{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:IEGEXXNPRXLWVF4HYCROVM43QX","short_pith_number":"pith:IEGEXXNP","canonical_record":{"source":{"id":"2008.02389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-08-05T22:54:09Z","cross_cats_sorted":["math.DS","stat.ML"],"title_canon_sha256":"278459ae3410ec30e92a9568350f7dd5eba7d26572cc656d0b1ad2fcdb48d135","abstract_canon_sha256":"abc9779cd7c20d2cee831a882ac05783b3a6525d0bc86c2e098912aafe32c474"},"schema_version":"1.0"},"canonical_sha256":"410c4bddaf8dd76a9787c0a2eab39b85dd41f6409eaccd0d0c077feff5bccc10","source":{"kind":"arxiv","id":"2008.02389","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.02389","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"2008.02389v1","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.02389","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"IEGEXXNPRXLW","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_16","alias_value":"IEGEXXNPRXLWVF4H","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_8","alias_value":"IEGEXXNP","created_at":"2026-07-05T01:25:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:IEGEXXNPRXLWVF4HYCROVM43QX","target":"record","payload":{"canonical_record":{"source":{"id":"2008.02389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-08-05T22:54:09Z","cross_cats_sorted":["math.DS","stat.ML"],"title_canon_sha256":"278459ae3410ec30e92a9568350f7dd5eba7d26572cc656d0b1ad2fcdb48d135","abstract_canon_sha256":"abc9779cd7c20d2cee831a882ac05783b3a6525d0bc86c2e098912aafe32c474"},"schema_version":"1.0"},"canonical_sha256":"410c4bddaf8dd76a9787c0a2eab39b85dd41f6409eaccd0d0c077feff5bccc10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:25:04.615979Z","signature_b64":"py20fi/cxLDtuVVhY635V1ZBUw84QNgMjHKSXVrqNHwNDlJRcr8/vqZdyavGCnG0tfdF5xm+J8SkZh/9oVVXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"410c4bddaf8dd76a9787c0a2eab39b85dd41f6409eaccd0d0c077feff5bccc10","last_reissued_at":"2026-07-05T01:25:04.615478Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:25:04.615478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2008.02389","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":"2026-07-05T01:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wLXGbBk+POBUbOC6SkIoKXAuGzGc43wmp44dW4W8oOjw5Bwq7CtppDRlr3qnpD94ZSxEJDlFWN96pZkIxhdXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:41:30.320600Z"},"content_sha256":"0f0a78a3442f2df7e94025a84a3ab6086944464f9451998a0af757dd51542c94","schema_version":"1.0","event_id":"sha256:0f0a78a3442f2df7e94025a84a3ab6086944464f9451998a0af757dd51542c94"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:IEGEXXNPRXLWVF4HYCROVM43QX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuous-in-Depth Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alejandro F. Queiruga, Dane Taylor, Michael W. Mahoney, N. Benjamin Erichson","submitted_at":"2020-08-05T22:54:09Z","abstract_excerpt":"Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete dynamical integrators of continuous dynamical systems, however, have a much richer structure. We first show that ResNets fail to be meaningful dynamical integrators in this richer sense. We then demonstrate that neural network models can learn to represent continuous dynamical systems, with this richer structure and properties, by embedding them into higher-ord"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.02389","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/2008.02389/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":"2026-07-05T01:25:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqoT6mw70VdTOps48MkTUQbGJi+LppNHXCEoV7uE2XfQJSxgK0kl6c4p/o9KyQsQIds1rG+Mp7MY6J7Vgs4QBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T19:41:30.321113Z"},"content_sha256":"a420b24ff4455dd30fd3e5b4690d19e8a847d75c29679680a68927da5dbc4910","schema_version":"1.0","event_id":"sha256:a420b24ff4455dd30fd3e5b4690d19e8a847d75c29679680a68927da5dbc4910"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IEGEXXNPRXLWVF4HYCROVM43QX/bundle.json","state_url":"https://pith.science