{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:MR5SIJMHXOV27HADRHLJQM2SBC","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":"8b46ec5b616370ebd48bb66193e5e376b717cb630888940ef4309b1bc4ab54e0","cross_cats_sorted":["cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T10:55:38Z","title_canon_sha256":"a2f2553be873d96f10c1d9a438fe13a940b1a0a19ab14f98c7b931cc58aeef89"},"schema_version":"1.0","source":{"id":"2405.15429","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.15429","created_at":"2026-07-05T10:10:23Z"},{"alias_kind":"arxiv_version","alias_value":"2405.15429v5","created_at":"2026-07-05T10:10:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15429","created_at":"2026-07-05T10:10:23Z"},{"alias_kind":"pith_short_12","alias_value":"MR5SIJMHXOV2","created_at":"2026-07-05T10:10:23Z"},{"alias_kind":"pith_short_16","alias_value":"MR5SIJMHXOV27HAD","created_at":"2026-07-05T10:10:23Z"},{"alias_kind":"pith_short_8","alias_value":"MR5SIJMH","created_at":"2026-07-05T10:10:23Z"}],"graph_snapshots":[{"event_id":"sha256:c25f96c90ad2b086db37f891e64233dd881bd232b161512399925c69d1f34643","target":"graph","created_at":"2026-07-05T10:10:23Z","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/2405.15429/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue. TDL enables the principled modeling of arbitrary multi-way, hierarchical higher-order interactions by operating on combinatorial topological spaces, such as simplicial or cell complexes, instead of graphs. However, little is known about how to leverage geometric features such as positions and velocities for TDL. This paper introduces E(n)-Equivariant Topolog","authors_text":"Claudio Battiloro, Ege Karaismailo\\u{g}lu, Francesca Dominici, George Dasoulas, Mauricio Tec, Michelle Audirac","cross_cats":["cs.NE"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T10:55:38Z","title":"E(n) Equivariant Topological Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15429","kind":"arxiv","version":5},"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":"sha256:835be3ff788872f5a345747d4a257af91e1d52b49823394c38b751a2b367f0a9","target":"record","created_at":"2026-07-05T10:10:23Z","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":"8b46ec5b616370ebd48bb66193e5e376b717cb630888940ef4309b1bc4ab54e0","cross_cats_sorted":["cs.NE"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-24T10:55:38Z","title_canon_sha256":"a2f2553be873d96f10c1d9a438fe13a940b1a0a19ab14f98c7b931cc58aeef89"},"schema_version":"1.0","source":{"id":"2405.15429","kind":"arxiv","version":5}},"canonical_sha256":"647b242587bbabaf9c0389d6983352088beaa29152dd61c00551b9c8d335bfbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"647b242587bbabaf9c0389d6983352088beaa29152dd61c00551b9c8d335bfbf","first_computed_at":"2026-07-05T10:10:23.409992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:10:23.409992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5kyrqRKoLKFSYbpgpxQ188swD255uWSEV2z6PQJkZoNzbzSc3mWl5EN6P5/gnH3NEoYHab70Q9Gff4Qto+EXDg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:10:23.410547Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.15429","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:835be3ff788872f5a345747d4a257af91e1d52b49823394c38b751a2b367f0a9","sha256:c25f96c90ad2b086db37f891e64233dd881bd232b161512399925c69d1f34643"],"state_sha256":"c4ea973ca482bad37b54deef76d5d76b4c0dba8503b7db120219353b5c539890"}