{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:42DPYWQRKSZ7MJESFBGSAIEX27","short_pith_number":"pith:42DPYWQR","canonical_record":{"source":{"id":"2311.02838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-06T02:58:05Z","cross_cats_sorted":["cs.LG","eess.SP"],"title_canon_sha256":"fbc570ce74a2091cdf9629cf0560b2b1b114e306c64efeee2a2cf9293d31c51d","abstract_canon_sha256":"79ecd15ff2e5c849eaefa732bc3750d78a6bb6ac22078075fb50f3ba86ef5a3f"},"schema_version":"1.0"},"canonical_sha256":"e686fc5a1154b3f62492284d202097d7c50f16d69fd6b4183470b33bd0e9b906","source":{"kind":"arxiv","id":"2311.02838","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.02838","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"arxiv_version","alias_value":"2311.02838v1","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02838","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"pith_short_12","alias_value":"42DPYWQRKSZ7","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"pith_short_16","alias_value":"42DPYWQRKSZ7MJES","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"pith_short_8","alias_value":"42DPYWQR","created_at":"2026-07-05T07:09:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:42DPYWQRKSZ7MJESFBGSAIEX27","target":"record","payload":{"canonical_record":{"source":{"id":"2311.02838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-06T02:58:05Z","cross_cats_sorted":["cs.LG","eess.SP"],"title_canon_sha256":"fbc570ce74a2091cdf9629cf0560b2b1b114e306c64efeee2a2cf9293d31c51d","abstract_canon_sha256":"79ecd15ff2e5c849eaefa732bc3750d78a6bb6ac22078075fb50f3ba86ef5a3f"},"schema_version":"1.0"},"canonical_sha256":"e686fc5a1154b3f62492284d202097d7c50f16d69fd6b4183470b33bd0e9b906","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:09:18.612495Z","signature_b64":"05PBpfYtyeafaemQcuJyzLqW/Zir7fpQ2JkM2lWYCUY0wiZ42AB5jMa0vD91WhLV5/gqNxxr+qBcyCL78EHEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e686fc5a1154b3f62492284d202097d7c50f16d69fd6b4183470b33bd0e9b906","last_reissued_at":"2026-07-05T07:09:18.612072Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:09:18.612072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.02838","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":"2026-07-05T07:09:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1o04qCaUoo3kublIBMsFi0kOyg9QEIyYspEtRudNxZcYI6QbHVaP4ALA7GWSEQc/UGqclZ13g/sko5t+zcjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:04:33.243051Z"},"content_sha256":"9453ef51da530d4bd46b2d5d8a48be99d8385dd12c22196b10ee94fb91e0b03f","schema_version":"1.0","event_id":"sha256:9453ef51da530d4bd46b2d5d8a48be99d8385dd12c22196b10ee94fb91e0b03f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:42DPYWQRKSZ7MJESFBGSAIEX27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Barron Space for Graph Convolution Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","eess.SP"],"primary_cat":"stat.ML","authors_text":"Qiyu Sun, Seok-Young Chung","submitted_at":"2023-11-06T02:58:05Z","abstract_excerpt":"Graph convolutional neural network (GCNN) operates on graph domain and it has achieved a superior performance to accomplish a wide range of tasks. In this paper, we introduce a Barron space of functions on a compact domain of graph signals. We prove that the proposed Barron space is a reproducing kernel Banach space, it can be decomposed into the union of a family of reproducing kernel Hilbert spaces with neuron kernels, and it could be dense in the space of continuous functions on the domain. Approximation property is one of the main principles to design neural networks. In this paper, we sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02838","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/2311.02838/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":"2026-07-05T07:09:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"21Z72NkIiAE3D4crrVFLRt+hCRozcJYC7DwXxte9HR9tETAF4GaBy0JQtEOrViX2BJeqlkN3Qd/3H8MVOQsPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T15:04:33.243384Z"},"content_sha256":"bc7ab44fb8dd2d1c08a370594f8ca82d6fc7972b1ff864126105326f144fc25a","schema_version":"1.0","event_id":"sha256:bc7ab44fb8dd2d1c08a370594f8ca82d6fc7972b1ff864126105326f144fc25a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42DPYWQRKSZ7MJESFBGSAIEX27/bundle.json","state_url":"