{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:4JCNKJUMCIYLF4JHJ63YNGGFOH","short_pith_number":"pith:4JCNKJUM","canonical_record":{"source":{"id":"2109.10096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-21T10:59:01Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"bb6c1c1f2aa7c1ac66ee2d95a24a2d10392c19c82384f1b24d2fe7e7b16f59a8","abstract_canon_sha256":"03bf3dba3174b0a40ef345fe84fe431baa8d8f0eb34bcaa658ceefc5615cda48"},"schema_version":"1.0"},"canonical_sha256":"e244d5268c1230b2f1274fb78698c571c1973aa4ba255e0d3ede0978224c4ef7","source":{"kind":"arxiv","id":"2109.10096","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10096","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10096v2","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10096","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"4JCNKJUMCIYL","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"pith_short_16","alias_value":"4JCNKJUMCIYLF4JH","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"pith_short_8","alias_value":"4JCNKJUM","created_at":"2026-07-05T04:34:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:4JCNKJUMCIYLF4JHJ63YNGGFOH","target":"record","payload":{"canonical_record":{"source":{"id":"2109.10096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-21T10:59:01Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"bb6c1c1f2aa7c1ac66ee2d95a24a2d10392c19c82384f1b24d2fe7e7b16f59a8","abstract_canon_sha256":"03bf3dba3174b0a40ef345fe84fe431baa8d8f0eb34bcaa658ceefc5615cda48"},"schema_version":"1.0"},"canonical_sha256":"e244d5268c1230b2f1274fb78698c571c1973aa4ba255e0d3ede0978224c4ef7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:34:47.258928Z","signature_b64":"Y3O5C8HByTDwCmz1mq0FhH6+sNKkyj4wnTGOnUOUsXBETwwvTdtovsbMCvloJOOTnYfVWW3JO8nyhlZC/1mVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e244d5268c1230b2f1274fb78698c571c1973aa4ba255e0d3ede0978224c4ef7","last_reissued_at":"2026-07-05T04:34:47.258445Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:34:47.258445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.10096","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":"2026-07-05T04:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KzqW9nYru2W4UOtyd8uy0THgEfztD2JLzFTfGds+62pgaTS+daxPqkcArpVI7Uymd8RjZsLOEw/Wjy4GYCbtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:24:04.188510Z"},"content_sha256":"cc46d5d4c1f4a6e9f779fb6262b64d4defd17c819ddc62b8035b0689f71133a4","schema_version":"1.0","event_id":"sha256:cc46d5d4c1f4a6e9f779fb6262b64d4defd17c819ddc62b8035b0689f71133a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:4JCNKJUMCIYLF4JHJ63YNGGFOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transferability of Graph Neural Networks: an Extended Graphon Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Gitta Kutyniok, Ron Levie, Sohir Maskey","submitted_at":"2021-09-21T10:59:01Z","abstract_excerpt":"We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be transferred between different graphs. It is hence important to study the GCNN transferability: the capacity of the network to have approximately the same repercussion on different graphs that represent the same phenomenon. Transferability ensures that GCNNs trained on certain graphs generalize if the graphs in the test set represent the same phenomena as th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10096","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/2109.10096/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":"2026-07-05T04:34:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u3JvyXjiQdH5Vjs4rNZfjxz64rCGRLy6jHzbiHyt+/+sxMnqm9Ebyc3svOGhhLb5OkgGq77qTd/d3uu2MGRZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T19:24:04.189691Z"},"content_sha256":"2e5dfa1330a1faa2413855dc6a28889784758975ef0ed6d99e8d6c3728c998c5","schema_version":"1.0","event_id":"sha256:2e5dfa1330a1faa2413855dc6a28889784758975ef0ed6d99e8d6c3728c998c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JCNKJUMCIYLF4JHJ63YNGGFOH/bundle.json","state_url":