{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OGHQ256BSYZUXUIML3EJ62ZK7K","short_pith_number":"pith:OGHQ256B","canonical_record":{"source":{"id":"2112.04629","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T00:08:09Z","cross_cats_sorted":["eess.SP"],"title_canon_sha256":"60ab9686b9e6bc3e2ae5fbfecf5112c9af31fe239db3de82e2218514d66bbd5f","abstract_canon_sha256":"51a97276c745839eca2f9d7ee1f17e12520fc493190541bc90e928754fc8ae57"},"schema_version":"1.0"},"canonical_sha256":"718f0d77c196334bd10c5ec89f6b2afa8ee8eb3fae1255e246c288614ffaefda","source":{"kind":"arxiv","id":"2112.04629","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04629","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04629v4","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04629","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"OGHQ256BSYZU","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"pith_short_16","alias_value":"OGHQ256BSYZUXUIM","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"pith_short_8","alias_value":"OGHQ256B","created_at":"2026-07-05T06:38:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OGHQ256BSYZUXUIML3EJ62ZK7K","target":"record","payload":{"canonical_record":{"source":{"id":"2112.04629","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T00:08:09Z","cross_cats_sorted":["eess.SP"],"title_canon_sha256":"60ab9686b9e6bc3e2ae5fbfecf5112c9af31fe239db3de82e2218514d66bbd5f","abstract_canon_sha256":"51a97276c745839eca2f9d7ee1f17e12520fc493190541bc90e928754fc8ae57"},"schema_version":"1.0"},"canonical_sha256":"718f0d77c196334bd10c5ec89f6b2afa8ee8eb3fae1255e246c288614ffaefda","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:38:24.110975Z","signature_b64":"NI7lNuxa979SgvQr8TIt853Uwpplnia1X0juhhwDqdwqRRvcf42rFk0XQKpQ/yRCZLbuNJnKmGISAsqeL/00DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"718f0d77c196334bd10c5ec89f6b2afa8ee8eb3fae1255e246c288614ffaefda","last_reissued_at":"2026-07-05T06:38:24.110540Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:38:24.110540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.04629","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcjEz2TYoLqPbFnJ1Edp/d1FWCTJqQzEfiFkOev+zQYJHEExEwNedOaRUGi1PskKCZdOicYEUJfhFXY7ZPNmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:16:59.985338Z"},"content_sha256":"e2e405c5a658e2122362d47cc3ffc9e3d69518afbbd9211c9b3c00fa27ab6237","schema_version":"1.0","event_id":"sha256:e2e405c5a658e2122362d47cc3ffc9e3d69518afbbd9211c9b3c00fa27ab6237"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OGHQ256BSYZUXUIML3EJ62ZK7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transferability Properties of Graph Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["eess.SP"],"primary_cat":"cs.LG","authors_text":"Alejandro Ribeiro, Luana Ruiz, Luiz F. O. Chamon","submitted_at":"2021-12-09T00:08:09Z","abstract_excerpt":"Graph neural networks (GNNs) are composed of layers consisting of graph convolutions and pointwise nonlinearities. Due to their invariance and stability properties, GNNs are provably successful at learning representations from data supported on moderate-scale graphs. However, they are difficult to learn on large-scale graphs. In this paper, we study the problem of training GNNs on graphs of moderate size and transferring them to large-scale graphs. We use graph limits called graphons to define limit objects for graph filters and GNNs -- graphon filters and graphon neural networks (WNNs) -- whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04629","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/2112.04629/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":"2026-07-05T06:38:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bamI7gpKlzEFgi6uvFG3Pp1a4nfmIa2V527yXbf0rQMIQQYtd1A2zzQaU4/ua3ucPSbD6lSmq9pPeJtDhXB/DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T01:16:59.986258Z"},"content_sha256":"b7d90507804896b1f778637ceaf523006eb2939d307df176b4fd2e8c959221a4","schema_version":"1.0","event_id":"sha256:b7d90507804896b1f778637ceaf523006eb2939d307df176b4fd2e8c959221a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OGHQ256BSYZUXUIML3EJ62ZK7K/bundle.json","state_url":"https://pith.science/pith/OGHQ256BSYZUXUIML3EJ62ZK7