{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VVIV5NISIIXR6SXQSOGRYHGISK","short_pith_number":"pith:VVIV5NIS","canonical_record":{"source":{"id":"1807.06888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-18T12:15:08Z","cross_cats_sorted":[],"title_canon_sha256":"81fe4651cc2b4809a6314b0890fdcaa29dd8eb8c7c4516e07fcdc5b03e718b72","abstract_canon_sha256":"3eabdf1368f9f493e11d5aea2104cdfb83484ca57809e171c209f4888f021b99"},"schema_version":"1.0"},"canonical_sha256":"ad515eb512422f1f4af0938d1c1cc892ada77ded098591cf07b164c4da22a0d8","source":{"kind":"arxiv","id":"1807.06888","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06888","created_at":"2026-05-18T00:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06888v1","created_at":"2026-05-18T00:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06888","created_at":"2026-05-18T00:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"VVIV5NISIIXR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VVIV5NISIIXR6SXQ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VVIV5NIS","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VVIV5NISIIXR6SXQSOGRYHGISK","target":"record","payload":{"canonical_record":{"source":{"id":"1807.06888","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-18T12:15:08Z","cross_cats_sorted":[],"title_canon_sha256":"81fe4651cc2b4809a6314b0890fdcaa29dd8eb8c7c4516e07fcdc5b03e718b72","abstract_canon_sha256":"3eabdf1368f9f493e11d5aea2104cdfb83484ca57809e171c209f4888f021b99"},"schema_version":"1.0"},"canonical_sha256":"ad515eb512422f1f4af0938d1c1cc892ada77ded098591cf07b164c4da22a0d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:25.433014Z","signature_b64":"DjxHWgfEZ7eYV+KomWwEMiuiafJKfa5MKcSmdxqGASHAAlGzE9NtLrk9WARcBdDSapt85zbP8MLqiyNS4bZfAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad515eb512422f1f4af0938d1c1cc892ada77ded098591cf07b164c4da22a0d8","last_reissued_at":"2026-05-18T00:10:25.432485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:25.432485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.06888","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":"2026-05-18T00:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LRa6NRJiEP+zyEDgd5xDpkEbG7ep9DyKg9Ylnu9pFyJzd85J+DVmxl2tZMuvuRXZvUDookRDGvq413FnRnN1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:17:48.379265Z"},"content_sha256":"217b1d8bae8d186fade95588ad19de4989f9b0043bcb382c2f5138da8fa1c635","schema_version":"1.0","event_id":"sha256:217b1d8bae8d186fade95588ad19de4989f9b0043bcb382c2f5138da8fa1c635"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VVIV5NISIIXR6SXQSOGRYHGISK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Guaranteed Error Bounds on Approximate Model Abstractions through Reachability Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SY","authors_text":"Andrea Vandin, Luca Cardelli, Max Tschaikowski, Mirco Tribastone","submitted_at":"2018-07-18T12:15:08Z","abstract_excerpt":"It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem for nonlinear ordinary differential equations (ODEs) with polynomial derivatives. We introduce approximate differential equivalence as a more permissive variant of a recently developed exact counterpart, allowing ODE variables to be related even when they are governed by nearby derivatives. We develop algorithms to (i) compute the largest approximate differ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06888","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":""},"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":"2026-05-18T00:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uR6ANXYpNlOCzbllncxbP4uj1ABJuowMCGcBwWzkQ/kgfkQcxsLQycgP/Dc7W07SNY1ca2hz+RDOyIL6zeOoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:17:48.379630Z"},"content_sha256":"20202a83598ff30b6e7b10a50ed8b6cafb12a428eb2ff7b67bcd55f81c41e456","schema_version":"1.0","event_id":"sha256:20202a83598ff30b6e7b10a50ed8b6cafb12a428eb2ff7b67bcd55f81c41e456"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VVIV5NISIIXR6SXQSOGRYHGISK/bundle.json","state_url":"https://pith.science/pith/VVIV5NISIIXR6SXQSOGRYHGISK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