{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:5GBRTQKYKIK3I44SMNF6DGORZN","short_pith_number":"pith:5GBRTQKY","canonical_record":{"source":{"id":"2202.01344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-03T00:17:00Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"7e3c99bd70f2b2bd4b224ddc12c529b17dffd62f2f5807ad55381b8ea8453901","abstract_canon_sha256":"c7dcaadf7ae61a4651bf7342e330a04251715ba77dc73c0dc524e39659da4be5"},"schema_version":"1.0"},"canonical_sha256":"e98319c1585215b47392634be199d1cb5ebde3a56212666bc22a6bcddd45abd6","source":{"kind":"arxiv","id":"2202.01344","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.01344","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"arxiv_version","alias_value":"2202.01344v1","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.01344","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"pith_short_12","alias_value":"5GBRTQKYKIK3","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"pith_short_16","alias_value":"5GBRTQKYKIK3I44S","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"pith_short_8","alias_value":"5GBRTQKY","created_at":"2026-07-05T03:53:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:5GBRTQKYKIK3I44SMNF6DGORZN","target":"record","payload":{"canonical_record":{"source":{"id":"2202.01344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-03T00:17:00Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"7e3c99bd70f2b2bd4b224ddc12c529b17dffd62f2f5807ad55381b8ea8453901","abstract_canon_sha256":"c7dcaadf7ae61a4651bf7342e330a04251715ba77dc73c0dc524e39659da4be5"},"schema_version":"1.0"},"canonical_sha256":"e98319c1585215b47392634be199d1cb5ebde3a56212666bc22a6bcddd45abd6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:53:53.205428Z","signature_b64":"WJS5+TIz0pxLrvDQdNV4P5YfRpYNAUXA7mCrRSHi/snS7XFb7gEE1Zsacxl9jj3eO/FTdSBd6gtj+pp8HPEgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e98319c1585215b47392634be199d1cb5ebde3a56212666bc22a6bcddd45abd6","last_reissued_at":"2026-07-05T03:53:53.204909Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:53:53.204909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.01344","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":"2026-07-05T03:53:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SG97Id+Mjlw+DG2+y4/1VoqJ/f2MBj4LU1BMu3vNZLjlrE7u2jrmiHA8r6cJBsL2ohILz49M0/nurSEVbUezDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:29:50.925840Z"},"content_sha256":"0dc76370ce3883e702d666eb87e4b1c6bbc9fd92627313a0cb0171fc9cb73636","schema_version":"1.0","event_id":"sha256:0dc76370ce3883e702d666eb87e4b1c6bbc9fd92627313a0cb0171fc9cb73636"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:5GBRTQKYKIK3I44SMNF6DGORZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Formal Mathematics Statement Curriculum Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Igor Babuschkin, Ilya Sutskever, Jesse Michael Han, Kunhao Zheng, Mantas Baksys, Stanislas Polu","submitted_at":"2022-02-03T00:17:00Z","abstract_excerpt":"We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only. We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.01344","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/2202.01344/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":"2026-07-05T03:53:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rEbnioJQ2yFyYT3x/uU0Ms1PNBBbSoc/jHRJFXOLfeh2OmyBooJy9Q9apQpOVxis2OUzWgni4oXPc3HBDDOlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T14:29:50.926739Z"},"content_sha256":"58f8b1695cbfb0675d82aa2f43569f2da19debf3ab5b7a128655d98ff1b2a25b","schema_version":"1.0","event_id":"sha256:58f8b1695cbfb0675d82aa2f43569f2da19debf3ab5b7a128655d98ff1b2a25b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GBRTQKYKIK3I44SMNF6DGORZN/bundle.json","state_url":"https://pith.science/pith/5GBRTQKYKIK3I44SMNF6DGORZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GBRTQKYKIK3I44SMNF6DGORZN/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":"2026-08-05T14:29:50Z","links":{"resolver":"https://pith.science/pith/5GBRTQKYKIK3I44SMNF6DGORZN","bundle":"https://pith.science/pith/5GBRTQKYKIK3I44SMNF6DGORZN/bundle.json","state":"https://pith.science/pith/5GBRTQKYKIK3I44SMNF6DGORZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GBRTQKYKIK3I44SMNF6DGORZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:5GBRTQKYKIK3I44SMNF6DGORZN","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":"c7dcaadf7ae61a4651bf7342e330a04251715ba77dc73c0dc524e39659da4be5","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-03T00:17:00Z","title_canon_sha256":"7e3c99bd70f2b2bd4b224ddc12c529b17dffd62f2f5807ad55381b8ea8453901"},"schema_version":"1.0","source":{"id":"2202.01344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.01344","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"arxiv_version","alias_value":"2202.01344v1","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.01344","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"pith_short_12","alias_value":"5GBRTQKYKIK3","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"pith_short_16","alias_value":"5GBRTQKYKIK3I44S","created_at":"2026-07-05T03:53:53Z"},{"alias_kind":"pith_short_8","alias_value":"5GBRTQKY","created_at":"2026-07-05T03:53:53Z"}],"graph_snapshots":[{"event_id":"sha256:58f8b1695cbfb0675d82aa2f43569f2da19debf3ab5b7a128655d98ff1b2a25b","target":"graph","created_at":"2026-07-05T03:53:53Z","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/2202.01344/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically outperforms proof search only. We also observe that when applied to a collection of formal statements of sufficiently varied difficulty, expert iteration is capable of finding and solving a curriculum of increasingly difficult problems, without the need for associated ground-truth proofs. Finally, by applying this expert iteration to a manually curated set of problem","authors_text":"Igor Babuschkin, Ilya Sutskever, Jesse Michael Han, Kunhao Zheng, Mantas Baksys, Stanislas Polu","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-03T00:17:00Z","title":"Formal Mathematics Statement Curriculum Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.01344","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":"sha256:0dc76370ce3883e702d666eb87e4b1c6bbc9fd92627313a0cb0171fc9cb73636","target":"record","created_at":"2026-07-05T03:53:53Z","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":"c7dcaadf7ae61a4651bf7342e330a04251715ba77dc73c0dc524e39659da4be5","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-02-03T00:17:00Z","title_canon_sha256":"7e3c99bd70f2b2bd4b224ddc12c529b17dffd62f2f5807ad55381b8ea8453901"},"schema_version":"1.0","source":{"id":"2202.01344","kind":"arxiv","version":1}},"canonical_sha256":"e98319c1585215b47392634be199d1cb5ebde3a56212666bc22a6bcddd45abd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e98319c1585215b47392634be199d1cb5ebde3a56212666bc22a6bcddd45abd6","first_computed_at":"2026-07-05T03:53:53.204909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:53:53.204909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WJS5+TIz0pxLrvDQdNV4P5YfRpYNAUXA7mCrRSHi/snS7XFb7gEE1Zsacxl9jj3eO/FTdSBd6gtj+pp8HPEgCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:53:53.205428Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.01344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dc76370ce3883e702d666eb87e4b1c6bbc9fd92627313a0cb0171fc9cb73636","sha256:58f8b1695cbfb0675d82aa2f43569f2da19debf3ab5b7a128655d98ff1b2a25b"],"state_sha256":"1c91dc03149dbf36db3fcc3be426d97bf08333f295466b64d839546654d53946"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hx8Y39/IAvmA+Z2wBCXAfrWaS4YwM35/sFvbr/uH2znM2VvfuypmsUx+reZqUX8lv4Z4Xg++d71n5KfeUCU0Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T14:29:50.932359Z","bundle_sha256":"083c1882a6013e779ac9113dc636aa855d3e73d006ebb10dc69db811e9f1380a"}}