{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YG4TVE66TKF5V75DZALSEON2E2","short_pith_number":"pith:YG4TVE66","canonical_record":{"source":{"id":"2112.15594","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-12-31T18:57:31Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"689f3ebac6443356f853290d607b1c18df3ed4b4a2435bd989ab283c48e9366b","abstract_canon_sha256":"3e011ca9554c8ff6c595ab2bfd29ebb33e8a5b74c2aa303fc549c8a9cc3d4f60"},"schema_version":"1.0"},"canonical_sha256":"c1b93a93de9a8bdaffa3c8172239ba26aac79186c67129a08f7c26dd6246c788","source":{"kind":"arxiv","id":"2112.15594","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.15594","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"arxiv_version","alias_value":"2112.15594v4","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.15594","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"pith_short_12","alias_value":"YG4TVE66TKF5","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"pith_short_16","alias_value":"YG4TVE66TKF5V75D","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"pith_short_8","alias_value":"YG4TVE66","created_at":"2026-07-05T04:57:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YG4TVE66TKF5V75DZALSEON2E2","target":"record","payload":{"canonical_record":{"source":{"id":"2112.15594","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-12-31T18:57:31Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"689f3ebac6443356f853290d607b1c18df3ed4b4a2435bd989ab283c48e9366b","abstract_canon_sha256":"3e011ca9554c8ff6c595ab2bfd29ebb33e8a5b74c2aa303fc549c8a9cc3d4f60"},"schema_version":"1.0"},"canonical_sha256":"c1b93a93de9a8bdaffa3c8172239ba26aac79186c67129a08f7c26dd6246c788","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:57:02.864692Z","signature_b64":"Mro5q++dMoHffZ+ZGwGnktNuU+UIosJ79A4dAHNeJH5PNff25DYjXUDjxMVPabXAnU+1Yo8k1WqPULphfs0eAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1b93a93de9a8bdaffa3c8172239ba26aac79186c67129a08f7c26dd6246c788","last_reissued_at":"2026-07-05T04:57:02.864255Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:57:02.864255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.15594","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:57:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cMZI5YFyub7oq7kN4sQrkUo8S4OMj8GnzgpNNaPZFnzXvdeBaz34KKLPT0Y3CRkTfKtPgJHZKdK0uG4IssY8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:07:29.572508Z"},"content_sha256":"8f18140bc3b396c8a2f2dc1393887fb6388ea99d60be439d447e9551efd2f279","schema_version":"1.0","event_id":"sha256:8f18140bc3b396c8a2f2dc1393887fb6388ea99d60be439d447e9551efd2f279"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YG4TVE66TKF5V75DZALSEON2E2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Albert Lu, Avi Shporer, Elizabeth Ke, Eugene Wu, Gilbert Strang, Iddo Drori, Jayson Lynch, Kevin Liu, Leonard Tang, Linda Chen, Nakul Verma, Newman Cheng, Nikhil Singh, Reece Shuttleworth, Roman Wang, Sarah Zhang, Sunny Tran, Taylor L. Patti","submitted_at":"2021-12-31T18:57:31Z","abstract_excerpt":"We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia U"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15594","kind":"arxiv","version":4},"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/2112.15594/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":"2026-07-05T04:57:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7zyACNqtdKBMCKwnD+B/ziPxfD6uBt0hdiUXqtW3DWoNIqHFnFMeLfe5zTqjQkvqOUa33mPiXb24PtdjjwLHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:07:29.573037Z"},"content_sha256":"7c15cee288c66402d28d3b3f07b17e739953c9f5f3294c6078e3d0e3400e6f17","schema_version":"1.0","event_id":"sha256:7c15cee288c66402d28d3b3f07b17e739953c9f5f3294c6078e3d0e3400e6f17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YG4TVE66TKF5V75DZALSEON2E2/bundle.json","state_url":"https://pith.science/pith/YG4TVE66TKF5V75DZALSEON2E2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YG4TVE66TKF5V75DZALSEON2E2/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":"2026-08-14T08:07:29Z","links":{"resolver":"https://pith.science/pith/YG4TVE66TKF5V75DZALSEON2E2","bundle":"https://pith.science/pith/YG4TVE66TKF5V75DZALSEON2E2/bundle.json","state":"https://pith