{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:A5RRF4MNGGGCY76ZMHRFYTA34T","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":"e6002b8363e805facd47b11d60766ceb14be30d1c21d6a10e521cfdf385fcacc","cross_cats_sorted":["cond-mat.mtrl-sci","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-28T19:57:50Z","title_canon_sha256":"b17438b4c544c000c5397837c3974000575cbd845f8bfdaef723db274b1e5ea3"},"schema_version":"1.0","source":{"id":"2606.29584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29584","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29584v1","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29584","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"A5RRF4MNGGGC","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"A5RRF4MNGGGCY76Z","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"A5RRF4MN","created_at":"2026-06-30T01:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:4f1bb171d58e401627a35b8c68b49f439e1b1ce83eba4e6ddf7cb600aab947d2","target":"graph","created_at":"2026-06-30T01:18:13Z","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/2606.29584/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"$\\mathrm{Cl}(3,0)$ interatomic potentials, despite their algebraic elegance, predict force magnitudes accurately but force directions poorly. Across ten rMD17 molecules, every $L \\leq 1$ baseline in our twelve-model study attains aggregate force-cosine similarity below $0.25$. The cause is structural. The geometric product of two vectors in $\\mathbb{R}^3$ realises only the $L=0$ and $L=1$ components of its irreducible representation content, leaving the symmetric-traceless rank-2 component absent from the per-edge bilinear that drives each message-passing layer. We address this with CliffordST","authors_text":"Can Polat, Erchin Serpedin, Hasan Kurban, Mustafa Kurban","cross_cats":["cond-mat.mtrl-sci","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-28T19:57:50Z","title":"Geometric Algebra Meets Cartesian Tensors: Higher-Order Equivariance for Interatomic Potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29584","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:bb967a13ed89811db486543b3085c44a6aa532639c1a4dbb0e12dfa1b40d61bc","target":"record","created_at":"2026-06-30T01:18:13Z","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":"e6002b8363e805facd47b11d60766ceb14be30d1c21d6a10e521cfdf385fcacc","cross_cats_sorted":["cond-mat.mtrl-sci","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.chem-ph","submitted_at":"2026-06-28T19:57:50Z","title_canon_sha256":"b17438b4c544c000c5397837c3974000575cbd845f8bfdaef723db274b1e5ea3"},"schema_version":"1.0","source":{"id":"2606.29584","kind":"arxiv","version":1}},"canonical_sha256":"076312f18d318c2c7fd961e25c4c1be4d15258b5f78546d052448b658759a3e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"076312f18d318c2c7fd961e25c4c1be4d15258b5f78546d052448b658759a3e6","first_computed_at":"2026-06-30T01:18:13.112312Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:18:13.112312Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hehQKQKShItw7F5yK+v7WPl+cYyXJwUqawO8BIRu7oaxhi3ZAOoBil3tBTwCzHmivGVK4peQJ3lQOQnirOc/BQ==","signature_status":"signed_v1","signed_at":"2026-06-30T01:18:13.112796Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb967a13ed89811db486543b3085c44a6aa532639c1a4dbb0e12dfa1b40d61bc","sha256:4f1bb171d58e401627a35b8c68b49f439e1b1ce83eba4e6ddf7cb600aab947d2"],"state_sha256":"7207306dc8fc167b4acccb21f639d6030aa521d1c7e74f6d53cb782f5bacd822"}