{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CDNVENGAHWF6CD5ZWFICY3EJRT","short_pith_number":"pith:CDNVENGA","canonical_record":{"source":{"id":"2602.15029","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T18:59:55Z","cross_cats_sorted":["cond-mat.dis-nn","cs.CL"],"title_canon_sha256":"cdb477d6e3431592fa4c69080e0fb6d016b1454f0edb4d8473f383a99aaa42b8","abstract_canon_sha256":"ca499596cd83a75d852b6a30dc0dda7c96e52911c565fa4a53ff2c41f9a1c433"},"schema_version":"1.0"},"canonical_sha256":"10db5234c03d8be10fb9b1502c6c898cfb421eaea5f0cadab1c67b1177460a95","source":{"kind":"arxiv","id":"2602.15029","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.15029","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2602.15029v3","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.15029","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"CDNVENGAHWF6","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"CDNVENGAHWF6CD5Z","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"CDNVENGA","created_at":"2026-07-01T00:17:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CDNVENGAHWF6CD5ZWFICY3EJRT","target":"record","payload":{"canonical_record":{"source":{"id":"2602.15029","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T18:59:55Z","cross_cats_sorted":["cond-mat.dis-nn","cs.CL"],"title_canon_sha256":"cdb477d6e3431592fa4c69080e0fb6d016b1454f0edb4d8473f383a99aaa42b8","abstract_canon_sha256":"ca499596cd83a75d852b6a30dc0dda7c96e52911c565fa4a53ff2c41f9a1c433"},"schema_version":"1.0"},"canonical_sha256":"10db5234c03d8be10fb9b1502c6c898cfb421eaea5f0cadab1c67b1177460a95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T00:17:10.354207Z","signature_b64":"p+7qXTpgqFtwPkeEMD/WkOGzw5YlrStaJVGOot7T/B1Z/5ESt5XNRnTKk3oXAsUA9ZeylDzpe78Eu15yAUVuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10db5234c03d8be10fb9b1502c6c898cfb421eaea5f0cadab1c67b1177460a95","last_reissued_at":"2026-07-01T00:17:10.353703Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T00:17:10.353703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.15029","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":"2026-07-01T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TKVwV5c8Ggx9cRfIWqSbjd1KtbhgwrmizUDN/LRd6Fiapm1NGsBUe/pz3zLxNAU5HbV28Om+BJB+C9USqCT2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:04:32.746297Z"},"content_sha256":"da87a04f1cab1d1847620dc4c9c4994d49f1b4b524587dd57c99fbfc943c0c42","schema_version":"1.0","event_id":"sha256:da87a04f1cab1d1847620dc4c9c4994d49f1b4b524587dd57c99fbfc943c0c42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CDNVENGAHWF6CD5ZWFICY3EJRT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetry in language statistics shapes the geometry of model representations","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["cond-mat.dis-nn","cs.CL"],"primary_cat":"cs.LG","authors_text":"Andres Nava, Daniel J. Korchinski, Dhruva Karkada, Matthieu Wyart, Yasaman Bahri","submitted_at":"2026-02-16T18:59:55Z","abstract_excerpt":"The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes can be decoded using a linear probe. To explain this neural code, we first show that language statistics exhibit translation symmetry (for example, the frequency with which any two months co-occur in text depends only on the time interval between them). We prove that this symmetry governs these geometric structures in high-dimensional word embedding models,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.15029","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/2602.15029/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":"2026-07-01T00:17:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"II7stluKEMvr8t+5sKGEhereY+CfcigfqJ1yADkFVSOTPNEjjU6CAl+ryyxJhXW6p2rb/ogKtfa1A4XxVxOZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T11:04:32.746704Z"},"content_sha256":"057db45c07edcf1f728b42d38c99e84f62f74e9d0448407dc6a9d54b35aed3c0","schema_version":"1.0","event_id":"sha256:057db45c07edcf1f728b42d38c99e84f62f74e9d0448407dc6a9d54b35aed3c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDNVENGAHWF6CD5ZWFICY3EJRT/bundle.json","state_url":"https://pith.science/pith/CDNVENGAHWF6CD5ZWFICY3EJRT