{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HQJE2HMGP7RXZQZDBZQLXKU3L2","short_pith_number":"pith:HQJE2HMG","canonical_record":{"source":{"id":"2502.01774","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-03T19:28:11Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"da4017afa373115508b04b156bcb0f5319310718f0e7d2cdda81d297ea8e64c5","abstract_canon_sha256":"529a820ac4ac00333de56aab3d6db757658693a152535e3bfb54e279176d6a39"},"schema_version":"1.0"},"canonical_sha256":"3c124d1d867fe37cc3230e60bbaa9b5e8b1174394fa375fef6fe8fb63a9dcb4e","source":{"kind":"arxiv","id":"2502.01774","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01774","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01774v1","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01774","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"pith_short_12","alias_value":"HQJE2HMGP7RX","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"pith_short_16","alias_value":"HQJE2HMGP7RXZQZD","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"pith_short_8","alias_value":"HQJE2HMG","created_at":"2026-07-05T10:09:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HQJE2HMGP7RXZQZDBZQLXKU3L2","target":"record","payload":{"canonical_record":{"source":{"id":"2502.01774","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-03T19:28:11Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"da4017afa373115508b04b156bcb0f5319310718f0e7d2cdda81d297ea8e64c5","abstract_canon_sha256":"529a820ac4ac00333de56aab3d6db757658693a152535e3bfb54e279176d6a39"},"schema_version":"1.0"},"canonical_sha256":"3c124d1d867fe37cc3230e60bbaa9b5e8b1174394fa375fef6fe8fb63a9dcb4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:09:18.883368Z","signature_b64":"ixlLyK/OBE8+CoWba2hJ8pGooXKvlH5SB/kd2HZpMl4Ky6XUMffeY9PyAv43k3Gyw+qMPL83/v81ub+Cbkx1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c124d1d867fe37cc3230e60bbaa9b5e8b1174394fa375fef6fe8fb63a9dcb4e","last_reissued_at":"2026-07-05T10:09:18.882883Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:09:18.882883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.01774","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":"2026-07-05T10:09:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3rWmbnMy90EoYIpOXxekAAAkF7HLzNKI7ssbg3U/zFyTSSlzHAxLOxWnH0eZc6leeYbw04CQKKJKRByVxCUHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:19:27.701661Z"},"content_sha256":"6c0108fd174e99936fcc8f9f504078e757fd55b97e13582ab2664f0a8bcdf9d9","schema_version":"1.0","event_id":"sha256:6c0108fd174e99936fcc8f9f504078e757fd55b97e13582ab2664f0a8bcdf9d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HQJE2HMGP7RXZQZDBZQLXKU3L2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grokking Explained: A Statistical Phenomenon","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Artur S. d'Avila Garcez, Breno W. Carvalho, Em\\'ilio Vital Brazil, Lu\\'is C. Lamb","submitted_at":"2025-02-03T19:28:11Z","abstract_excerpt":"Grokking, or delayed generalization, is an intriguing learning phenomenon where test set loss decreases sharply only after a model's training set loss has converged. This challenges conventional understanding of the training dynamics in deep learning networks. In this paper, we formalize and investigate grokking, highlighting that a key factor in its emergence is a distribution shift between training and test data. We introduce two synthetic datasets specifically designed to analyze grokking. One dataset examines the impact of limited sampling, and the other investigates transfer learning's ro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01774","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/2502.01774/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":"2026-07-05T10:09:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wjna7Gb0FB0zGnzGbNB5JNw0irUpakqi5Ao1Hmn2Dk30M0qgUSVGCXcEywrBfsOspCcdevxS2olkg6QGn09zBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T20:19:27.702153Z"},"content_sha256":"dee30ee127f66b1f4a15d418283e0dcf4d15aeb1cee55043405e8902797daa75","schema_version":"1.0","event_id":"sha256:dee30ee127f66b1f4a15d418283e0dcf4d15aeb1cee55043405e8902797daa75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HQJE2HMGP7RXZQZDBZQLXKU3L2/bundle.json","state_url":"https://pith.science/pith/HQJE2HMGP7RXZQZDBZQLXKU3L2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HQJE2HMGP7RXZQZDBZQLXKU3L2/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":"2026-08-03T20:19:27Z","links":{"resolver":"https://pith.science/pith/HQJE2HMGP7RXZQZDBZQLXKU3L2","bundle":"https://pith.science/pith/HQJE2HMGP7RXZQZDBZQLXKU3L2/bundle.json","state":"https://pith.science/pith/HQJE2HMGP7RXZQZDBZQLXKU3L2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HQJE2HMGP7RXZQZDBZQLXKU3L2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HQJE2HMGP7RXZQZDBZQLXKU3L2","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":"529a820ac4ac00333de56aab3d6db757658693a152535e3bfb54e279176d6a39","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-03T19:28:11Z","title_canon_sha256":"da4017afa373115508b04b156bcb0f5319310718f0e7d2cdda81d297ea8e64c5"},"schema_version":"1.0","source":{"id":"2502.01774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.01774","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"arxiv_version","alias_value":"2502.01774v1","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.01774","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"pith_short_12","alias_value":"HQJE2HMGP7RX","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"pith_short_16","alias_value":"HQJE2HMGP7RXZQZD","created_at":"2026-07-05T10:09:18Z"},{"alias_kind":"pith_short_8","alias_value":"HQJE2HMG","created_at":"2026-07-05T10:09:18Z"}],"graph_snapshots":[{"event_id":"sha256:dee30ee127f66b1f4a15d418283e0dcf4d15aeb1cee55043405e8902797daa75","target":"graph","created_at":"2026-07-05T10:09:18Z","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/2502.01774/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Grokking, or delayed generalization, is an intriguing learning phenomenon where test set loss decreases sharply only after a model's training set loss has converged. This challenges conventional understanding of the training dynamics in deep learning networks. In this paper, we formalize and investigate grokking, highlighting that a key factor in its emergence is a distribution shift between training and test data. We introduce two synthetic datasets specifically designed to analyze grokking. One dataset examines the impact of limited sampling, and the other investigates transfer learning's ro","authors_text":"Artur S. d'Avila Garcez, Breno W. Carvalho, Em\\'ilio Vital Brazil, Lu\\'is C. Lamb","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-03T19:28:11Z","title":"Grokking Explained: A Statistical Phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01774","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":"sha256:6c0108fd174e99936fcc8f9f504078e757fd55b97e13582ab2664f0a8bcdf9d9","target":"record","created_at":"2026-07-05T10:09:18Z","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":"529a820ac4ac00333de56aab3d6db757658693a152535e3bfb54e279176d6a39","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-02-03T19:28:11Z","title_canon_sha256":"da4017afa373115508b04b156bcb0f5319310718f0e7d2cdda81d297ea8e64c5"},"schema_version":"1.0","source":{"id":"2502.01774","kind":"arxiv","version":1}},"canonical_sha256":"3c124d1d867fe37cc3230e60bbaa9b5e8b1174394fa375fef6fe8fb63a9dcb4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c124d1d867fe37cc3230e60bbaa9b5e8b1174394fa375fef6fe8fb63a9dcb4e","first_computed_at":"2026-07-05T10:09:18.882883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:09:18.882883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ixlLyK/OBE8+CoWba2hJ8pGooXKvlH5SB/kd2HZpMl4Ky6XUMffeY9PyAv43k3Gyw+qMPL83/v81ub+Cbkx1Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:09:18.883368Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.01774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c0108fd174e99936fcc8f9f504078e757fd55b97e13582ab2664f0a8bcdf9d9","sha256:dee30ee127f66b1f4a15d418283e0dcf4d15aeb1cee55043405e8902797daa75"],"state_sha256":"b160a0c51a9755d13b97fae8ab8880864d947ffde8ece5ac8a2abab3b30f0ad1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hzV5fCTe1Xf8achcmscB9aQa2rrEBxfDAbRPjBxWRZtIW1rwJbB1mDCfFWTen8OIr7IZC4ByGxV85QYgB4G+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T20:19:27.705741Z","bundle_sha256":"85c20f5b5361c350b46b4883b4649592919f8374689a979dbb54306705960928"}}