{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RC5UNS3VXYOOINVZ75IXLRHPLU","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":"161ab89b453476f2bb41e8a55f218e106d59053d46867b66afa85d2db7cdfb5d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-12T05:28:48Z","title_canon_sha256":"2cc6d496d60ec79cc888ff4d7fe00231c409f505e64c392b8220a5556d615183"},"schema_version":"1.0","source":{"id":"2607.10578","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10578","created_at":"2026-07-14T01:21:22Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10578v1","created_at":"2026-07-14T01:21:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10578","created_at":"2026-07-14T01:21:22Z"},{"alias_kind":"pith_short_12","alias_value":"RC5UNS3VXYOO","created_at":"2026-07-14T01:21:22Z"},{"alias_kind":"pith_short_16","alias_value":"RC5UNS3VXYOOINVZ","created_at":"2026-07-14T01:21:22Z"},{"alias_kind":"pith_short_8","alias_value":"RC5UNS3V","created_at":"2026-07-14T01:21:22Z"}],"graph_snapshots":[{"event_id":"sha256:1c8800a6a4869ee4f735aad9d0dcdf571c568f113f4edc5050a15a7e7de40376","target":"graph","created_at":"2026-07-14T01:21:22Z","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/2607.10578/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge. Here, we show that concept geometry can be precisely characterized via Laguerre Geometry, in which a concept is defined as a region--a Laguerre-Voronoi cell or a union of cells--allowing us to strictly define, measure, and separate concepts. Building on this formulation, we show that finer-grained concept structures, such as inclusion and hierarchy, are naturally revealed by the Laguerre weights. We then push this geometry in","authors_text":"Chunwei Ma, Russell Wolfinger","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-12T05:28:48Z","title":"Laguerre Geometry for Interpreting Large Language Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10578","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":"sha256:2ea83460150168a4369b642ece6846d95998e7f3c6aecfedb4fde375bf78eb11","target":"record","created_at":"2026-07-14T01:21:22Z","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":"161ab89b453476f2bb41e8a55f218e106d59053d46867b66afa85d2db7cdfb5d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-07-12T05:28:48Z","title_canon_sha256":"2cc6d496d60ec79cc888ff4d7fe00231c409f505e64c392b8220a5556d615183"},"schema_version":"1.0","source":{"id":"2607.10578","kind":"arxiv","version":1}},"canonical_sha256":"88bb46cb75be1ce436b9ff5175c4ef5d07e514eb4e2d92090458f1ea089194bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88bb46cb75be1ce436b9ff5175c4ef5d07e514eb4e2d92090458f1ea089194bc","first_computed_at":"2026-07-14T01:21:22.179301Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:21:22.179301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"U30dB9IGggrS3Wdw7ed6pe8sWzvksSZa5W6yRLaVM3tYBybrQt+Frcy9ic/VO5n6IBPVu8yfzFK+z5RtqNJWAA==","signature_status":"signed_v1","signed_at":"2026-07-14T01:21:22.180035Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.10578","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ea83460150168a4369b642ece6846d95998e7f3c6aecfedb4fde375bf78eb11","sha256:1c8800a6a4869ee4f735aad9d0dcdf571c568f113f4edc5050a15a7e7de40376"],"state_sha256":"dfbec5ea0392578eac2a7b10e41a1340301ae92c5aa05ff92f937ad7b10f2304"}