{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4QZ67YOEOQ7NLASUB6VWT66CED","short_pith_number":"pith:4QZ67YOE","canonical_record":{"source":{"id":"2010.02449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-06T03:14:16Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"4c1d296ca526dbbbf07be101a6cf73b22d39c84f4a8c9907f592d6866c97b7f0","abstract_canon_sha256":"51927245fc5e7fcbbb5ca8e9f7e103acd1c8347574d16d0e003896a1a697b4b4"},"schema_version":"1.0"},"canonical_sha256":"e433efe1c4743ed582540fab69fbc220f09e8b042846a4bbee58bac3738a20a6","source":{"kind":"arxiv","id":"2010.02449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.02449","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"2010.02449v1","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.02449","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"4QZ67YOEOQ7N","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"pith_short_16","alias_value":"4QZ67YOEOQ7NLASU","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"pith_short_8","alias_value":"4QZ67YOE","created_at":"2026-07-05T01:40:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4QZ67YOEOQ7NLASUB6VWT66CED","target":"record","payload":{"canonical_record":{"source":{"id":"2010.02449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-06T03:14:16Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"4c1d296ca526dbbbf07be101a6cf73b22d39c84f4a8c9907f592d6866c97b7f0","abstract_canon_sha256":"51927245fc5e7fcbbb5ca8e9f7e103acd1c8347574d16d0e003896a1a697b4b4"},"schema_version":"1.0"},"canonical_sha256":"e433efe1c4743ed582540fab69fbc220f09e8b042846a4bbee58bac3738a20a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:40:49.986500Z","signature_b64":"KRXHU2+WJ7LHOzx8n4Gwpwepov+HzXBH+C5QSP20Rt3nJAR1e+HNxsRck6ioZXVEM5itvOYXgCXDFBg+m8PCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e433efe1c4743ed582540fab69fbc220f09e8b042846a4bbee58bac3738a20a6","last_reissued_at":"2026-07-05T01:40:49.986012Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:40:49.986012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.02449","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:40:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weQ3gmKb0yIGuvo+RH4tF2otMJJM49ObNcovpgwyul8a9oMi+d0wZzuClYrLV/gxlPIcL9hFctHILjaghTZdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:54:34.788312Z"},"content_sha256":"4427938a8f72c89236e5272afea6286d489d13d575eaad874bbbb823ae650ee7","schema_version":"1.0","event_id":"sha256:4427938a8f72c89236e5272afea6286d489d13d575eaad874bbbb823ae650ee7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4QZ67YOEOQ7NLASUB6VWT66CED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Universality of Rotation Equivariant Point Cloud Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.LG","authors_text":"Haggai Maron, Nadav Dym","submitted_at":"2020-10-06T03:14:16Z","abstract_excerpt":"Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry. Recently, there has been a growing interest in neural architectures that are invariant or equivariant to all three shape-preserving transformations of point clouds: translation, rotation, and permutation.\n  In this paper, we present a first study of the approximation power of these architectures. We first derive two sufficient conditions for an equivariant architecture to have the universal approximation property, based on a novel characterization of the spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.02449","kind":"arxiv","version":1},"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/2010.02449/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:40:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbKyMn9oglk6bTiWxH/Q5myVdNn2KO8Qpv4F58kCXyMOQe9DouUh4Sxldy/05f+h+pzkx/pe5mV6WzdM9zoFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T06:54:34.788702Z"},"content_sha256":"ad27d27008d026876be7bcefaabf3ec0d193658a3855cab999cdc1720c6f826d","schema_version":"1.0","event_id":"sha256:ad27d27008d026876be7bcefaabf3ec0d193658a3855cab999cdc1720c6f826d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4QZ67YOEOQ7NLASUB6VWT66CED/bundle.json","state_url":"https://pith.science/pith/4QZ67YOEOQ7NLASUB6VWT66CED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4QZ67YOEOQ7NLASUB6VWT66CED/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-07T06:54:34Z","links":{"resolver":"https://pith.science/pith/4QZ67YOEOQ7NLASUB6VWT66CED","bundle":"https://pith.science/pith/4QZ67YOEOQ7NLASUB6VWT66CED/bundle.json","state":"https://pith.science/pith/4QZ67YOEOQ7NLASUB6VWT66CED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4QZ67YOEOQ7NLASUB6VWT66CED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4QZ67YOEOQ7NLASUB6VWT66CED","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":"51927245fc5e7fcbbb5ca8e9f7e103acd1c8347574d16d0e003896a1a697b4b4","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-06T03:14:16Z","title_canon_sha256":"4c1d296ca526dbbbf07be101a6cf73b22d39c84f4a8c9907f592d6866c97b7f0"},"schema_version":"1.0","source":{"id":"2010.02449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.02449","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"2010.02449v1","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.02449","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"4QZ67YOEOQ7N","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"pith_short_16","alias_value":"4QZ67YOEOQ7NLASU","created_at":"2026-07-05T01:40:49Z"},{"alias_kind":"pith_short_8","alias_value":"4QZ67YOE","created_at":"2026-07-05T01:40:49Z"}],"graph_snapshots":[{"event_id":"sha256:ad27d27008d026876be7bcefaabf3ec0d193658a3855cab999cdc1720c6f826d","target":"graph","created_at":"2026-07-05T01:40:49Z","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/2010.02449/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Learning functions on point clouds has applications in many fields, including computer vision, computer graphics, physics, and chemistry. Recently, there has been a growing interest in neural architectures that are invariant or equivariant to all three shape-preserving transformations of point clouds: translation, rotation, and permutation.\n  In this paper, we present a first study of the approximation power of these architectures. We first derive two sufficient conditions for an equivariant architecture to have the universal approximation property, based on a novel characterization of the spa","authors_text":"Haggai Maron, Nadav Dym","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-06T03:14:16Z","title":"On the Universality of Rotation Equivariant Point Cloud Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.02449","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":"sha256:4427938a8f72c89236e5272afea6286d489d13d575eaad874bbbb823ae650ee7","target":"record","created_at":"2026-07-05T01:40:49Z","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":"51927245fc5e7fcbbb5ca8e9f7e103acd1c8347574d16d0e003896a1a697b4b4","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-10-06T03:14:16Z","title_canon_sha256":"4c1d296ca526dbbbf07be101a6cf73b22d39c84f4a8c9907f592d6866c97b7f0"},"schema_version":"1.0","source":{"id":"2010.02449","kind":"arxiv","version":1}},"canonical_sha256":"e433efe1c4743ed582540fab69fbc220f09e8b042846a4bbee58bac3738a20a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e433efe1c4743ed582540fab69fbc220f09e8b042846a4bbee58bac3738a20a6","first_computed_at":"2026-07-05T01:40:49.986012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:40:49.986012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KRXHU2+WJ7LHOzx8n4Gwpwepov+HzXBH+C5QSP20Rt3nJAR1e+HNxsRck6ioZXVEM5itvOYXgCXDFBg+m8PCDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:40:49.986500Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.02449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4427938a8f72c89236e5272afea6286d489d13d575eaad874bbbb823ae650ee7","sha256:ad27d27008d026876be7bcefaabf3ec0d193658a3855cab999cdc1720c6f826d"],"state_sha256":"e401a7dd6985011d578db05d6485cb45a7fe777a43a42ba9e299b426bb40d89d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vm0p11XgDKsmSg7keM+oKmByXKS1LOoKiEVt5gcpG++qUNmKPxWOLWEPAYlTau1utmstFnvXz35ZgipGrzBRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T06:54:34.792095Z","bundle_sha256":"91816c6f631c70a1984db5845229ecc5a23965d6892b54ac455501f70234b694"}}