{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:3Y6ZLO5XDENUGPPZ25K2TR5QPE","short_pith_number":"pith:3Y6ZLO5X","canonical_record":{"source":{"id":"2501.18666","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-30T15:56:25Z","cross_cats_sorted":["cs.AI","cs.NE"],"title_canon_sha256":"412750e7145cf99a087f4711df4aec78cba5d6f70d5cd534a8d91674cc215273","abstract_canon_sha256":"24263b553eb708cba279333cd53c502bd6ff13698728c08136c65d858a534eca"},"schema_version":"1.0"},"canonical_sha256":"de3d95bbb7191b433df9d755a9c7b0790d766a8016dabb915f0dbd241dbeb0c3","source":{"kind":"arxiv","id":"2501.18666","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18666","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18666v1","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18666","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"3Y6ZLO5XDENU","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"pith_short_16","alias_value":"3Y6ZLO5XDENUGPPZ","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"pith_short_8","alias_value":"3Y6ZLO5X","created_at":"2026-07-05T10:07:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:3Y6ZLO5XDENUGPPZ25K2TR5QPE","target":"record","payload":{"canonical_record":{"source":{"id":"2501.18666","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-30T15:56:25Z","cross_cats_sorted":["cs.AI","cs.NE"],"title_canon_sha256":"412750e7145cf99a087f4711df4aec78cba5d6f70d5cd534a8d91674cc215273","abstract_canon_sha256":"24263b553eb708cba279333cd53c502bd6ff13698728c08136c65d858a534eca"},"schema_version":"1.0"},"canonical_sha256":"de3d95bbb7191b433df9d755a9c7b0790d766a8016dabb915f0dbd241dbeb0c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:07:49.848873Z","signature_b64":"b7792sFb7wOjrNvBcLeyYOdC0Ey2kndRgzPSk9eEEf6aDNoVTohngui/9ddNAu3YkzXkkp5K1onzeyvN7UsWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de3d95bbb7191b433df9d755a9c7b0790d766a8016dabb915f0dbd241dbeb0c3","last_reissued_at":"2026-07-05T10:07:49.848362Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:07:49.848362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.18666","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":"2026-07-05T10:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t/q5328Z18aGkiGbD/yFvPR0iUw2HEiLXZm/Bm/PsPinSLIhNmeCq/JwdD5cWG+AG2mu8Y/5AvPUzAgO5gmdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:34:41.787859Z"},"content_sha256":"af6de4977dc92537e50f29c5031e38473f21900500583735d529692eff7d76cf","schema_version":"1.0","event_id":"sha256:af6de4977dc92537e50f29c5031e38473f21900500583735d529692eff7d76cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:3Y6ZLO5XDENUGPPZ25K2TR5QPE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structure Development in List-Sorting Transformers","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.NE"],"primary_cat":"cs.LG","authors_text":"Einar Urdshals, Jasmina Urdshals","submitted_at":"2025-01-30T15:56:25Z","abstract_excerpt":"We study how a one-layer attention-only transformer develops relevant structures while learning to sort lists of numbers. At the end of training, the model organizes its attention heads in two main modes that we refer to as vocabulary-splitting and copy-suppression. Both represent simpler modes than having multiple heads handle overlapping ranges of numbers. Interestingly, vocabulary-splitting is present regardless of whether we use weight decay, a common regularization technique thought to drive simplification, supporting the thesis that neural networks naturally prefer simpler solutions. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18666","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/2501.18666/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":"2026-07-05T10:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFtidlzNuBdhy4ZUWvRvMaRtI+duMcujdlbY9anP09ClIkzpZYg//GJ4spqD8y2Ind7GYOhgJzmyv1wL0h76Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T00:34:41.788353Z"},"content_sha256":"da58ea058bf91f1edf3d2491676a1d9327d54fecd239f4819c944ec076b399c1","schema_version":"1.0","event_id":"sha256:da58ea058bf91f1edf3d2491676a1d9327d54fecd239f4819c944ec076b399c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3Y6ZLO5XDENUGPPZ25K2TR5QPE/bundle.json","state_url":"https://