{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:YIIQOQMVSCAURE6S34NIGT4FVA","short_pith_number":"pith:YIIQOQMV","canonical_record":{"source":{"id":"2305.08955","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-05-15T18:48:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"5351f03744c383da30ec2eeca28734fa5ae98f728f51762f86fdeb4b775b1f6d","abstract_canon_sha256":"9216c11dbc755eacc4ce8ad754eea561d6a9a67c7f873ba847801feb3fb379e8"},"schema_version":"1.0"},"canonical_sha256":"c21107419590814893d2df1a834f85a82d1372987ca0ff00415fdd0242f1a1d1","source":{"kind":"arxiv","id":"2305.08955","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.08955","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"2305.08955v2","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.08955","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"YIIQOQMVSCAU","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"pith_short_16","alias_value":"YIIQOQMVSCAURE6S","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"pith_short_8","alias_value":"YIIQOQMV","created_at":"2026-07-05T06:12:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:YIIQOQMVSCAURE6S34NIGT4FVA","target":"record","payload":{"canonical_record":{"source":{"id":"2305.08955","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-05-15T18:48:31Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"5351f03744c383da30ec2eeca28734fa5ae98f728f51762f86fdeb4b775b1f6d","abstract_canon_sha256":"9216c11dbc755eacc4ce8ad754eea561d6a9a67c7f873ba847801feb3fb379e8"},"schema_version":"1.0"},"canonical_sha256":"c21107419590814893d2df1a834f85a82d1372987ca0ff00415fdd0242f1a1d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:12:02.956937Z","signature_b64":"IWBgDqzj1I0zyXk/dpcWUmKV4zwyD2SQiTyKi5B2Tb66uOpBeXyXrYjhFr0jygic5SCfZN5JnEehcoJVFNEdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c21107419590814893d2df1a834f85a82d1372987ca0ff00415fdd0242f1a1d1","last_reissued_at":"2026-07-05T06:12:02.956599Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:12:02.956599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.08955","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:12:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LbBtBWp+q7h3sK+hAbcLSrFWViQ7p4wxig2+/seWO61PbOgJ+NelxeeE8FlMrDRHa5fVscR9pZsDaUersjPICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:24:51.181756Z"},"content_sha256":"2d272b97bc637025d9dd72eb1796660bad561ffedeb2058fe3e36479c2888c04","schema_version":"1.0","event_id":"sha256:2d272b97bc637025d9dd72eb1796660bad561ffedeb2058fe3e36479c2888c04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:YIIQOQMVSCAURE6S34NIGT4FVA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fermat's Last Theorem for regular primes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"cs.LO","authors_text":"Alex J. Best, Christopher Birkbeck, Eric Rodriguez Boidi, Riccardo Brasca","submitted_at":"2023-05-15T18:48:31Z","abstract_excerpt":"We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \\emph{Lean} theorem prover and its mathematical library \\emph{mathlib}. This is an important 19th century result that motivated the development of modern algebraic number theory. Besides explaining the mathematics behind this result, we analyze in this paper the difficulties we faced in the formalisation process and how we solved them. For example, we had to deal with a diamond about characteristic zero fields and problems arising from multiple nested coercions related to number fields. We also expla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08955","kind":"arxiv","version":2},"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/2305.08955/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":"2026-07-05T06:12:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nH4Vj50srdw047vDAMJT94HPPT0o+KBJyrbVny9z93P0MByjaezzYzeE+XXMhUGLs7k1eDc1QBj8TB9E8DljAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:24:51.182270Z"},"content_sha256":"457a3721479ab59032567711a2b95f641be79404fdfadc13ea46e2fbb1caed4f","schema_version":"1.0","event_id":"sha256:457a3721479ab59032567711a2b95f641be79404fdfadc13ea46e2fbb1caed4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIIQOQMVSCAURE6S34NIGT4FVA/bundle.json","state_url":"https://pith.science/pith/YIIQOQMVSCAURE6S34NIGT4FVA