{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GG2BKORGPBXO76QYEC52X37TCC","short_pith_number":"pith:GG2BKORG","canonical_record":{"source":{"id":"2505.20869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-05-27T08:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"23976bf43442dbab9d1032107f3b1f2f16a707299020d6f4d2685246632e91c8","abstract_canon_sha256":"d6491a9a62396017d0882f1b642c74481e6815f0ef78ffcbe82530f43b8153c3"},"schema_version":"1.0"},"canonical_sha256":"31b4153a26786eeffa1820bbabeff3108912ce88887f2940c6a4eda89386bdbe","source":{"kind":"arxiv","id":"2505.20869","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.20869","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"2505.20869v1","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.20869","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"GG2BKORGPBXO","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"pith_short_16","alias_value":"GG2BKORGPBXO76QY","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"pith_short_8","alias_value":"GG2BKORG","created_at":"2026-07-05T11:10:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GG2BKORGPBXO76QYEC52X37TCC","target":"record","payload":{"canonical_record":{"source":{"id":"2505.20869","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-05-27T08:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"23976bf43442dbab9d1032107f3b1f2f16a707299020d6f4d2685246632e91c8","abstract_canon_sha256":"d6491a9a62396017d0882f1b642c74481e6815f0ef78ffcbe82530f43b8153c3"},"schema_version":"1.0"},"canonical_sha256":"31b4153a26786eeffa1820bbabeff3108912ce88887f2940c6a4eda89386bdbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:20.139424Z","signature_b64":"A3niun0vgMJpA1wdn8Bb2NjxAChuGx63ftXie/mMr94T3Gaon6eR59aroNiZxWp1b3xmUMlkqJdvtrSDn6tnAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31b4153a26786eeffa1820bbabeff3108912ce88887f2940c6a4eda89386bdbe","last_reissued_at":"2026-07-05T11:10:20.138915Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:20.138915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.20869","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:10:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dYDvVmbvq+TG1z9cBr+F1rHeXWS+PqtejVxUPqDDxkRqgmYRzNHayJiFIHY3q+Pw3+XFbmxrqJV31gPM3PwAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:50:16.871013Z"},"content_sha256":"6605b2edae1949651ebab2d34210ebcdf7e9c4e72fef7f9f8dec5ac6629ba743","schema_version":"1.0","event_id":"sha256:6605b2edae1949651ebab2d34210ebcdf7e9c4e72fef7f9f8dec5ac6629ba743"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GG2BKORGPBXO76QYEC52X37TCC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Kuo Zhou, Lu Zhang","submitted_at":"2025-05-27T08:21:07Z","abstract_excerpt":"Large Language Models (LLMs) have demonstrated formidable capabilities in solving mathematical problems, yet they may still commit logical reasoning and computational errors during the problem-solving process. Thus, this paper proposes a framework, MATH-VF, which includes a Formalizer and a Critic, for formally verifying the correctness of the solutions generated by large language models. Our framework first utilizes a Formalizer which employs an LLM to translate a natural language solution into a formal context. Afterward, our Critic (which integrates various external tools such as a Computer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.20869","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/2505.20869/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:10:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AEhXWF1hpPwBZlIhWbuNwzNrkAzLEiVfrf/CZZKEVW5qi5X4Ig81aieDmOysa6+b3rKknb1ieVcTnjub6+hVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T23:50:16.871496Z"},"content_sha256":"723e362e942a919a3e01e86134def66e2bae72941b7fb44e41847123c9f499a9","schema_version":"1.0","event_id":"sha256:723e362e942a919a3e01e86134def66e2bae72941b7fb44e41847123c9f499a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GG2BKORGPBXO76QYEC52X37TCC/bundle.json","state_url":"https://pith.science/pith/GG2BKORGPBXO76QYEC52X37TCC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GG2BKORGPBXO76QYEC52X37TCC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-07T23:50:16Z","links":{"resolver":"https://pith.science/pith/GG2BKORGPBXO76QYEC52X37TCC","bundle":"https://pith.science/pith/GG2BKORGPBXO76QYEC52X37TCC/bundle.json","state":"https://pith.science/pith/GG2BKORGPBXO76QYEC52X37TCC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GG2BKORGPBXO76QYEC52X37TCC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GG2BKORGPBXO76QYEC52X37TCC","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":"d6491a9a62396017d0882f1b642c74481e6815f0ef78ffcbe82530f43b8153c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-05-27T08:21:07Z","title_canon_sha256":"23976bf43442dbab9d1032107f3b1f2f16a707299020d6f4d2685246632e91c8"},"schema_version":"1.0","source":{"id":"2505.20869","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.20869","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"2505.20869v1","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.20869","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"GG2BKORGPBXO","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"pith_short_16","alias_value":"GG2BKORGPBXO76QY","created_at":"2026-07-05T11:10:20Z"},{"alias_kind":"pith_short_8","alias_value":"GG2BKORG","created_at":"2026-07-05T11:10:20Z"}],"graph_snapshots":[{"event_id":"sha256:723e362e942a919a3e01e86134def66e2bae72941b7fb44e41847123c9f499a9","target":"graph","created_at":"2026-07-05T11:10:20Z","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/2505.20869/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Large Language Models (LLMs) have demonstrated formidable capabilities in solving mathematical problems, yet they may still commit logical reasoning and computational errors during the problem-solving process. Thus, this paper proposes a framework, MATH-VF, which includes a Formalizer and a Critic, for formally verifying the correctness of the solutions generated by large language models. Our framework first utilizes a Formalizer which employs an LLM to translate a natural language solution into a formal context. Afterward, our Critic (which integrates various external tools such as a Computer","authors_text":"Kuo Zhou, Lu Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-05-27T08:21:07Z","title":"Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.20869","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":"sha256:6605b2edae1949651ebab2d34210ebcdf7e9c4e72fef7f9f8dec5ac6629ba743","target":"record","created_at":"2026-07-05T11:10:20Z","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":"d6491a9a62396017d0882f1b642c74481e6815f0ef78ffcbe82530f43b8153c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2025-05-27T08:21:07Z","title_canon_sha256":"23976bf43442dbab9d1032107f3b1f2f16a707299020d6f4d2685246632e91c8"},"schema_version":"1.0","source":{"id":"2505.20869","kind":"arxiv","version":1}},"canonical_sha256":"31b4153a26786eeffa1820bbabeff3108912ce88887f2940c6a4eda89386bdbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31b4153a26786eeffa1820bbabeff3108912ce88887f2940c6a4eda89386bdbe","first_computed_at":"2026-07-05T11:10:20.138915Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:20.138915Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A3niun0vgMJpA1wdn8Bb2NjxAChuGx63ftXie/mMr94T3Gaon6eR59aroNiZxWp1b3xmUMlkqJdvtrSDn6tnAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:20.139424Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.20869","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6605b2edae1949651ebab2d34210ebcdf7e9c4e72fef7f9f8dec5ac6629ba743","sha256:723e362e942a919a3e01e86134def66e2bae72941b7fb44e41847123c9f499a9"],"state_sha256":"65b9ff6e36f59464ef01117208a388a69f4562578ced8a99f473726686a01ceb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lb8how9mBEBrCuYYVpdjEZKbxz9uQohWZhklDPYeM+kfLIpHE1MWWnFAlnBDmZsKGijZnJgfjCqF/9Nyz0X+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T23:50:16.875305Z","bundle_sha256":"6992d787e85e9faa22d9f9a7a470a780895fc4f9004eaf10927832e50064f714"}}