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDNVENGAHWF6CD5ZWFICY3EJRT/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":"2026-07-01T11:04:32Z","links":{"resolver":"https://pith.science/pith/CDNVENGAHWF6CD5ZWFICY3EJRT","bundle":"https://pith.science/pith/CDNVENGAHWF6CD5ZWFICY3EJRT/bundle.json","state":"https://pith.science/pith/CDNVENGAHWF6CD5ZWFICY3EJRT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDNVENGAHWF6CD5ZWFICY3EJRT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CDNVENGAHWF6CD5ZWFICY3EJRT","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":"ca499596cd83a75d852b6a30dc0dda7c96e52911c565fa4a53ff2c41f9a1c433","cross_cats_sorted":["cond-mat.dis-nn","cs.CL"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T18:59:55Z","title_canon_sha256":"cdb477d6e3431592fa4c69080e0fb6d016b1454f0edb4d8473f383a99aaa42b8"},"schema_version":"1.0","source":{"id":"2602.15029","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.15029","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"arxiv_version","alias_value":"2602.15029v3","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.15029","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"pith_short_12","alias_value":"CDNVENGAHWF6","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"pith_short_16","alias_value":"CDNVENGAHWF6CD5Z","created_at":"2026-07-01T00:17:10Z"},{"alias_kind":"pith_short_8","alias_value":"CDNVENGA","created_at":"2026-07-01T00:17:10Z"}],"graph_snapshots":[{"event_id":"sha256:057db45c07edcf1f728b42d38c99e84f62f74e9d0448407dc6a9d54b35aed3c0","target":"graph","created_at":"2026-07-01T00:17:10Z","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/2602.15029/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes can be decoded using a linear probe. To explain this neural code, we first show that language statistics exhibit translation symmetry (for example, the frequency with which any two months co-occur in text depends only on the time interval between them). We prove that this symmetry governs these geometric structures in high-dimensional word embedding models,","authors_text":"Andres Nava, Daniel J. Korchinski, Dhruva Karkada, Matthieu Wyart, Yasaman Bahri","cross_cats":["cond-mat.dis-nn","cs.CL"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T18:59:55Z","title":"Symmetry in language statistics shapes the geometry of model representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.15029","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:da87a04f1cab1d1847620dc4c9c4994d49f1b4b524587dd57c99fbfc943c0c42","target":"record","created_at":"2026-07-01T00:17:10Z","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":"ca499596cd83a75d852b6a30dc0dda7c96e52911c565fa4a53ff2c41f9a1c433","cross_cats_sorted":["cond-mat.dis-nn","cs.CL"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-16T18:59:55Z","title_canon_sha256":"cdb477d6e3431592fa4c69080e0fb6d016b1454f0edb4d8473f383a99aaa42b8"},"schema_version":"1.0","source":{"id":"2602.15029","kind":"arxiv","version":3}},"canonical_sha256":"10db5234c03d8be10fb9b1502c6c898cfb421eaea5f0cadab1c67b1177460a95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10db5234c03d8be10fb9b1502c6c898cfb421eaea5f0cadab1c67b1177460a95","first_computed_at":"2026-07-01T00:17:10.353703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T00:17:10.353703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p+7qXTpgqFtwPkeEMD/WkOGzw5YlrStaJVGOot7T/B1Z/5ESt5XNRnTKk3oXAsUA9ZeylDzpe78Eu15yAUVuCA==","signature_status":"signed_v1","signed_at":"2026-07-01T00:17:10.354207Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.15029","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da87a04f1cab1d1847620dc4c9c4994d49f1b4b524587dd57c99fbfc943c0c42","sha256:057db45c07edcf1f728b42d38c99e84f62f74e9d0448407dc6a9d54b35aed3c0"],"state_sha256":"75f74b6ffcd2ffaf2dae7cbccaabdcf48ebb17dd8a865e3dc40cdde81e030d1a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j5+hbLQXLsExFi4EeTg1toaExWiFDjcDfBpw+PthPk/rzLiqP2Dg8c6eh8vTcG8nYs/Q55B2jyKKDCQC/XVrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T11:04:32.748709Z","bundle_sha256":"ef51f4f5ad81b067db2467607834be502ae68ad45b34c6a5a7fbc638977a99bc"}}