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIIQOQMVSCAURE6S34NIGT4FVA/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":"2026-08-04T19:24:51Z","links":{"resolver":"https://pith.science/pith/YIIQOQMVSCAURE6S34NIGT4FVA","bundle":"https://pith.science/pith/YIIQOQMVSCAURE6S34NIGT4FVA/bundle.json","state":"https://pith.science/pith/YIIQOQMVSCAURE6S34NIGT4FVA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIIQOQMVSCAURE6S34NIGT4FVA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:YIIQOQMVSCAURE6S34NIGT4FVA","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":"9216c11dbc755eacc4ce8ad754eea561d6a9a67c7f873ba847801feb3fb379e8","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-05-15T18:48:31Z","title_canon_sha256":"5351f03744c383da30ec2eeca28734fa5ae98f728f51762f86fdeb4b775b1f6d"},"schema_version":"1.0","source":{"id":"2305.08955","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.08955","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"arxiv_version","alias_value":"2305.08955v2","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.08955","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"pith_short_12","alias_value":"YIIQOQMVSCAU","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"pith_short_16","alias_value":"YIIQOQMVSCAURE6S","created_at":"2026-07-05T06:12:02Z"},{"alias_kind":"pith_short_8","alias_value":"YIIQOQMV","created_at":"2026-07-05T06:12:02Z"}],"graph_snapshots":[{"event_id":"sha256:457a3721479ab59032567711a2b95f641be79404fdfadc13ea46e2fbb1caed4f","target":"graph","created_at":"2026-07-05T06:12:02Z","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/2305.08955/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We formalise the proof of the first case of Fermat's Last Theorem for regular primes using the \\emph{Lean} theorem prover and its mathematical library \\emph{mathlib}. This is an important 19th century result that motivated the development of modern algebraic number theory. Besides explaining the mathematics behind this result, we analyze in this paper the difficulties we faced in the formalisation process and how we solved them. For example, we had to deal with a diamond about characteristic zero fields and problems arising from multiple nested coercions related to number fields. We also expla","authors_text":"Alex J. Best, Christopher Birkbeck, Eric Rodriguez Boidi, Riccardo Brasca","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-05-15T18:48:31Z","title":"Fermat's Last Theorem for regular primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.08955","kind":"arxiv","version":2},"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":"sha256:2d272b97bc637025d9dd72eb1796660bad561ffedeb2058fe3e36479c2888c04","target":"record","created_at":"2026-07-05T06:12:02Z","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":"9216c11dbc755eacc4ce8ad754eea561d6a9a67c7f873ba847801feb3fb379e8","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LO","submitted_at":"2023-05-15T18:48:31Z","title_canon_sha256":"5351f03744c383da30ec2eeca28734fa5ae98f728f51762f86fdeb4b775b1f6d"},"schema_version":"1.0","source":{"id":"2305.08955","kind":"arxiv","version":2}},"canonical_sha256":"c21107419590814893d2df1a834f85a82d1372987ca0ff00415fdd0242f1a1d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c21107419590814893d2df1a834f85a82d1372987ca0ff00415fdd0242f1a1d1","first_computed_at":"2026-07-05T06:12:02.956599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:12:02.956599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IWBgDqzj1I0zyXk/dpcWUmKV4zwyD2SQiTyKi5B2Tb66uOpBeXyXrYjhFr0jygic5SCfZN5JnEehcoJVFNEdBg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:12:02.956937Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.08955","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d272b97bc637025d9dd72eb1796660bad561ffedeb2058fe3e36479c2888c04","sha256:457a3721479ab59032567711a2b95f641be79404fdfadc13ea46e2fbb1caed4f"],"state_sha256":"6438fd517f98580f1eb6e7e9b4353ebf879131548707d8e7ea2ca5af54708ebb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D98kIIiPgyr6DhrLIbQvQXI1utn5pVMVQqH/KkBNO2VWa0kRgsnPz+Q5tqdXjkQC1oMOTBpJIks8F6XVypsrDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:24:51.186132Z","bundle_sha256":"0abec9fa1875196b1110c497e93a49bc86531fdaa994c87cbc0d239d6bbeec65"}}