{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:JIHVYSHDYO2CNSQGW3WTOP44WO","short_pith_number":"pith:JIHVYSHD","canonical_record":{"source":{"id":"2406.01506","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2024-06-03T16:34:01Z","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"title_canon_sha256":"8616a674f7fe7ffc57362fe989500db6acc6bb2794d4d0797ab591699289ea2b","abstract_canon_sha256":"999efc8566365635d72cd13f3aae2d38bcd703ca6c4802218afc817008d77feb"},"schema_version":"1.0"},"canonical_sha256":"4a0f5c48e3c3b426ca06b6ed373f9cb3b3043e0ccc8a1029d0292eb8870cd681","source":{"kind":"arxiv","id":"2406.01506","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.01506","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"2406.01506v3","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01506","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"JIHVYSHDYO2C","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"pith_short_16","alias_value":"JIHVYSHDYO2CNSQG","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"pith_short_8","alias_value":"JIHVYSHD","created_at":"2026-07-05T10:15:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:JIHVYSHDYO2CNSQGW3WTOP44WO","target":"record","payload":{"canonical_record":{"source":{"id":"2406.01506","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2024-06-03T16:34:01Z","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"title_canon_sha256":"8616a674f7fe7ffc57362fe989500db6acc6bb2794d4d0797ab591699289ea2b","abstract_canon_sha256":"999efc8566365635d72cd13f3aae2d38bcd703ca6c4802218afc817008d77feb"},"schema_version":"1.0"},"canonical_sha256":"4a0f5c48e3c3b426ca06b6ed373f9cb3b3043e0ccc8a1029d0292eb8870cd681","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:15:43.900374Z","signature_b64":"9AM8Q8XwC7Ijt/rLLaoGLR3W366WiXwx2UufvAnLqR8qkPSehtJXl9oJ9aFoqt0Wa3IwdejH30eruLjGpCp+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a0f5c48e3c3b426ca06b6ed373f9cb3b3043e0ccc8a1029d0292eb8870cd681","last_reissued_at":"2026-07-05T10:15:43.899864Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:15:43.899864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.01506","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ZNItuhF3LyEiRKtBsfgGl5UdIpjSyHzrvAWWd8o3EcdZULcBAxCXG6D3cuRNzLjxs6FZLxXk3St5CQ280f9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T17:42:26.800921Z"},"content_sha256":"971be59d3844580c41dd50714a09911685d7d9d809b808b15088ec451f82ecf8","schema_version":"1.0","event_id":"sha256:971be59d3844580c41dd50714a09911685d7d9d809b808b15088ec451f82ecf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:JIHVYSHDYO2CNSQGW3WTOP44WO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Categorical and Hierarchical Concepts in Large Language Models","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.AI","cs.LG","stat.ML"],"primary_cat":"cs.CL","authors_text":"Kiho Park, Victor Veitch, Yibo Jiang, Yo Joong Choe","submitted_at":"2024-06-03T16:34:01Z","abstract_excerpt":"The linear representation hypothesis is the informal idea that semantic concepts are encoded as linear directions in the representation spaces of large language models (LLMs). Previous work has shown how to make this notion precise for representing binary concepts that have natural contrasts (e.g., {male, female}) as directions in representation space. However, many natural concepts do not have natural contrasts (e.g., whether the output is about an animal). In this work, we show how to extend the formalization of the linear representation hypothesis to represent features (e.g., is_animal) as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01506","kind":"arxiv","version":3},"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/2406.01506/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":"2026-07-05T10:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0UxQeaVMgKIk+D+35I5zbHKvOOrzepQyUH8KiuPX/G5m7db6+XgVZmizpSxAUctWsxz0ZRA8rJyfv7xX/70ECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-10T17:42:26.801328Z"},"content_sha256":"6269bed063128191ae59ffd92d070e41b3ebf791e3dcd6898a4d86b18d64af0e","schema_version":"1.0","event_id":"sha256:6269bed063128191ae59ffd92d070e41b3ebf791e3dcd6898a4d86b18d64af0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIHVYSHDYO2CNSQGW3WTOP44WO/bundle.json","state_url":"https://pith.science