{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EWDMYLIISYCRUZM2QI6X5IXA3Z","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":"5d43e458498153775933eef88a56b2843f8b3255219123c41dc29d75c322a778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-09T05:25:07Z","title_canon_sha256":"4a6e051ef3d6665c0a1e253865b3f1545b132cb53f1f1b5f3cccc9e708bb4434"},"schema_version":"1.0","source":{"id":"1708.03219","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.03219","created_at":"2026-05-18T00:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"1708.03219v1","created_at":"2026-05-18T00:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.03219","created_at":"2026-05-18T00:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"EWDMYLIISYCR","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EWDMYLIISYCRUZM2","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EWDMYLII","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:7347ab9a3bc1ca9a58ec9926c35803bcef026dd9c6aa0f81aa1c31f0f2a18964","target":"graph","created_at":"2026-05-18T00:38:14Z","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":"We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a particular point in time. The proposed method is based on an extension of barrier certificates to infinite-dimensional systems. In this respect, we introduce barrier functionals, which are functionals of the dependent and independent variables. Given a set of initial conditions and an unsafe set, we demonstrate that if such a functional exists satisfying two (int","authors_text":"Antonis Papachristodoulou, Giorgio Valmorbida, Mohamadreza Ahmadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-09T05:25:07Z","title":"Safety Verification for Distributed Parameter Systems Using Barrier Functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03219","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:b1f51846add3fba2fc49afccf62139e221388e295ee3acd681c79ceffd4193e6","target":"record","created_at":"2026-05-18T00:38:14Z","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":"5d43e458498153775933eef88a56b2843f8b3255219123c41dc29d75c322a778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-09T05:25:07Z","title_canon_sha256":"4a6e051ef3d6665c0a1e253865b3f1545b132cb53f1f1b5f3cccc9e708bb4434"},"schema_version":"1.0","source":{"id":"1708.03219","kind":"arxiv","version":1}},"canonical_sha256":"2586cc2d0896051a659a823d7ea2e0de622289db07533770372fbcac7ceb69f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2586cc2d0896051a659a823d7ea2e0de622289db07533770372fbcac7ceb69f7","first_computed_at":"2026-05-18T00:38:14.443746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:14.443746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OxFynDtvqraHLrZeXtIY4CHeHrMgzEekCLxGwxCcusnhNH3HXfTMsJPIXHFpYbY7cLoAOdUtU6L6CYnpz6UxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:14.444548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.03219","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1f51846add3fba2fc49afccf62139e221388e295ee3acd681c79ceffd4193e6","sha256:7347ab9a3bc1ca9a58ec9926c35803bcef026dd9c6aa0f81aa1c31f0f2a18964"],"state_sha256":"576d4cf46dfad14ffa778983bfa76b403942aef4ccb0ca16f029ec464499fcc0"}