https://pith.science/pith/42DPYWQRKSZ7MJESFBGSAIEX27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42DPYWQRKSZ7MJESFBGSAIEX27/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":"2026-08-06T15:04:33Z","links":{"resolver":"https://pith.science/pith/42DPYWQRKSZ7MJESFBGSAIEX27","bundle":"https://pith.science/pith/42DPYWQRKSZ7MJESFBGSAIEX27/bundle.json","state":"https://pith.science/pith/42DPYWQRKSZ7MJESFBGSAIEX27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42DPYWQRKSZ7MJESFBGSAIEX27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:42DPYWQRKSZ7MJESFBGSAIEX27","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":"79ecd15ff2e5c849eaefa732bc3750d78a6bb6ac22078075fb50f3ba86ef5a3f","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-06T02:58:05Z","title_canon_sha256":"fbc570ce74a2091cdf9629cf0560b2b1b114e306c64efeee2a2cf9293d31c51d"},"schema_version":"1.0","source":{"id":"2311.02838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.02838","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"arxiv_version","alias_value":"2311.02838v1","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02838","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"pith_short_12","alias_value":"42DPYWQRKSZ7","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"pith_short_16","alias_value":"42DPYWQRKSZ7MJES","created_at":"2026-07-05T07:09:18Z"},{"alias_kind":"pith_short_8","alias_value":"42DPYWQR","created_at":"2026-07-05T07:09:18Z"}],"graph_snapshots":[{"event_id":"sha256:bc7ab44fb8dd2d1c08a370594f8ca82d6fc7972b1ff864126105326f144fc25a","target":"graph","created_at":"2026-07-05T07:09:18Z","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/2311.02838/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph convolutional neural network (GCNN) operates on graph domain and it has achieved a superior performance to accomplish a wide range of tasks. In this paper, we introduce a Barron space of functions on a compact domain of graph signals. We prove that the proposed Barron space is a reproducing kernel Banach space, it can be decomposed into the union of a family of reproducing kernel Hilbert spaces with neuron kernels, and it could be dense in the space of continuous functions on the domain. Approximation property is one of the main principles to design neural networks. In this paper, we sho","authors_text":"Qiyu Sun, Seok-Young Chung","cross_cats":["cs.LG","eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-06T02:58:05Z","title":"Barron Space for Graph Convolution Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02838","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":"sha256:9453ef51da530d4bd46b2d5d8a48be99d8385dd12c22196b10ee94fb91e0b03f","target":"record","created_at":"2026-07-05T07:09:18Z","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":"79ecd15ff2e5c849eaefa732bc3750d78a6bb6ac22078075fb50f3ba86ef5a3f","cross_cats_sorted":["cs.LG","eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-06T02:58:05Z","title_canon_sha256":"fbc570ce74a2091cdf9629cf0560b2b1b114e306c64efeee2a2cf9293d31c51d"},"schema_version":"1.0","source":{"id":"2311.02838","kind":"arxiv","version":1}},"canonical_sha256":"e686fc5a1154b3f62492284d202097d7c50f16d69fd6b4183470b33bd0e9b906","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e686fc5a1154b3f62492284d202097d7c50f16d69fd6b4183470b33bd0e9b906","first_computed_at":"2026-07-05T07:09:18.612072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:09:18.612072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"05PBpfYtyeafaemQcuJyzLqW/Zir7fpQ2JkM2lWYCUY0wiZ42AB5jMa0vD91WhLV5/gqNxxr+qBcyCL78EHEAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:09:18.612495Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.02838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9453ef51da530d4bd46b2d5d8a48be99d8385dd12c22196b10ee94fb91e0b03f","sha256:bc7ab44fb8dd2d1c08a370594f8ca82d6fc7972b1ff864126105326f144fc25a"],"state_sha256":"4f886a4164dbcd23039bc219a320303a6236f28f645a6e84633ae8c9426794e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CoGpyMFt1ssjl/BQsQ/XiQdVJoBcgiSvkBHZSjyfVbvlVGwBndC7HUiE4gczsURJkjQPGtRVR/O0MLTBJlpeDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T15:04:33.247424Z","bundle_sha256":"0343b585239e859b8375188e177548419307a6229395095d68c8bbba9b872d4e"}}