{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XZVZTXGAVZ5LOTBOA2CZSUZKEA","short_pith_number":"pith:XZVZTXGA","canonical_record":{"source":{"id":"2006.01868","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-02T18:36:19Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"11f163e3db6ae0fd26286e71f1d43c3d8267209f0ce80c49de1f9975e4b56485","abstract_canon_sha256":"52ff2e311a90431635756763d64cc3dc18b551268ba46886d4b9a905f10cbafb"},"schema_version":"1.0"},"canonical_sha256":"be6b99dcc0ae7ab74c2e068599532a201d77b7a95146e505862e7bbbaf84cc9e","source":{"kind":"arxiv","id":"2006.01868","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.01868","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"2006.01868v2","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.01868","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"XZVZTXGAVZ5L","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"pith_short_16","alias_value":"XZVZTXGAVZ5LOTBO","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"pith_short_8","alias_value":"XZVZTXGA","created_at":"2026-07-05T01:45:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XZVZTXGAVZ5LOTBOA2CZSUZKEA","target":"record","payload":{"canonical_record":{"source":{"id":"2006.01868","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-02T18:36:19Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"11f163e3db6ae0fd26286e71f1d43c3d8267209f0ce80c49de1f9975e4b56485","abstract_canon_sha256":"52ff2e311a90431635756763d64cc3dc18b551268ba46886d4b9a905f10cbafb"},"schema_version":"1.0"},"canonical_sha256":"be6b99dcc0ae7ab74c2e068599532a201d77b7a95146e505862e7bbbaf84cc9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:45:27.289015Z","signature_b64":"+7SYkmNzdy9ziahw4Th8Q0mNcjwDBLIpwHSlCS+/ygfRkq15VLZHyxQYSivoBIECRI86ESg1WD88Qne8l1+iDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be6b99dcc0ae7ab74c2e068599532a201d77b7a95146e505862e7bbbaf84cc9e","last_reissued_at":"2026-07-05T01:45:27.288585Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:45:27.288585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.01868","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3pcN7nyttGZMPF5vpUjQpD8eCS4zVTwj7Pqnr3eCLO3cuFTZhj5S+B2z49kupc4DbbOymBnqLpwAauBlKJ3tBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:26:02.473314Z"},"content_sha256":"dfb5a59c2bd17fc5f3c6454979b7a18adc8a3d6885a19f1bc2cce633a5e16fd5","schema_version":"1.0","event_id":"sha256:dfb5a59c2bd17fc5f3c6454979b7a18adc8a3d6885a19f1bc2cce633a5e16fd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XZVZTXGAVZ5LOTBOA2CZSUZKEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence and Stability of Graph Convolutional Networks on Large Random Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Alberto Bietti, Nicolas Keriven, Samuel Vaiter","submitted_at":"2020-06-02T18:36:19Z","abstract_excerpt":"We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This allows us to overcome the difficulties of dealing with discrete notions such as isomorphisms on very large graphs, by considering instead more natural geometric aspects. We first study the convergence of GCNs to their continuous counterpart as the number of nodes grows. Our results are fully non-asymptotic and are valid for relatively sparse graphs with an ave"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.01868","kind":"arxiv","version":2},"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/2006.01868/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":"2026-07-05T01:45:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dhqsm4JKpiFgWBOA95Puyjg0+GMcNmSvM4r/XsDEEXlBMY6k24RBhbiQTm6yU3RW1cApLe2b/NGq+qq4jpcEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:26:02.473835Z"},"content_sha256":"957daf9d24763a22dd018e387ebf976e4eafb68aaf3c64d4b1cd90991622f877","schema_version":"1.0","event_id":"sha256:957daf9d24763a22dd018e387ebf976e4eafb68aaf3c64d4b1cd90991622f877"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZVZTXGAVZ5LOTBOA2CZSUZKEA/bundle.json","state_url":"https://pith.science/pith/XZVZTXGAVZ5LOTBOA2CZSUZKEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZVZTXGAVZ5LOTBOA2CZSUZKEA/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":"2026-08-15T23:26:02Z","links":{"resolver":"https://pith.science/pith/XZVZTXGAVZ5LOTBOA2CZSUZKEA","bundle":"https://pith.science/pith/XZVZTXGAVZ5LOTBOA2CZSUZKEA/bundle.json","state":"https://pith.science/pith/XZVZTXGAVZ5LOTBOA2CZSUZKEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZVZTXGAVZ5LOTBOA2CZSUZKEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XZVZTXGAVZ5LOTBOA2CZSUZKEA","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":"52ff2e311a90431635756763d64cc3dc18b551268ba46886d4b9a905f10cbafb","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-02T18:36:19Z","title_canon_sha256":"11f163e3db6ae0fd26286e71f1d43c3d8267209f0ce80c49de1f9975e4b56485"},"schema_version":"1.0","source":{"id":"2006.01868","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.01868","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"arxiv_version","alias_value":"2006.01868v2","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.01868","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"pith_short_12","alias_value":"XZVZTXGAVZ5L","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"pith_short_16","alias_value":"XZVZTXGAVZ5LOTBO","created_at":"2026-07-05T01:45:27Z"},{"alias_kind":"pith_short_8","alias_value":"XZVZTXGA","created_at":"2026-07-05T01:45:27Z"}],"graph_snapshots":[{"event_id":"sha256:957daf9d24763a22dd018e387ebf976e4eafb68aaf3c64d4b1cd90991622f877","target":"graph","created_at":"2026-07-05T01:45:27Z","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/2006.01868/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This allows us to overcome the difficulties of dealing with discrete notions such as isomorphisms on very large graphs, by considering instead more natural geometric aspects. We first study the convergence of GCNs to their continuous counterpart as the number of nodes grows. Our results are fully non-asymptotic and are valid for relatively sparse graphs with an ave","authors_text":"Alberto Bietti, Nicolas Keriven, Samuel Vaiter","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-02T18:36:19Z","title":"Convergence and Stability of Graph Convolutional Networks on Large Random Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.01868","kind":"arxiv","version":2},"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:dfb5a59c2bd17fc5f3c6454979b7a18adc8a3d6885a19f1bc2cce633a5e16fd5","target":"record","created_at":"2026-07-05T01:45:27Z","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":"52ff2e311a90431635756763d64cc3dc18b551268ba46886d4b9a905f10cbafb","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2020-06-02T18:36:19Z","title_canon_sha256":"11f163e3db6ae0fd26286e71f1d43c3d8267209f0ce80c49de1f9975e4b56485"},"schema_version":"1.0","source":{"id":"2006.01868","kind":"arxiv","version":2}},"canonical_sha256":"be6b99dcc0ae7ab74c2e068599532a201d77b7a95146e505862e7bbbaf84cc9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be6b99dcc0ae7ab74c2e068599532a201d77b7a95146e505862e7bbbaf84cc9e","first_computed_at":"2026-07-05T01:45:27.288585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:45:27.288585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+7SYkmNzdy9ziahw4Th8Q0mNcjwDBLIpwHSlCS+/ygfRkq15VLZHyxQYSivoBIECRI86ESg1WD88Qne8l1+iDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:45:27.289015Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.01868","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfb5a59c2bd17fc5f3c6454979b7a18adc8a3d6885a19f1bc2cce633a5e16fd5","sha256:957daf9d24763a22dd018e387ebf976e4eafb68aaf3c64d4b1cd90991622f877"],"state_sha256":"e67be82f9d894e27a6577e588b5977826eec67ed0defe83bf9c8c7cee45ef47b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0aScgFaFxXDGhi/w/8efWeFwXW8nrhQkn4wr4BzK1BZ3GhDWwujzzC3+0zO4+sKrE8aL1Ffa1SsOcrQ/hsjYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T23:26:02.477588Z","bundle_sha256":"4c0ae57ba04e0cb0cc4ba0851c02d60a88ccece6c0795251b54d6b65c0b0bfa0"}}