"agent_actions":{"view_html":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X","download_json":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X.json","view_paper":"https://pith.science/paper/PP2Z4HY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.4646&json=true","fetch_graph":"https://pith.science/api/pith-number/PP2Z4HY74HCS734LGTXTUSGS5X/graph.json","fetch_events":"https://pith.science/api/pith-number/PP2Z4HY74HCS734LGTXTUSGS5X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X/action/storage_attestation","attest_author":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X/action/author_attestation","sign_citation":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X/action/citation_signature","submit_replication":"https://pith.science/pith/PP2Z4HY74HCS734LGTXTUSGS5X/action/replication_record"}},"created_at":"2026-05-18T04:22:40.060364+00:00","updated_at":"2026-05-18T04:22:40.060364+00:00"}