.science/pith/YG4TVE66TKF5V75DZALSEON2E2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YG4TVE66TKF5V75DZALSEON2E2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YG4TVE66TKF5V75DZALSEON2E2","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":"3e011ca9554c8ff6c595ab2bfd29ebb33e8a5b74c2aa303fc549c8a9cc3d4f60","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-12-31T18:57:31Z","title_canon_sha256":"689f3ebac6443356f853290d607b1c18df3ed4b4a2435bd989ab283c48e9366b"},"schema_version":"1.0","source":{"id":"2112.15594","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.15594","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"arxiv_version","alias_value":"2112.15594v4","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.15594","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"pith_short_12","alias_value":"YG4TVE66TKF5","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"pith_short_16","alias_value":"YG4TVE66TKF5V75D","created_at":"2026-07-05T04:57:02Z"},{"alias_kind":"pith_short_8","alias_value":"YG4TVE66","created_at":"2026-07-05T04:57:02Z"}],"graph_snapshots":[{"event_id":"sha256:7c15cee288c66402d28d3b3f07b17e739953c9f5f3294c6078e3d0e3400e6f17","target":"graph","created_at":"2026-07-05T04:57:02Z","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/2112.15594/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We demonstrate that a neural network pre-trained on text and fine-tuned on code solves mathematics course problems, explains solutions, and generates new questions at a human level. We automatically synthesize programs using few-shot learning and OpenAI's Codex transformer and execute them to solve course problems at 81% automatic accuracy. We curate a new dataset of questions from MIT's largest mathematics courses (Single Variable and Multivariable Calculus, Differential Equations, Introduction to Probability and Statistics, Linear Algebra, and Mathematics for Computer Science) and Columbia U","authors_text":"Albert Lu, Avi Shporer, Elizabeth Ke, Eugene Wu, Gilbert Strang, Iddo Drori, Jayson Lynch, Kevin Liu, Leonard Tang, Linda Chen, Nakul Verma, Newman Cheng, Nikhil Singh, Reece Shuttleworth, Roman Wang, Sarah Zhang, Sunny Tran, Taylor L. Patti","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-12-31T18:57:31Z","title":"A Neural Network Solves, Explains, and Generates University Math Problems by Program Synthesis and Few-Shot Learning at Human Level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15594","kind":"arxiv","version":4},"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":"sha256:8f18140bc3b396c8a2f2dc1393887fb6388ea99d60be439d447e9551efd2f279","target":"record","created_at":"2026-07-05T04:57:02Z","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":"3e011ca9554c8ff6c595ab2bfd29ebb33e8a5b74c2aa303fc549c8a9cc3d4f60","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-12-31T18:57:31Z","title_canon_sha256":"689f3ebac6443356f853290d607b1c18df3ed4b4a2435bd989ab283c48e9366b"},"schema_version":"1.0","source":{"id":"2112.15594","kind":"arxiv","version":4}},"canonical_sha256":"c1b93a93de9a8bdaffa3c8172239ba26aac79186c67129a08f7c26dd6246c788","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1b93a93de9a8bdaffa3c8172239ba26aac79186c67129a08f7c26dd6246c788","first_computed_at":"2026-07-05T04:57:02.864255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:57:02.864255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mro5q++dMoHffZ+ZGwGnktNuU+UIosJ79A4dAHNeJH5PNff25DYjXUDjxMVPabXAnU+1Yo8k1WqPULphfs0eAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:57:02.864692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.15594","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f18140bc3b396c8a2f2dc1393887fb6388ea99d60be439d447e9551efd2f279","sha256:7c15cee288c66402d28d3b3f07b17e739953c9f5f3294c6078e3d0e3400e6f17"],"state_sha256":"ab9525f674acf59d57ccb64380de334961ed36f3297b0d6c5b171b1ab0e823f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2MjDyQP3YQQ0oq2/WUDdLqS6bG9ugC2yJ1J+JAgCwNVcIaIa9I4btxvs0iIPFzFp28CkSrU+IgewuxTLmtg4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:07:29.579115Z","bundle_sha256":"96203ff648a564442f40fc584786ecc5eb17c888110d44d83ea515831e934207"}}