{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6CERFW2NHLMUCXZDACYRYIT2OO","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":"48844f37b8dc1f754544121364fa7239492838757613cd0d8e26d2736270c626","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-07-08T06:23:46Z","title_canon_sha256":"60c24c87fa0929529916ca69ee02fd237d25ccb2143b12a95e53405c098498e0"},"schema_version":"1.0","source":{"id":"2607.07047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07047","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07047v1","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07047","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"pith_short_12","alias_value":"6CERFW2NHLMU","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"pith_short_16","alias_value":"6CERFW2NHLMUCXZD","created_at":"2026-07-09T01:20:13Z"},{"alias_kind":"pith_short_8","alias_value":"6CERFW2N","created_at":"2026-07-09T01:20:13Z"}],"graph_snapshots":[{"event_id":"sha256:4bdcdd564665d1efad1526fe5fa821ad1b776ba4fffcc197d3aa250b76eda99d","target":"graph","created_at":"2026-07-09T01:20:13Z","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/2607.07047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety. We ask whether sentence-level classification signal lives in the Riemannian geometry of contextual token embeddings, and probe it by extracting per-token pullback metrics from a learned encoder's analytical Jacobian and aggregating them with the Fr\\'echet mean on the symmetric positive definite (SPD) manifold; we call this procedure Riemannian Mean Pooling (RMP). Across three datasets with non-trivial linguistic structure (CoLA, CREAK, RTE), RMP outperforms Euclidean mean poo","authors_text":"Alexandre Quemy, Bart{\\l}omiej Sobieski, Gr\\'egoire Cattan, Przemys{\\l}aw Klocek, Szczepan Konior","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-07-08T06:23:46Z","title":"Riemannian Geometry for Pre-trained Language Model Embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07047","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":"sha256:381e18a39b3de79d7342fa68ee22eea916e1305aaabe992a2581c2d9e85d6b3e","target":"record","created_at":"2026-07-09T01:20:13Z","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":"48844f37b8dc1f754544121364fa7239492838757613cd0d8e26d2736270c626","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2026-07-08T06:23:46Z","title_canon_sha256":"60c24c87fa0929529916ca69ee02fd237d25ccb2143b12a95e53405c098498e0"},"schema_version":"1.0","source":{"id":"2607.07047","kind":"arxiv","version":1}},"canonical_sha256":"f08912db4d3ad9415f2300b11c227a73b423e8a3c1d445405a35e6b6411e98d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f08912db4d3ad9415f2300b11c227a73b423e8a3c1d445405a35e6b6411e98d2","first_computed_at":"2026-07-09T01:20:13.188251Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:13.188251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rep9XC//AjqDAq9w9TmsUKySbgvUW/VqPcPjOqgzxxwC761ePr9Aa+V6RDGCGqkflXJbfpy4n7Qz70ds0O+1DA==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:13.188603Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:381e18a39b3de79d7342fa68ee22eea916e1305aaabe992a2581c2d9e85d6b3e","sha256:4bdcdd564665d1efad1526fe5fa821ad1b776ba4fffcc197d3aa250b76eda99d"],"state_sha256":"9cc5b68cb303080b2079d69fb5156c8c71475fc578ae4bb802ce0ea6cab5d57b"}