"https://pith.science/pith/4JCNKJUMCIYLF4JHJ63YNGGFOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JCNKJUMCIYLF4JHJ63YNGGFOH/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":"2026-08-10T19:24:04Z","links":{"resolver":"https://pith.science/pith/4JCNKJUMCIYLF4JHJ63YNGGFOH","bundle":"https://pith.science/pith/4JCNKJUMCIYLF4JHJ63YNGGFOH/bundle.json","state":"https://pith.science/pith/4JCNKJUMCIYLF4JHJ63YNGGFOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JCNKJUMCIYLF4JHJ63YNGGFOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:4JCNKJUMCIYLF4JHJ63YNGGFOH","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":"03bf3dba3174b0a40ef345fe84fe431baa8d8f0eb34bcaa658ceefc5615cda48","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-21T10:59:01Z","title_canon_sha256":"bb6c1c1f2aa7c1ac66ee2d95a24a2d10392c19c82384f1b24d2fe7e7b16f59a8"},"schema_version":"1.0","source":{"id":"2109.10096","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10096","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10096v2","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10096","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"pith_short_12","alias_value":"4JCNKJUMCIYL","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"pith_short_16","alias_value":"4JCNKJUMCIYLF4JH","created_at":"2026-07-05T04:34:47Z"},{"alias_kind":"pith_short_8","alias_value":"4JCNKJUM","created_at":"2026-07-05T04:34:47Z"}],"graph_snapshots":[{"event_id":"sha256:2e5dfa1330a1faa2413855dc6a28889784758975ef0ed6d99e8d6c3728c998c5","target":"graph","created_at":"2026-07-05T04:34:47Z","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/2109.10096/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be transferred between different graphs. It is hence important to study the GCNN transferability: the capacity of the network to have approximately the same repercussion on different graphs that represent the same phenomenon. Transferability ensures that GCNNs trained on certain graphs generalize if the graphs in the test set represent the same phenomena as th","authors_text":"Gitta Kutyniok, Ron Levie, Sohir Maskey","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-21T10:59:01Z","title":"Transferability of Graph Neural Networks: an Extended Graphon Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10096","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:cc46d5d4c1f4a6e9f779fb6262b64d4defd17c819ddc62b8035b0689f71133a4","target":"record","created_at":"2026-07-05T04:34:47Z","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":"03bf3dba3174b0a40ef345fe84fe431baa8d8f0eb34bcaa658ceefc5615cda48","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-09-21T10:59:01Z","title_canon_sha256":"bb6c1c1f2aa7c1ac66ee2d95a24a2d10392c19c82384f1b24d2fe7e7b16f59a8"},"schema_version":"1.0","source":{"id":"2109.10096","kind":"arxiv","version":2}},"canonical_sha256":"e244d5268c1230b2f1274fb78698c571c1973aa4ba255e0d3ede0978224c4ef7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e244d5268c1230b2f1274fb78698c571c1973aa4ba255e0d3ede0978224c4ef7","first_computed_at":"2026-07-05T04:34:47.258445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:34:47.258445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y3O5C8HByTDwCmz1mq0FhH6+sNKkyj4wnTGOnUOUsXBETwwvTdtovsbMCvloJOOTnYfVWW3JO8nyhlZC/1mVAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:34:47.258928Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.10096","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc46d5d4c1f4a6e9f779fb6262b64d4defd17c819ddc62b8035b0689f71133a4","sha256:2e5dfa1330a1faa2413855dc6a28889784758975ef0ed6d99e8d6c3728c998c5"],"state_sha256":"674248eae40ad01f41d23a0ed2ea8b469618e7ef7e57ba14b82ad93e61f4a629"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AE6M+efJ3jQljhtok9biub83eZf66A34kapyb2LF0e37r6ykHWpRM2tLH+SvlAvpkLkSGs9M2XCy4drCSYZDBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T19:24:04.197178Z","bundle_sha256":"0196aa8eeb68fd47f5845cc49f9f72ebd20f0b0b62441a34fed935a574e0c4cf"}}