pith.science/pith/3Y6ZLO5XDENUGPPZ25K2TR5QPE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3Y6ZLO5XDENUGPPZ25K2TR5QPE/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":"2026-08-05T00:34:41Z","links":{"resolver":"https://pith.science/pith/3Y6ZLO5XDENUGPPZ25K2TR5QPE","bundle":"https://pith.science/pith/3Y6ZLO5XDENUGPPZ25K2TR5QPE/bundle.json","state":"https://pith.science/pith/3Y6ZLO5XDENUGPPZ25K2TR5QPE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3Y6ZLO5XDENUGPPZ25K2TR5QPE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3Y6ZLO5XDENUGPPZ25K2TR5QPE","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":"24263b553eb708cba279333cd53c502bd6ff13698728c08136c65d858a534eca","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-30T15:56:25Z","title_canon_sha256":"412750e7145cf99a087f4711df4aec78cba5d6f70d5cd534a8d91674cc215273"},"schema_version":"1.0","source":{"id":"2501.18666","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.18666","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"2501.18666v1","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18666","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"3Y6ZLO5XDENU","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"pith_short_16","alias_value":"3Y6ZLO5XDENUGPPZ","created_at":"2026-07-05T10:07:49Z"},{"alias_kind":"pith_short_8","alias_value":"3Y6ZLO5X","created_at":"2026-07-05T10:07:49Z"}],"graph_snapshots":[{"event_id":"sha256:da58ea058bf91f1edf3d2491676a1d9327d54fecd239f4819c944ec076b399c1","target":"graph","created_at":"2026-07-05T10:07:49Z","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/2501.18666/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study how a one-layer attention-only transformer develops relevant structures while learning to sort lists of numbers. At the end of training, the model organizes its attention heads in two main modes that we refer to as vocabulary-splitting and copy-suppression. Both represent simpler modes than having multiple heads handle overlapping ranges of numbers. Interestingly, vocabulary-splitting is present regardless of whether we use weight decay, a common regularization technique thought to drive simplification, supporting the thesis that neural networks naturally prefer simpler solutions. We ","authors_text":"Einar Urdshals, Jasmina Urdshals","cross_cats":["cs.AI","cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-30T15:56:25Z","title":"Structure Development in List-Sorting Transformers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18666","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:af6de4977dc92537e50f29c5031e38473f21900500583735d529692eff7d76cf","target":"record","created_at":"2026-07-05T10:07:49Z","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":"24263b553eb708cba279333cd53c502bd6ff13698728c08136c65d858a534eca","cross_cats_sorted":["cs.AI","cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-30T15:56:25Z","title_canon_sha256":"412750e7145cf99a087f4711df4aec78cba5d6f70d5cd534a8d91674cc215273"},"schema_version":"1.0","source":{"id":"2501.18666","kind":"arxiv","version":1}},"canonical_sha256":"de3d95bbb7191b433df9d755a9c7b0790d766a8016dabb915f0dbd241dbeb0c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de3d95bbb7191b433df9d755a9c7b0790d766a8016dabb915f0dbd241dbeb0c3","first_computed_at":"2026-07-05T10:07:49.848362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:07:49.848362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b7792sFb7wOjrNvBcLeyYOdC0Ey2kndRgzPSk9eEEf6aDNoVTohngui/9ddNAu3YkzXkkp5K1onzeyvN7UsWBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:07:49.848873Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.18666","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af6de4977dc92537e50f29c5031e38473f21900500583735d529692eff7d76cf","sha256:da58ea058bf91f1edf3d2491676a1d9327d54fecd239f4819c944ec076b399c1"],"state_sha256":"a0095adb135c4ea2f2c07e0076df52985434f8af0198d007330a26c6b67b03f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9DOvSC8d0S31+Z9qjXJIYcu/zwtt6al1XjfD3GTeQlx5du5PTqiVqwN2NXMhd2sjQPU+u7gbsOUwVZdJ+NfUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T00:34:41.793115Z","bundle_sha256":"b461f3b90bd1b631ba826b67b30b2ced052eaa6d9c731f250c07f46adde465df"}}