{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HUBOGQ3G7RJBBM33OSIXSZFCDO","short_pith_number":"pith:HUBOGQ3G","canonical_record":{"source":{"id":"2605.23821","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-22T16:24:30Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a0e64886d294b0fe65ab78588c1665d715193d33c024d31994191c250cc1f4bf","abstract_canon_sha256":"3dd421076734bd8ca3953f80c3955c2940f1760a5f966af739958b3c621267e6"},"schema_version":"1.0"},"canonical_sha256":"3d02e34366fc5210b37b74917964a21b897ffdc90e1c59c53dc37e1cae64cdf6","source":{"kind":"arxiv","id":"2605.23821","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23821","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23821v1","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23821","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"HUBOGQ3G7RJB","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"HUBOGQ3G7RJBBM33","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"HUBOGQ3G","created_at":"2026-05-25T02:02:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HUBOGQ3G7RJBBM33OSIXSZFCDO","target":"record","payload":{"canonical_record":{"source":{"id":"2605.23821","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-22T16:24:30Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"a0e64886d294b0fe65ab78588c1665d715193d33c024d31994191c250cc1f4bf","abstract_canon_sha256":"3dd421076734bd8ca3953f80c3955c2940f1760a5f966af739958b3c621267e6"},"schema_version":"1.0"},"canonical_sha256":"3d02e34366fc5210b37b74917964a21b897ffdc90e1c59c53dc37e1cae64cdf6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-25T02:02:34.147105Z","signature_b64":"e2/ormBLVG6GGvF0QXuaLH29p0Mqpl5LLEY2C9v02HCbIy6Zcz2uhlMUl6+ArkUfR2DzTEid2dcaPMrEVe3ADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d02e34366fc5210b37b74917964a21b897ffdc90e1c59c53dc37e1cae64cdf6","last_reissued_at":"2026-05-25T02:02:34.146289Z","signature_status":"signed_v1","first_computed_at":"2026-05-25T02:02:34.146289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.23821","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":"2026-05-25T02:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+jahJowI8Jrysa1Z/ODBOozw2c8JwjTTkmtu/W/M6CxBNM3ipqzridkkuP84BLqcDORcWPqKZTzG6mLoCrJ9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:10:55.485832Z"},"content_sha256":"4e5b149e8e8639d724e10996a1dc04e859a363565c8ccd6353372715e1cb6cfa","schema_version":"1.0","event_id":"sha256:4e5b149e8e8639d724e10996a1dc04e859a363565c8ccd6353372715e1cb6cfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HUBOGQ3G7RJBBM33OSIXSZFCDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hierarchical Concept Geometry in Language Models Emerges from Word Co-occurrence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Andres Nava, Matthieu Wyart","submitted_at":"2026-05-22T16:24:30Z","abstract_excerpt":"We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer on the WordNet hypernym graph co-occur more often, we characterize theoretically the spectrum of the resulting embedding Gram matrix of word2vec embeddings. Under mild positivity and decay conditions on the co-occurrence kernel, we prove that the leading eigenvectors first separate broad taxonomic branches and then progressively finer sub-branches, producing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23821","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/2605.23821/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":"2026-05-25T02:02:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+BN6pKXYtOw4CEscbL7BSzhUFkES8a5E8d66HZS3eNwC0t08j6VLm/fMxtF2eUrhB6n+ayVViUqDgWTMBDHxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:10:55.486568Z"},"content_sha256":"d10170dcbebf7003257fe30b12d98f1bd28f61e54c124031836b010b8f672c23","schema_version":"1.0","event_id":"sha256:d10170dcbebf7003257fe30b12d98f1bd28f61e54c124031836b010b8f672c23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUBOGQ3G7RJBBM33OSIXSZFCDO/bundle.json","state_url":"https://pith.science/pith/HUBOGQ3G7RJBBM33OSIXSZFCDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUBOGQ3G7RJBBM33OSIXSZFCDO/