/pith/IEGEXXNPRXLWVF4HYCROVM43QX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IEGEXXNPRXLWVF4HYCROVM43QX/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":"2026-08-11T19:41:30Z","links":{"resolver":"https://pith.science/pith/IEGEXXNPRXLWVF4HYCROVM43QX","bundle":"https://pith.science/pith/IEGEXXNPRXLWVF4HYCROVM43QX/bundle.json","state":"https://pith.science/pith/IEGEXXNPRXLWVF4HYCROVM43QX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IEGEXXNPRXLWVF4HYCROVM43QX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:IEGEXXNPRXLWVF4HYCROVM43QX","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":"abc9779cd7c20d2cee831a882ac05783b3a6525d0bc86c2e098912aafe32c474","cross_cats_sorted":["math.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-08-05T22:54:09Z","title_canon_sha256":"278459ae3410ec30e92a9568350f7dd5eba7d26572cc656d0b1ad2fcdb48d135"},"schema_version":"1.0","source":{"id":"2008.02389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.02389","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"2008.02389v1","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.02389","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"IEGEXXNPRXLW","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_16","alias_value":"IEGEXXNPRXLWVF4H","created_at":"2026-07-05T01:25:04Z"},{"alias_kind":"pith_short_8","alias_value":"IEGEXXNP","created_at":"2026-07-05T01:25:04Z"}],"graph_snapshots":[{"event_id":"sha256:a420b24ff4455dd30fd3e5b4690d19e8a847d75c29679680a68927da5dbc4910","target":"graph","created_at":"2026-07-05T01:25:04Z","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/2008.02389/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete dynamical integrators of continuous dynamical systems, however, have a much richer structure. We first show that ResNets fail to be meaningful dynamical integrators in this richer sense. We then demonstrate that neural network models can learn to represent continuous dynamical systems, with this richer structure and properties, by embedding them into higher-ord","authors_text":"Alejandro F. Queiruga, Dane Taylor, Michael W. Mahoney, N. Benjamin Erichson","cross_cats":["math.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-08-05T22:54:09Z","title":"Continuous-in-Depth Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.02389","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":"sha256:0f0a78a3442f2df7e94025a84a3ab6086944464f9451998a0af757dd51542c94","target":"record","created_at":"2026-07-05T01:25:04Z","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":"abc9779cd7c20d2cee831a882ac05783b3a6525d0bc86c2e098912aafe32c474","cross_cats_sorted":["math.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2020-08-05T22:54:09Z","title_canon_sha256":"278459ae3410ec30e92a9568350f7dd5eba7d26572cc656d0b1ad2fcdb48d135"},"schema_version":"1.0","source":{"id":"2008.02389","kind":"arxiv","version":1}},"canonical_sha256":"410c4bddaf8dd76a9787c0a2eab39b85dd41f6409eaccd0d0c077feff5bccc10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"410c4bddaf8dd76a9787c0a2eab39b85dd41f6409eaccd0d0c077feff5bccc10","first_computed_at":"2026-07-05T01:25:04.615478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:25:04.615478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"py20fi/cxLDtuVVhY635V1ZBUw84QNgMjHKSXVrqNHwNDlJRcr8/vqZdyavGCnG0tfdF5xm+J8SkZh/9oVVXDA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:25:04.615979Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.02389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f0a78a3442f2df7e94025a84a3ab6086944464f9451998a0af757dd51542c94","sha256:a420b24ff4455dd30fd3e5b4690d19e8a847d75c29679680a68927da5dbc4910"],"state_sha256":"16cd075f2f70cf2e7b6713dcb1cf600b2d54f519921683d1581478dcc3ba0cb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIyUra9YoCB9TTzhu7s5CDTmZsmcisB89G0SZssnrtSdGHky83UtXcpxuGxc9BC6e+T9ihahX84c9GpUHOdiDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T19:41:30.324362Z","bundle_sha256":"457e152a15414675675aba78a63173d1f3a4cd069268eda6f361270e775f4492"}}