{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PD4RE53BMUCRZGGSPKFXXRLXOZ","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":"cd56e3a6ded53379ff6b999dc1b88f0b5f13b80e9c702b96e249faa28e90a98f","cross_cats_sorted":["cs.AI","cs.DS","cs.LO","cs.PL"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.GT","submitted_at":"2025-08-16T02:18:43Z","title_canon_sha256":"91dbcbef9223ead65a4e47fed1615ab38a78b626fc202d1ae32e451de8f840ec"},"schema_version":"1.0","source":{"id":"2508.11874","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.11874","created_at":"2026-06-09T02:07:06Z"},{"alias_kind":"arxiv_version","alias_value":"2508.11874v2","created_at":"2026-06-09T02:07:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.11874","created_at":"2026-06-09T02:07:06Z"},{"alias_kind":"pith_short_12","alias_value":"PD4RE53BMUCR","created_at":"2026-06-09T02:07:06Z"},{"alias_kind":"pith_short_16","alias_value":"PD4RE53BMUCRZGGS","created_at":"2026-06-09T02:07:06Z"},{"alias_kind":"pith_short_8","alias_value":"PD4RE53B","created_at":"2026-06-09T02:07:06Z"}],"graph_snapshots":[{"event_id":"sha256:27245be7ad31e6cf2626d858adf76026e7d8fa1b4ecf34cf00aa806c92bfe7c9","target":"graph","created_at":"2026-06-09T02:07:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.11874/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Designing polynomial-time algorithms for approximate Nash equilibria (ANE) with provable worst-case guarantees is a fundamental open problem in algorithmic game theory. While large language models (LLMs) can generate candidate algorithms at scale, certifying worst-case guarantees requires formal analysis over all game instances -- a task for which no automated system previously existed. Here, we present LegoNE, a framework encoding expert proof strategies into a symbolic language that automatically compiles any candidate algorithm into a finite optimization problem certifying its worst-case gu","authors_text":"Dongchen Li, Hanyu Li, Xiaotie Deng","cross_cats":["cs.AI","cs.DS","cs.LO","cs.PL"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.GT","submitted_at":"2025-08-16T02:18:43Z","title":"Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11874","kind":"arxiv","version":2},"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":"sha256:4da75b5cc1df82c35bd03a8439b8f6a34ee16ed8e039a5c23c41f0bddb519e57","target":"record","created_at":"2026-06-09T02:07:06Z","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":"cd56e3a6ded53379ff6b999dc1b88f0b5f13b80e9c702b96e249faa28e90a98f","cross_cats_sorted":["cs.AI","cs.DS","cs.LO","cs.PL"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.GT","submitted_at":"2025-08-16T02:18:43Z","title_canon_sha256":"91dbcbef9223ead65a4e47fed1615ab38a78b626fc202d1ae32e451de8f840ec"},"schema_version":"1.0","source":{"id":"2508.11874","kind":"arxiv","version":2}},"canonical_sha256":"78f912776165051c98d27a8b7bc577766a8409a02b16f8a45b67c3d8d9159cd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f912776165051c98d27a8b7bc577766a8409a02b16f8a45b67c3d8d9159cd0","first_computed_at":"2026-06-09T02:07:06.581284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:06.581284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UoT8xYSO0MmigdvzcfvjC7NpJfTqhe/i63yacFiRx5mrxz4rnlst1Qsxjob/WP0CeI4DKMNa28so+xq1cO5aAA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:06.582223Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.11874","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4da75b5cc1df82c35bd03a8439b8f6a34ee16ed8e039a5c23c41f0bddb519e57","sha256:27245be7ad31e6cf2626d858adf76026e7d8fa1b4ecf34cf00aa806c92bfe7c9"],"state_sha256":"1336e312a4e0e375d42b07fac5d35dd219dcb2ddab9f85c7be373d5cd5f428c5"}