{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JO4WUZPRBQXDSJG7LVMQC3MS7A","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":"2f5642e9675b00d38a7aa3536f15aaaf1874904525235cd331d64db2c574b88b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T18:50:10Z","title_canon_sha256":"14bbbb104580a19d7df43f4afb60a89bf4caabb29671159dae49bbb6c87ff45f"},"schema_version":"1.0","source":{"id":"2410.08304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08304","created_at":"2026-07-05T09:18:55Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08304v1","created_at":"2026-07-05T09:18:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08304","created_at":"2026-07-05T09:18:55Z"},{"alias_kind":"pith_short_12","alias_value":"JO4WUZPRBQXD","created_at":"2026-07-05T09:18:55Z"},{"alias_kind":"pith_short_16","alias_value":"JO4WUZPRBQXDSJG7","created_at":"2026-07-05T09:18:55Z"},{"alias_kind":"pith_short_8","alias_value":"JO4WUZPR","created_at":"2026-07-05T09:18:55Z"}],"graph_snapshots":[{"event_id":"sha256:c7e206307d8f10e891f751cfe61c9963ba921734974d779e186e94bdfe36048f","target":"graph","created_at":"2026-07-05T09:18:55Z","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/2410.08304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems. We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on","authors_text":"Alberto Alfarano, Amaury Hayat, Fran\\c{c}ois Charton","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T18:50:10Z","title":"Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08304","kind":"arxiv","version":1},"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:c0c62c5967baa980b19918ba215569e200cb3ed6d8e91798611606c3898d7595","target":"record","created_at":"2026-07-05T09:18:55Z","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":"2f5642e9675b00d38a7aa3536f15aaaf1874904525235cd331d64db2c574b88b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-10T18:50:10Z","title_canon_sha256":"14bbbb104580a19d7df43f4afb60a89bf4caabb29671159dae49bbb6c87ff45f"},"schema_version":"1.0","source":{"id":"2410.08304","kind":"arxiv","version":1}},"canonical_sha256":"4bb96a65f10c2e3924df5d59016d92f8317f47f63e438c9a4421559ae7563a00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bb96a65f10c2e3924df5d59016d92f8317f47f63e438c9a4421559ae7563a00","first_computed_at":"2026-07-05T09:18:55.887257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:18:55.887257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Z3qfgwguu4FePWxiFF+dEl633uOLEUYcOLHIqRfIlUocIr/FIqzNS5CAXETS1tmQb14dipxr/ax9cVUc286RBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:18:55.887711Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.08304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0c62c5967baa980b19918ba215569e200cb3ed6d8e91798611606c3898d7595","sha256:c7e206307d8f10e891f751cfe61c9963ba921734974d779e186e94bdfe36048f"],"state_sha256":"2df7b934012396b3fa4460740bd9027e973288ba1716fc8350888d35e518b6fa"}