/pith/JIHVYSHDYO2CNSQGW3WTOP44WO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIHVYSHDYO2CNSQGW3WTOP44WO/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":"2026-07-10T17:42:26Z","links":{"resolver":"https://pith.science/pith/JIHVYSHDYO2CNSQGW3WTOP44WO","bundle":"https://pith.science/pith/JIHVYSHDYO2CNSQGW3WTOP44WO/bundle.json","state":"https://pith.science/pith/JIHVYSHDYO2CNSQGW3WTOP44WO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIHVYSHDYO2CNSQGW3WTOP44WO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JIHVYSHDYO2CNSQGW3WTOP44WO","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":"999efc8566365635d72cd13f3aae2d38bcd703ca6c4802218afc817008d77feb","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2024-06-03T16:34:01Z","title_canon_sha256":"8616a674f7fe7ffc57362fe989500db6acc6bb2794d4d0797ab591699289ea2b"},"schema_version":"1.0","source":{"id":"2406.01506","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.01506","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"2406.01506v3","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01506","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"JIHVYSHDYO2C","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"pith_short_16","alias_value":"JIHVYSHDYO2CNSQG","created_at":"2026-07-05T10:15:43Z"},{"alias_kind":"pith_short_8","alias_value":"JIHVYSHD","created_at":"2026-07-05T10:15:43Z"}],"graph_snapshots":[{"event_id":"sha256:6269bed063128191ae59ffd92d070e41b3ebf791e3dcd6898a4d86b18d64af0e","target":"graph","created_at":"2026-07-05T10:15:43Z","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/2406.01506/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The linear representation hypothesis is the informal idea that semantic concepts are encoded as linear directions in the representation spaces of large language models (LLMs). Previous work has shown how to make this notion precise for representing binary concepts that have natural contrasts (e.g., {male, female}) as directions in representation space. However, many natural concepts do not have natural contrasts (e.g., whether the output is about an animal). In this work, we show how to extend the formalization of the linear representation hypothesis to represent features (e.g., is_animal) as ","authors_text":"Kiho Park, Victor Veitch, Yibo Jiang, Yo Joong Choe","cross_cats":["cs.AI","cs.LG","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2024-06-03T16:34:01Z","title":"The Geometry of Categorical and Hierarchical Concepts in Large Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01506","kind":"arxiv","version":3},"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":"sha256:971be59d3844580c41dd50714a09911685d7d9d809b808b15088ec451f82ecf8","target":"record","created_at":"2026-07-05T10:15:43Z","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":"999efc8566365635d72cd13f3aae2d38bcd703ca6c4802218afc817008d77feb","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.CL","submitted_at":"2024-06-03T16:34:01Z","title_canon_sha256":"8616a674f7fe7ffc57362fe989500db6acc6bb2794d4d0797ab591699289ea2b"},"schema_version":"1.0","source":{"id":"2406.01506","kind":"arxiv","version":3}},"canonical_sha256":"4a0f5c48e3c3b426ca06b6ed373f9cb3b3043e0ccc8a1029d0292eb8870cd681","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a0f5c48e3c3b426ca06b6ed373f9cb3b3043e0ccc8a1029d0292eb8870cd681","first_computed_at":"2026-07-05T10:15:43.899864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:15:43.899864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9AM8Q8XwC7Ijt/rLLaoGLR3W366WiXwx2UufvAnLqR8qkPSehtJXl9oJ9aFoqt0Wa3IwdejH30eruLjGpCp+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:15:43.900374Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.01506","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:971be59d3844580c41dd50714a09911685d7d9d809b808b15088ec451f82ecf8","sha256:6269bed063128191ae59ffd92d070e41b3ebf791e3dcd6898a4d86b18d64af0e"],"state_sha256":"171dbdb43dd4bef0ae832e09e9bcb6570a533b9ac7c8b1026c2c2137f07ceb63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7qtf78CbvKQPslJA1M3Dh5vz/9muoroIACzA/hSSqslfR0ku6ZGKOvxu49HRAL/TUTy4uuuPEKaKOP0+pPZqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-10T17:42:26.804603Z","bundle_sha256":"8cc6e6849da9bd44faeb8eb2d4c0834c56e86065d156c91888fd24388fa2675e"}}