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Purely symbolic approaches provide strong guarantees but often scale poorly as the number of variables or the degree increases, due to expensive algebraic manipulations and rapidly growing intermediate expressions. In parallel, LLM-guided methods have made notable progress, particularly on competition-style inequalities with a small number of variables. To address the remaining scalability challenges, we propose NSPI, a neuro-symbolic framework that combines the complementary strengths of LLMs and symbolic computation for polynomial-inequality proving. Concretely, an LLM proposes a conjecture in the form of an approximate polynomial Sum-Of-Squares (SOS) decomposition; we refine it via symbolic computation to obtain an exact polynomial","title":"From LLM-Generated Conjectures to Lean Formalizations: Automated Polynomial Inequality Proving via Sum-of-Squares Certificates","url":"https://arxiv.org/abs/2605.15445","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.15445v1 Announce Type: new \nAbstract: Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability. Purely symbolic approaches provide strong guarantees but often scale poorly as the number of variables or the degree increases, due to expensive algebraic manipulations and rapidly growing intermediate expressions. In parallel, LLM-guided methods have made notable progress, particularly on competition-style inequalities with a small number of variables. To address the remaining scalability challenges, we propose NSPI, a neuro-symbolic framework that combines the complementary strengths of LLMs and symbolic computation for polynomial-inequality proving. Concretely, an LLM proposes a conjecture in the form of an approximate polynomial Sum-Of-Squares (SOS) decomposition; we refine it via symbolic computation to obtain an exact polynomial","title":"From LLM-Generated Conjectures to Lean Formalizations: Automated Polynomial Inequality Proving via Sum-of-Squares Certificates","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-18T04:43:11Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.15445"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:7f375745982195560e584990a0204441b998cc8562fc9b4fee6456acdb52cba054035e5c3e57eafb3b63116097532fbfc69ec451e3291902b5f66686b2e1d007","signer":"crovia.substrate","subject":{"observed_at":"2026-05-18T04:43:11Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.15445"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"3d8224313182b30ef0c9cbeef619698f897547f4fdc9e74c98ffd8425176a5ae","leaf_index":140517,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"a354ca1281f507f0a76a92243e2b00721da6de8513a522003847dd9bab68dfb4","side":"left"},{"sibling":"86621b8a1de5ed37a4f72b5d26f04b803d0a02904472049296ada142952ef810","side":"right"},{"sibling":"17f793cb93c2f61115c164c79167f139657ca71dd3f500bcf75d15fc9c3a4697","side":"left"},{"sibling":"15326eda745a441bc2889984324aaf6755bd7d3da6c9bc7dbdfd6b63f6cd8e09","side":"right"},{"sibling":"053c1dd7cf8e6dce5d39c41de014e3693f4a3e244da410b7539a0f82064a5094","side":"right"},{"sibling":"96bc02da49c1ddea9d233101a2dcd46391fa8323dfc6b89fa2a5f2a422ffbfad","side":"left"},{"sibling":"ac4d8fd82d26e4a1d7cd769b05134f3ffc727d30067d8493078e2e1f990de915","side":"left"},{"sibling":"aa12701da7eb982274dc9d39660430c01b4600169201b42a8dfc61c6bc7ef399","side":"left"},{"sibling":"12ff3a9a0c9ee98dcc421928be42a94362f83bd65bffafeece0428e048eaeb7e","side":"right"},{"sibling":"07abc3bad689e74e6304772503dc9372a118e6f66883b8e88c43414efddac063","side":"right"},{"sibling":"28b78fb112bcf26b6801664db97eb8f52a9bccbf0a7ae6766e11845d443692df","side":"left"},{"sibling":"68d0a4634c1460a19c92edd9480df3aa733b814463e7420d1e14471bf61b2f83","side":"right"},{"sibling":"8af64f275b862349aa3bbb9d5cd7fa9a7fdd5620af3bf1b36b2a4519b0b53bdf","side":"right"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"b98c2afadb358e5387e88f19588f8343a81b488d9b44a6f7e57a032db3a1b030","side":"right"},{"sibling":"11b0c1591747f09f7c8971a6caa19befcd81317ca9dfd417b143234df4e10c79","side":"right"},{"sibling":"87206f3bcc342797c990d87f7235c01f78d32ca59cfaf8ad18d71afc879ba477","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":140892,"merkle_root":"6cca56ead155990456b8a014cc50bddbe710f409b26e3d1bfa6fb12b0bfcf6bf","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260518T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-18T05:37:30Z","sig_algorithm":"ed25519","signature":"1e1135f7595f79b14fb11f5fa81a2e17ad31b11b44b427a5e40a7d511cd86447daf492babd368ab571cf26404c8c74c450d460130fca4b064eb2760367489a0f","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_ccfd32b826b90cec997293aa2208c5528850dfc320181d1338fc7e187f2f7f45"}}