{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JZREYXGMDWZXG7O2XTA2PJHUND","short_pith_number":"pith:JZREYXGM","schema_version":"1.0","canonical_sha256":"4e624c5ccc1db3737ddabcc1a7a4f468e1d987a990f7fb160888ac49ac07994a","source":{"kind":"arxiv","id":"2502.00790","version":1},"attestation_state":"computed","paper":{"title":"On minimal model program and Zariski decomposition of potential triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dae-Won Lee, Sung Rak Choi, Sungwook Jang","submitted_at":"2025-02-02T13:09:25Z","abstract_excerpt":"In this paper, we investigate properties of potential triples $(X,\\Delta,D)$ which consists of a pair $(X,\\Delta)$ and a pseudoeffective $\\mathbb{R}$-Cartier divisor $D$. In particular, we show that if $D$ admits a birational Zariski decomposition, then one can associate a generalized pair structure to the potential triple $(X,\\Delta,D)$. Moreover, we can run the generalized MMP on $(K_X+\\Delta+D)$ as special cases. As an application, we also show that for a pklt pair $(X,\\Delta)$, if $-(K_X+\\Delta)$ admits a birational Zariski decomposition with $\\mathrm{NQC}$ positive part, then there exists"},"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":"2502.00790","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-02-02T13:09:25Z","cross_cats_sorted":[],"title_canon_sha256":"593cc700bee47fc74db70c5b1bcf1c191b3b7f5298b5c629b3b3f38da3b6b061","abstract_canon_sha256":"ab56330be5fd3e0329f92d9e5024f13e24951db9f0f2da091cbfbd44d777f8dd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:08:38.485357Z","signature_b64":"LHoRd1cSjeMekrk6tMdgqXob9ert6Qs0R49zQlLFb8PpCkq2Vs0n91rf/I/vvfK3/f/BJJ4tWu71WSZPnnnSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e624c5ccc1db3737ddabcc1a7a4f468e1d987a990f7fb160888ac49ac07994a","last_reissued_at":"2026-07-05T10:08:38.484899Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:08:38.484899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On minimal model program and Zariski decomposition of potential triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dae-Won Lee, Sung Rak Choi, Sungwook Jang","submitted_at":"2025-02-02T13:09:25Z","abstract_excerpt":"In this paper, we investigate properties of potential triples $(X,\\Delta,D)$ which consists of a pair $(X,\\Delta)$ and a pseudoeffective $\\mathbb{R}$-Cartier divisor $D$. In particular, we show that if $D$ admits a birational Zariski decomposition, then one can associate a generalized pair structure to the potential triple $(X,\\Delta,D)$. Moreover, we can run the generalized MMP on $(K_X+\\Delta+D)$ as special cases. As an application, we also show that for a pklt pair $(X,\\Delta)$, if $-(K_X+\\Delta)$ admits a birational Zariski decomposition with $\\mathrm{NQC}$ positive part, then there exists"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00790","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.00790/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2502.00790","created_at":"2026-07-05T10:08:38.484954+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.00790v1","created_at":"2026-07-05T10:08:38.484954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00790","created_at":"2026-07-05T10:08:38.484954+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZREYXGMDWZX","created_at":"2026-07-05T10:08:38.484954+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZREYXGMDWZXG7O2","created_at":"2026-07-05T10:08:38.484954+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZREYXGM","created_at":"2026-07-05T10:08:38.484954+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/JZREYXGMDWZXG7O2XTA2PJHUND","json":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND.json","graph_json":"https://pith.science/api/pith-number/JZREYXGMDWZXG7O2XTA2PJHUND/graph.json","events_json":"https://pith.science/api/pith-number/JZREYXGMDWZXG7O2XTA2PJHUND/events.json","paper":"https://pith.science/paper/JZREYXGM"},"agent_actions":{"view_html":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND","download_json":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND.json","view_paper":"https://pith.science/paper/JZREYXGM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.00790&json=true","fetch_graph":"https://pith.science/api/pith-number/JZREYXGMDWZXG7O2XTA2PJHUND/graph.json","fetch_events":"https://pith.science/api/pith-number/JZREYXGMDWZXG7O2XTA2PJHUND/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND/action/storage_attestation","attest_author":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND/action/author_attestation","sign_citation":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND/action/citation_signature","submit_replication":"https://pith.science/pith/JZREYXGMDWZXG7O2XTA2PJHUND/action/replication_record"}},"created_at":"2026-07-05T10:08:38.484954+00:00","updated_at":"2026-07-05T10:08:38.484954+00:00"}