{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5NKJE5ERGAMKVGTDN5XUJ4XSX5","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":"3b44116cbf25e7672990118fdeb0ef1280c038220836edc7b8f1dff201950e13","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-03-19T15:30:03Z","title_canon_sha256":"60e77aa65965f5c4cadcd893c059faab0026c9a1d053f3a7a1491de80d3495c2"},"schema_version":"1.0","source":{"id":"2503.15336","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.15336","created_at":"2026-07-05T10:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"2503.15336v1","created_at":"2026-07-05T10:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.15336","created_at":"2026-07-05T10:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"5NKJE5ERGAMK","created_at":"2026-07-05T10:35:24Z"},{"alias_kind":"pith_short_16","alias_value":"5NKJE5ERGAMKVGTD","created_at":"2026-07-05T10:35:24Z"},{"alias_kind":"pith_short_8","alias_value":"5NKJE5ER","created_at":"2026-07-05T10:35:24Z"}],"graph_snapshots":[{"event_id":"sha256:dbbb9b80061eb0565eedff137e0792dc1dae95a95f9067c4cbe47981b89d69d2","target":"graph","created_at":"2026-07-05T10:35:24Z","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/2503.15336/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the exponential scaling often associated with analyses over high-dimensional spaces. This paper presents automated methods for constructing functional decompositions used to form set-based over-approximations of nonlinear functions, with particular focus on the hybrid zonotope set representation. To demonstrate these methods, we construct a hybrid zonotope set ","authors_text":"Andrew F. Thompson, Herschel C. Pangborn, Jacob A. Siefert, Jonah J. Glunt, Justin Ruths","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-03-19T15:30:03Z","title":"Automated Functional Decomposition for Hybrid Zonotope Over-approximations with Application to LSTM Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.15336","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:eb379abb30a861bdbe7284ecfe526837fe095b4c9bc5ffbc6484c849eda8e9a9","target":"record","created_at":"2026-07-05T10:35:24Z","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":"3b44116cbf25e7672990118fdeb0ef1280c038220836edc7b8f1dff201950e13","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-03-19T15:30:03Z","title_canon_sha256":"60e77aa65965f5c4cadcd893c059faab0026c9a1d053f3a7a1491de80d3495c2"},"schema_version":"1.0","source":{"id":"2503.15336","kind":"arxiv","version":1}},"canonical_sha256":"eb549274913018aa9a636f6f44f2f2bf480bfe99db5b05a7e2801e3588be75b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb549274913018aa9a636f6f44f2f2bf480bfe99db5b05a7e2801e3588be75b4","first_computed_at":"2026-07-05T10:35:24.227715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:35:24.227715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EjyKZaCLex94gV3q/sDltcklsQkEpDFZVB5O0+BBRevffqmpCk3QqN/HD98RfUqD4RLinyn9ht35C9EdyDURDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:35:24.228218Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.15336","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb379abb30a861bdbe7284ecfe526837fe095b4c9bc5ffbc6484c849eda8e9a9","sha256:dbbb9b80061eb0565eedff137e0792dc1dae95a95f9067c4cbe47981b89d69d2"],"state_sha256":"8e4cd8eb82d99df4e2f985a3a4568f74cd58dd586bf20bbb470691a7e4e66750"}