{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:VPPLCT3XAB2GGB4UEUZC2RCQND","short_pith_number":"pith:VPPLCT3X","schema_version":"1.0","canonical_sha256":"abdeb14f77007463079425322d445068fb89ed01dcd2003b6ba3cd86ed50781b","source":{"kind":"arxiv","id":"2005.09836","version":1},"attestation_state":"computed","paper":{"title":"Computations and Complexities of Tarski's Fixed Points and Supermodular Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","econ.TH"],"primary_cat":"cs.GT","authors_text":"Chuangyin Dang, Qi Qi, Yinyu Ye","submitted_at":"2020-05-20T03:32:37Z","abstract_excerpt":"We consider two models of computation for Tarski's order preserving function f related to fixed points in a complete lattice: the oracle function model and the polynomial function model. In both models, we find the first polynomial time algorithm for finding a Tarski's fixed point. In addition, we provide a matching oracle bound for determining the uniqueness in the oracle function model and prove it is Co-NP hard in the polynomial function model. The existence of the pure Nash equilibrium in supermodular games is proved by Tarski's fixed point theorem. Exploring the difference between supermo"},"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":"2005.09836","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2020-05-20T03:32:37Z","cross_cats_sorted":["cs.CC","econ.TH"],"title_canon_sha256":"480cf9bbe08c63acf563e0f1b2ff2faf010e348ad7768b5c2c943207968eb4ae","abstract_canon_sha256":"a9a74f056cd730bdc1a41e27bb116bd5ab23157585b56fb1f92ac2911fab7805"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:04:34.460088Z","signature_b64":"MMkuuUxlKS2+OnY0Sget3WjEA06vHgQ44C/VmcCyIBd3p6GtHCIXwxka/2SzK4RW5xf+KHO/US+1gQ2qPVSzBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abdeb14f77007463079425322d445068fb89ed01dcd2003b6ba3cd86ed50781b","last_reissued_at":"2026-07-05T01:04:34.459651Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:04:34.459651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computations and Complexities of Tarski's Fixed Points and Supermodular Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","econ.TH"],"primary_cat":"cs.GT","authors_text":"Chuangyin Dang, Qi Qi, Yinyu Ye","submitted_at":"2020-05-20T03:32:37Z","abstract_excerpt":"We consider two models of computation for Tarski's order preserving function f related to fixed points in a complete lattice: the oracle function model and the polynomial function model. In both models, we find the first polynomial time algorithm for finding a Tarski's fixed point. In addition, we provide a matching oracle bound for determining the uniqueness in the oracle function model and prove it is Co-NP hard in the polynomial function model. The existence of the pure Nash equilibrium in supermodular games is proved by Tarski's fixed point theorem. Exploring the difference between supermo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.09836","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/2005.09836/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":"2005.09836","created_at":"2026-07-05T01:04:34.459718+00:00"},{"alias_kind":"arxiv_version","alias_value":"2005.09836v1","created_at":"2026-07-05T01:04:34.459718+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.09836","created_at":"2026-07-05T01:04:34.459718+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPPLCT3XAB2G","created_at":"2026-07-05T01:04:34.459718+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPPLCT3XAB2GGB4U","created_at":"2026-07-05T01:04:34.459718+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPPLCT3X","created_at":"2026-07-05T01:04:34.459718+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2308.07923","citing_title":"On the enumeration of Tarski fixed points","ref_index":14,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND","json":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND.json","graph_json":"https://pith.science/api/pith-number/VPPLCT3XAB2GGB4UEUZC2RCQND/graph.json","events_json":"https://pith.science/api/pith-number/VPPLCT3XAB2GGB4UEUZC2RCQND/events.json","paper":"https://pith.science/paper/VPPLCT3X"},"agent_actions":{"view_html":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND","download_json":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND.json","view_paper":"https://pith.science/paper/VPPLCT3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2005.09836&json=true","fetch_graph":"https://pith.science/api/pith-number/VPPLCT3XAB2GGB4UEUZC2RCQND/graph.json","fetch_events":"https://pith.science/api/pith-number/VPPLCT3XAB2GGB4UEUZC2RCQND/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND/action/storage_attestation","attest_author":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND/action/author_attestation","sign_citation":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND/action/citation_signature","submit_replication":"https://pith.science/pith/VPPLCT3XAB2GGB4UEUZC2RCQND/action/replication_record"}},"created_at":"2026-07-05T01:04:34.459718+00:00","updated_at":"2026-07-05T01:04:34.459718+00:00"}