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":"2026-06-07T16:10:55Z","links":{"resolver":"https://pith.science/pith/HUBOGQ3G7RJBBM33OSIXSZFCDO","bundle":"https://pith.science/pith/HUBOGQ3G7RJBBM33OSIXSZFCDO/bundle.json","state":"https://pith.science/pith/HUBOGQ3G7RJBBM33OSIXSZFCDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUBOGQ3G7RJBBM33OSIXSZFCDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HUBOGQ3G7RJBBM33OSIXSZFCDO","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":"3dd421076734bd8ca3953f80c3955c2940f1760a5f966af739958b3c621267e6","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-22T16:24:30Z","title_canon_sha256":"a0e64886d294b0fe65ab78588c1665d715193d33c024d31994191c250cc1f4bf"},"schema_version":"1.0","source":{"id":"2605.23821","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23821","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23821v1","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23821","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"pith_short_12","alias_value":"HUBOGQ3G7RJB","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"pith_short_16","alias_value":"HUBOGQ3G7RJBBM33","created_at":"2026-05-25T02:02:34Z"},{"alias_kind":"pith_short_8","alias_value":"HUBOGQ3G","created_at":"2026-05-25T02:02:34Z"}],"graph_snapshots":[{"event_id":"sha256:d10170dcbebf7003257fe30b12d98f1bd28f61e54c124031836b010b8f672c23","target":"graph","created_at":"2026-05-25T02:02:34Z","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/2605.23821/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a distributional theory of how hypernymy -- the ``is-a'' relation between general and specific concepts -- is encoded geometrically in language representations. Starting from the empirically verified assumption that words closer on the WordNet hypernym graph co-occur more often, we characterize theoretically the spectrum of the resulting embedding Gram matrix of word2vec embeddings. Under mild positivity and decay conditions on the co-occurrence kernel, we prove that the leading eigenvectors first separate broad taxonomic branches and then progressively finer sub-branches, producing","authors_text":"Andres Nava, Matthieu Wyart","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-22T16:24:30Z","title":"Hierarchical Concept Geometry in Language Models Emerges from Word Co-occurrence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23821","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":"sha256:4e5b149e8e8639d724e10996a1dc04e859a363565c8ccd6353372715e1cb6cfa","target":"record","created_at":"2026-05-25T02:02:34Z","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":"3dd421076734bd8ca3953f80c3955c2940f1760a5f966af739958b3c621267e6","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CL","submitted_at":"2026-05-22T16:24:30Z","title_canon_sha256":"a0e64886d294b0fe65ab78588c1665d715193d33c024d31994191c250cc1f4bf"},"schema_version":"1.0","source":{"id":"2605.23821","kind":"arxiv","version":1}},"canonical_sha256":"3d02e34366fc5210b37b74917964a21b897ffdc90e1c59c53dc37e1cae64cdf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d02e34366fc5210b37b74917964a21b897ffdc90e1c59c53dc37e1cae64cdf6","first_computed_at":"2026-05-25T02:02:34.146289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:34.146289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e2/ormBLVG6GGvF0QXuaLH29p0Mqpl5LLEY2C9v02HCbIy6Zcz2uhlMUl6+ArkUfR2DzTEid2dcaPMrEVe3ADg==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:34.147105Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23821","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e5b149e8e8639d724e10996a1dc04e859a363565c8ccd6353372715e1cb6cfa","sha256:d10170dcbebf7003257fe30b12d98f1bd28f61e54c124031836b010b8f672c23"],"state_sha256":"837c7bc8973d18cc30dfc3a833203a8d7fdcf8de438b1040c2c923b7ee97ccfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwcvJhVolDaot6y2QnmGkdQtF0DZFHPPrTs1RXl3AE6hSwz4+nweGga8EVyCrRABX0IHeoFh2epwcZ1EWTAEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:10:55.490676Z","bundle_sha256":"819aeb64cc973146b460faf83418b62f83211e0c23e15c6de759c3fc32fac575"}}