{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:7S24O4C7X2F4JMM5SVYROZ7IT6","short_pith_number":"pith:7S24O4C7","canonical_record":{"source":{"id":"1911.07532","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T10:46:15Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"6712a8decc72faf81e76e5a20626cfa88a2fa8bfc23a0ccce6772900e0606b11","abstract_canon_sha256":"457d31c9dc62f78943ebcfc8b5e990759b87ceb1aec88a4551f7c00d82be359d"},"schema_version":"1.0"},"canonical_sha256":"fcb5c7705fbe8bc4b19d95711767e89f94a388a3b420553d855f42bfaa144ec3","source":{"kind":"arxiv","id":"1911.07532","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.07532","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1911.07532v4","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.07532","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"7S24O4C7X2F4","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"pith_short_16","alias_value":"7S24O4C7X2F4JMM5","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"pith_short_8","alias_value":"7S24O4C7","created_at":"2026-07-05T02:51:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:7S24O4C7X2F4JMM5SVYROZ7IT6","target":"record","payload":{"canonical_record":{"source":{"id":"1911.07532","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T10:46:15Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"6712a8decc72faf81e76e5a20626cfa88a2fa8bfc23a0ccce6772900e0606b11","abstract_canon_sha256":"457d31c9dc62f78943ebcfc8b5e990759b87ceb1aec88a4551f7c00d82be359d"},"schema_version":"1.0"},"canonical_sha256":"fcb5c7705fbe8bc4b19d95711767e89f94a388a3b420553d855f42bfaa144ec3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:51:05.959139Z","signature_b64":"1jfcC9FOqpL+zXP8vvzlbuF90E8p9XSNjImPOLL0rCabzBLclV3tn5woMeBvL88tABIxOldyt7xpbDDTLXmrAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcb5c7705fbe8bc4b19d95711767e89f94a388a3b420553d855f42bfaa144ec3","last_reissued_at":"2026-07-05T02:51:05.958650Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:51:05.958650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1911.07532","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":"2026-07-05T02:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pMJZzPONVUAiTRxm+ELJ86wfUQ1cho0bhvk5tHpUBak9YxP8n9j0dJngEH101Dcah1kqBMf9azw5sLBZ8WQGCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T02:09:49.871805Z"},"content_sha256":"4470a3b5a93b1f666549b235fe5b2f432c63d0213082eed81c27b3dfc2c98f56","schema_version":"1.0","event_id":"sha256:4470a3b5a93b1f666549b235fe5b2f432c63d0213082eed81c27b3dfc2c98f56"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:7S24O4C7X2F4JMM5SVYROZ7IT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graph Neural Ordinary Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Atsushi Yamashita, Hajime Asama, Jinkyoo Park, Junyoung Park, Michael Poli, Stefano Massaroli","submitted_at":"2019-11-18T10:46:15Z","abstract_excerpt":"We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with various static and autoregressive GNN models. Results prove general effectiveness of GDEs: in static settings they offer computational advantages by incorporating numerical methods in their forward pass; in dynamic settings, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.07532","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/1911.07532/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":"2026-07-05T02:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pwrFEszclVQ9nxvdVPMujH8DMRmLJSHBiBDkMWS2Xaj99rL5iJGj1I3vqJKWqq4ADw0anRVPRZFcGIfuh/5aBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T02:09:49.872720Z"},"content_sha256":"025faf909f52d2a37436c8fdb2546e060fbb41d58f6a2e327047e0d4b4e6f744","schema_version":"1.0","event_id":"sha256:025faf909f52d2a37436c8fdb2546e060fbb41d58f6a2e327047e0d4b4e6f744"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7S24O4C7X2F4JMM5SVYROZ7IT6/bundle.json","state_url":"https://pith.science/pith/7S24O4C7X2F4JMM5SVYROZ7IT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7S24O4C7X2F4JMM5SVYROZ7IT6/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":"2026-08-19T02:09:49Z","links":{"resolver":"https://pith.science/pith/7S24O4C7X2F4JMM5SVYROZ7IT6","bundle":"https://pith.science/pith/7S24O4C7X2F4JMM5SVYROZ7IT6/bundle.json","state":"https://pith.science/pith/7S24O4C7X2F4JMM5SVYROZ7IT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7S24O4C7X2F4JMM5SVYROZ7IT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7S24O4C7X2F4JMM5SVYROZ7IT6","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":"457d31c9dc62f78943ebcfc8b5e990759b87ceb1aec88a4551f7c00d82be359d","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T10:46:15Z","title_canon_sha256":"6712a8decc72faf81e76e5a20626cfa88a2fa8bfc23a0ccce6772900e0606b11"},"schema_version":"1.0","source":{"id":"1911.07532","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.07532","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1911.07532v4","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.07532","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"7S24O4C7X2F4","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"pith_short_16","alias_value":"7S24O4C7X2F4JMM5","created_at":"2026-07-05T02:51:05Z"},{"alias_kind":"pith_short_8","alias_value":"7S24O4C7","created_at":"2026-07-05T02:51:05Z"}],"graph_snapshots":[{"event_id":"sha256:025faf909f52d2a37436c8fdb2546e060fbb41d58f6a2e327047e0d4b4e6f744","target":"graph","created_at":"2026-07-05T02:51:05Z","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/1911.07532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with various static and autoregressive GNN models. Results prove general effectiveness of GDEs: in static settings they offer computational advantages by incorporating numerical methods in their forward pass; in dynamic settings, ","authors_text":"Atsushi Yamashita, Hajime Asama, Jinkyoo Park, Junyoung Park, Michael Poli, Stefano Massaroli","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T10:46:15Z","title":"Graph Neural Ordinary Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.07532","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":"sha256:4470a3b5a93b1f666549b235fe5b2f432c63d0213082eed81c27b3dfc2c98f56","target":"record","created_at":"2026-07-05T02:51:05Z","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":"457d31c9dc62f78943ebcfc8b5e990759b87ceb1aec88a4551f7c00d82be359d","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-11-18T10:46:15Z","title_canon_sha256":"6712a8decc72faf81e76e5a20626cfa88a2fa8bfc23a0ccce6772900e0606b11"},"schema_version":"1.0","source":{"id":"1911.07532","kind":"arxiv","version":4}},"canonical_sha256":"fcb5c7705fbe8bc4b19d95711767e89f94a388a3b420553d855f42bfaa144ec3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcb5c7705fbe8bc4b19d95711767e89f94a388a3b420553d855f42bfaa144ec3","first_computed_at":"2026-07-05T02:51:05.958650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:51:05.958650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1jfcC9FOqpL+zXP8vvzlbuF90E8p9XSNjImPOLL0rCabzBLclV3tn5woMeBvL88tABIxOldyt7xpbDDTLXmrAw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:51:05.959139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.07532","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4470a3b5a93b1f666549b235fe5b2f432c63d0213082eed81c27b3dfc2c98f56","sha256:025faf909f52d2a37436c8fdb2546e060fbb41d58f6a2e327047e0d4b4e6f744"],"state_sha256":"4e914a0b3beb68a15babf352244b98b90eb00fb204624c0659be5c4fe3336490"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UQ2AczriQYzpEdDRYTqJJAzTG9o4WkzR6nZT6npbBUnQzhw6KjoUHFFKTr7Fuc6cFsKNjcI/123yuLgB+5HpBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T02:09:49.879457Z","bundle_sha256":"5220c00d4f1dc8e5b0820f4025c5d343fc4572138995b8efd5cb6c402b16945b"}}