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OGHQ256BSYZUXUIML3EJ62ZK7K/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":"2026-08-16T01:16:59Z","links":{"resolver":"https://pith.science/pith/OGHQ256BSYZUXUIML3EJ62ZK7K","bundle":"https://pith.science/pith/OGHQ256BSYZUXUIML3EJ62ZK7K/bundle.json","state":"https://pith.science/pith/OGHQ256BSYZUXUIML3EJ62ZK7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OGHQ256BSYZUXUIML3EJ62ZK7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OGHQ256BSYZUXUIML3EJ62ZK7K","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":"51a97276c745839eca2f9d7ee1f17e12520fc493190541bc90e928754fc8ae57","cross_cats_sorted":["eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T00:08:09Z","title_canon_sha256":"60ab9686b9e6bc3e2ae5fbfecf5112c9af31fe239db3de82e2218514d66bbd5f"},"schema_version":"1.0","source":{"id":"2112.04629","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.04629","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"2112.04629v4","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.04629","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"OGHQ256BSYZU","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"pith_short_16","alias_value":"OGHQ256BSYZUXUIM","created_at":"2026-07-05T06:38:24Z"},{"alias_kind":"pith_short_8","alias_value":"OGHQ256B","created_at":"2026-07-05T06:38:24Z"}],"graph_snapshots":[{"event_id":"sha256:b7d90507804896b1f778637ceaf523006eb2939d307df176b4fd2e8c959221a4","target":"graph","created_at":"2026-07-05T06:38:24Z","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/2112.04629/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Graph neural networks (GNNs) are composed of layers consisting of graph convolutions and pointwise nonlinearities. Due to their invariance and stability properties, GNNs are provably successful at learning representations from data supported on moderate-scale graphs. However, they are difficult to learn on large-scale graphs. In this paper, we study the problem of training GNNs on graphs of moderate size and transferring them to large-scale graphs. We use graph limits called graphons to define limit objects for graph filters and GNNs -- graphon filters and graphon neural networks (WNNs) -- whi","authors_text":"Alejandro Ribeiro, Luana Ruiz, Luiz F. O. Chamon","cross_cats":["eess.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T00:08:09Z","title":"Transferability Properties of Graph Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.04629","kind":"arxiv","version":4},"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:e2e405c5a658e2122362d47cc3ffc9e3d69518afbbd9211c9b3c00fa27ab6237","target":"record","created_at":"2026-07-05T06:38:24Z","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":"51a97276c745839eca2f9d7ee1f17e12520fc493190541bc90e928754fc8ae57","cross_cats_sorted":["eess.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-12-09T00:08:09Z","title_canon_sha256":"60ab9686b9e6bc3e2ae5fbfecf5112c9af31fe239db3de82e2218514d66bbd5f"},"schema_version":"1.0","source":{"id":"2112.04629","kind":"arxiv","version":4}},"canonical_sha256":"718f0d77c196334bd10c5ec89f6b2afa8ee8eb3fae1255e246c288614ffaefda","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"718f0d77c196334bd10c5ec89f6b2afa8ee8eb3fae1255e246c288614ffaefda","first_computed_at":"2026-07-05T06:38:24.110540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:38:24.110540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NI7lNuxa979SgvQr8TIt853Uwpplnia1X0juhhwDqdwqRRvcf42rFk0XQKpQ/yRCZLbuNJnKmGISAsqeL/00DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:38:24.110975Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.04629","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2e405c5a658e2122362d47cc3ffc9e3d69518afbbd9211c9b3c00fa27ab6237","sha256:b7d90507804896b1f778637ceaf523006eb2939d307df176b4fd2e8c959221a4"],"state_sha256":"a9a60e61df1ace7bddead7163e726826a658119b6d363af4b407f699aa65f17f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qJF8zWgLZILsHedjuEYBSoxoIU6jCfHxratPKkysQaLY6YpWo5CQHfpglLPRrvOJvfdD8whpo6Lo5T1QB8sSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T01:16:59.993663Z","bundle_sha256":"76dda1555b13cd0807fa232dae729611492d8f68ae54d8415a3441918493d63c"}}