{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XIYZ6OIY5LAEEPWTKTW46VS56C","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":"27588cb01691aecf6da0b2b5d8b13c27e540f064ff4898e080966c91b5660bcb","cross_cats_sorted":["cs.CV","cs.GR","cs.RO","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T17:56:17Z","title_canon_sha256":"3d45ee421e48f2c38f795819b85b8722f0e61bf24a8ef8364f8d0ba1d039d583"},"schema_version":"1.0","source":{"id":"2606.20547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20547","created_at":"2026-06-19T16:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20547v1","created_at":"2026-06-19T16:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20547","created_at":"2026-06-19T16:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"XIYZ6OIY5LAE","created_at":"2026-06-19T16:13:14Z"},{"alias_kind":"pith_short_16","alias_value":"XIYZ6OIY5LAEEPWT","created_at":"2026-06-19T16:13:14Z"},{"alias_kind":"pith_short_8","alias_value":"XIYZ6OIY","created_at":"2026-06-19T16:13:14Z"}],"graph_snapshots":[{"event_id":"sha256:24e33f66c08a8a0219dadbb3f8020de6425ae9096d2936eaa70c8f326e808938","target":"graph","created_at":"2026-06-19T16:13:14Z","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/2606.20547/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $\\rho(g)$ carrying it. To our knowledge this is the first attention construction whose tokens are bare matrix Lie group elements: their score is the closed-form algebra norm of the relative pose rather than a learned kernel, and it reaches the affine full-frame groups that every irrep- or surjective-exp-based method must exclude. We call it Lie-Algebra Attention. Once tokens are group elements, the rest follows with none of th","authors_text":"Przemyslaw Musialski","cross_cats":["cs.CV","cs.GR","cs.RO","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T17:56:17Z","title":"The Token Is a Group Element: On Lie-Algebra Attention over Matrix Lie Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20547","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:d9f99549112f646f48c8cbe0f631ad53a0244e055ec6dc6d0466f30aec79078e","target":"record","created_at":"2026-06-19T16:13:14Z","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":"27588cb01691aecf6da0b2b5d8b13c27e540f064ff4898e080966c91b5660bcb","cross_cats_sorted":["cs.CV","cs.GR","cs.RO","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-18T17:56:17Z","title_canon_sha256":"3d45ee421e48f2c38f795819b85b8722f0e61bf24a8ef8364f8d0ba1d039d583"},"schema_version":"1.0","source":{"id":"2606.20547","kind":"arxiv","version":1}},"canonical_sha256":"ba319f3918eac0423ed354edcf565df09f00551c3d212221aee6f1690fe61554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba319f3918eac0423ed354edcf565df09f00551c3d212221aee6f1690fe61554","first_computed_at":"2026-06-19T16:13:14.992950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:13:14.992950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RDUH7DbU0NJP9Ph8LmTVUO4wpUY2Dj2ACSdGy6veGMQ+jzzOsgjL3tf0wdwn2MM6ni5mMqD00gDLi//746ALCQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:13:14.993296Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f99549112f646f48c8cbe0f631ad53a0244e055ec6dc6d0466f30aec79078e","sha256:24e33f66c08a8a0219dadbb3f8020de6425ae9096d2936eaa70c8f326e808938"],"state_sha256":"c11a4ec379eb0c1220726b4631785528d759baa30e9f7672a1964ea437082215"}