{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:5XCCJCNMWMENUKSCD4Y56ZKFA7","short_pith_number":"pith:5XCCJCNM","schema_version":"1.0","canonical_sha256":"edc42489acb308da2a421f31df654507e91c2a9fb5e92cf59aa03ad169926261","source":{"kind":"arxiv","id":"2301.13821","version":4},"attestation_state":"computed","paper":{"title":"Complete Neural Networks for Complete Euclidean Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nadav Dym, Snir Hordan, Steven J. Gortler, Tal Amir","submitted_at":"2023-01-31T18:07:26Z","abstract_excerpt":"Neural networks for point clouds, which respect their natural invariance to permutation and rigid motion, have enjoyed recent success in modeling geometric phenomena, from molecular dynamics to recommender systems. Yet, to date, no model with polynomial complexity is known to be complete, that is, able to distinguish between any pair of non-isomorphic point clouds. We fill this theoretical gap by showing that point clouds can be completely determined, up to permutation and rigid motion, by applying the 3-WL graph isomorphism test to the point cloud's centralized Gram matrix. Moreover, we formu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2301.13821","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-01-31T18:07:26Z","cross_cats_sorted":[],"title_canon_sha256":"61ca389659cacd28cdf1124b8586c86597ee4b362b7fba7203d3266fdf73e8dd","abstract_canon_sha256":"5c2283989f8ba75d600be3ffb57ac645209b9942fe3215f848a5eb87e60f7bc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:05:47.811127Z","signature_b64":"iLq84UGmmYitqGEogtzcMpQoApiYKtJNzyntAfYWbkz0enG9WPAbaEQNKpeqAaApKsul7XdtEJMixgwxJVS4BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edc42489acb308da2a421f31df654507e91c2a9fb5e92cf59aa03ad169926261","last_reissued_at":"2026-07-05T08:05:47.810686Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:05:47.810686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete Neural Networks for Complete Euclidean Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Nadav Dym, Snir Hordan, Steven J. Gortler, Tal Amir","submitted_at":"2023-01-31T18:07:26Z","abstract_excerpt":"Neural networks for point clouds, which respect their natural invariance to permutation and rigid motion, have enjoyed recent success in modeling geometric phenomena, from molecular dynamics to recommender systems. Yet, to date, no model with polynomial complexity is known to be complete, that is, able to distinguish between any pair of non-isomorphic point clouds. We fill this theoretical gap by showing that point clouds can be completely determined, up to permutation and rigid motion, by applying the 3-WL graph isomorphism test to the point cloud's centralized Gram matrix. Moreover, we formu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.13821","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2301.13821/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2301.13821","created_at":"2026-07-05T08:05:47.810739+00:00"},{"alias_kind":"arxiv_version","alias_value":"2301.13821v4","created_at":"2026-07-05T08:05:47.810739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.13821","created_at":"2026-07-05T08:05:47.810739+00:00"},{"alias_kind":"pith_short_12","alias_value":"5XCCJCNMWMEN","created_at":"2026-07-05T08:05:47.810739+00:00"},{"alias_kind":"pith_short_16","alias_value":"5XCCJCNMWMENUKSC","created_at":"2026-07-05T08:05:47.810739+00:00"},{"alias_kind":"pith_short_8","alias_value":"5XCCJCNM","created_at":"2026-07-05T08:05:47.810739+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2303.13486","citing_title":"Complete invariants of atomic clouds under rigid motion with Lipschitz continuous metrics in a polynomial time","ref_index":37,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7","json":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7.json","graph_json":"https://pith.science/api/pith-number/5XCCJCNMWMENUKSCD4Y56ZKFA7/graph.json","events_json":"https://pith.science/api/pith-number/5XCCJCNMWMENUKSCD4Y56ZKFA7/events.json","paper":"https://pith.science/paper/5XCCJCNM"},"agent_actions":{"view_html":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7","download_json":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7.json","view_paper":"https://pith.science/paper/5XCCJCNM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2301.13821&json=true","fetch_graph":"https://pith.science/api/pith-number/5XCCJCNMWMENUKSCD4Y56ZKFA7/graph.json","fetch_events":"https://pith.science/api/pith-number/5XCCJCNMWMENUKSCD4Y56ZKFA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7/action/storage_attestation","attest_author":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7/action/author_attestation","sign_citation":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7/action/citation_signature","submit_replication":"https://pith.science/pith/5XCCJCNMWMENUKSCD4Y56ZKFA7/action/replication_record"}},"created_at":"2026-07-05T08:05:47.810739+00:00","updated_at":"2026-07-05T08:05:47.810739+00:00"}