VVIV5NISIIXR6SXQSOGRYHGISK/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":"2026-06-01T22:17:48Z","links":{"resolver":"https://pith.science/pith/VVIV5NISIIXR6SXQSOGRYHGISK","bundle":"https://pith.science/pith/VVIV5NISIIXR6SXQSOGRYHGISK/bundle.json","state":"https://pith.science/pith/VVIV5NISIIXR6SXQSOGRYHGISK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VVIV5NISIIXR6SXQSOGRYHGISK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VVIV5NISIIXR6SXQSOGRYHGISK","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":"3eabdf1368f9f493e11d5aea2104cdfb83484ca57809e171c209f4888f021b99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-18T12:15:08Z","title_canon_sha256":"81fe4651cc2b4809a6314b0890fdcaa29dd8eb8c7c4516e07fcdc5b03e718b72"},"schema_version":"1.0","source":{"id":"1807.06888","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06888","created_at":"2026-05-18T00:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06888v1","created_at":"2026-05-18T00:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06888","created_at":"2026-05-18T00:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"VVIV5NISIIXR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VVIV5NISIIXR6SXQ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VVIV5NIS","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:20202a83598ff30b6e7b10a50ed8b6cafb12a428eb2ff7b67bcd55f81c41e456","target":"graph","created_at":"2026-05-18T00:10:25Z","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"},"paper":{"abstract_excerpt":"It is well known that exact notions of model abstraction and reduction for dynamical systems may not be robust enough in practice because they are highly sensitive to the specific choice of parameters. In this paper we consider this problem for nonlinear ordinary differential equations (ODEs) with polynomial derivatives. We introduce approximate differential equivalence as a more permissive variant of a recently developed exact counterpart, allowing ODE variables to be related even when they are governed by nearby derivatives. We develop algorithms to (i) compute the largest approximate differ","authors_text":"Andrea Vandin, Luca Cardelli, Max Tschaikowski, Mirco Tribastone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-18T12:15:08Z","title":"Guaranteed Error Bounds on Approximate Model Abstractions through Reachability Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06888","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":"sha256:217b1d8bae8d186fade95588ad19de4989f9b0043bcb382c2f5138da8fa1c635","target":"record","created_at":"2026-05-18T00:10:25Z","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":"3eabdf1368f9f493e11d5aea2104cdfb83484ca57809e171c209f4888f021b99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2018-07-18T12:15:08Z","title_canon_sha256":"81fe4651cc2b4809a6314b0890fdcaa29dd8eb8c7c4516e07fcdc5b03e718b72"},"schema_version":"1.0","source":{"id":"1807.06888","kind":"arxiv","version":1}},"canonical_sha256":"ad515eb512422f1f4af0938d1c1cc892ada77ded098591cf07b164c4da22a0d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad515eb512422f1f4af0938d1c1cc892ada77ded098591cf07b164c4da22a0d8","first_computed_at":"2026-05-18T00:10:25.432485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:25.432485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DjxHWgfEZ7eYV+KomWwEMiuiafJKfa5MKcSmdxqGASHAAlGzE9NtLrk9WARcBdDSapt85zbP8MLqiyNS4bZfAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:25.433014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06888","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:217b1d8bae8d186fade95588ad19de4989f9b0043bcb382c2f5138da8fa1c635","sha256:20202a83598ff30b6e7b10a50ed8b6cafb12a428eb2ff7b67bcd55f81c41e456"],"state_sha256":"71ffeede896b5535ad73bf718a7e623d326d85d4b8b112c5a9b01ccdb381c9d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eg1LJfo955gXdCuhcfNmwe4+t2Y1mseQTjYkLeF5ZYtLIeOnRiIZVMLNYW0YmHy+3H0F8mi5BDp7ZQEeKy1DBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:17:48.381501Z","bundle_sha256":"f4b4b59f40a99b01518c958058e01b58616806610bd3e3c96b3ded7ef3e93f54"}}