{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EWDMYLIISYCRUZM2QI6X5IXA3Z","short_pith_number":"pith:EWDMYLII","canonical_record":{"source":{"id":"1708.03219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-09T05:25:07Z","cross_cats_sorted":[],"title_canon_sha256":"4a6e051ef3d6665c0a1e253865b3f1545b132cb53f1f1b5f3cccc9e708bb4434","abstract_canon_sha256":"5d43e458498153775933eef88a56b2843f8b3255219123c41dc29d75c322a778"},"schema_version":"1.0"},"canonical_sha256":"2586cc2d0896051a659a823d7ea2e0de622289db07533770372fbcac7ceb69f7","source":{"kind":"arxiv","id":"1708.03219","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EWDMYLIISYCRUZM2QI6X5IXA3Z","target":"record","payload":{"canonical_record":{"source":{"id":"1708.03219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-09T05:25:07Z","cross_cats_sorted":[],"title_canon_sha256":"4a6e051ef3d6665c0a1e253865b3f1545b132cb53f1f1b5f3cccc9e708bb4434","abstract_canon_sha256":"5d43e458498153775933eef88a56b2843f8b3255219123c41dc29d75c322a778"},"schema_version":"1.0"},"canonical_sha256":"2586cc2d0896051a659a823d7ea2e0de622289db07533770372fbcac7ceb69f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:14.444548Z","signature_b64":"OxFynDtvqraHLrZeXtIY4CHeHrMgzEekCLxGwxCcusnhNH3HXfTMsJPIXHFpYbY7cLoAOdUtU6L6CYnpz6UxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2586cc2d0896051a659a823d7ea2e0de622289db07533770372fbcac7ceb69f7","last_reissued_at":"2026-05-18T00:38:14.443746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:14.443746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.03219","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":"2026-05-18T00:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jrKX2nE+JVSfoVtRAnXU0+9J8K8tuxaUYCr5gVMoJanpKfNWsSg+1nAzHLPpoMp3tS5liiA2I7E/dtz/kz9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T21:05:58.572278Z"},"content_sha256":"b1f51846add3fba2fc49afccf62139e221388e295ee3acd681c79ceffd4193e6","schema_version":"1.0","event_id":"sha256:b1f51846add3fba2fc49afccf62139e221388e295ee3acd681c79ceffd4193e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EWDMYLIISYCRUZM2QI6X5IXA3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Safety Verification for Distributed Parameter Systems Using Barrier Functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antonis Papachristodoulou, Giorgio Valmorbida, Mohamadreza Ahmadi","submitted_at":"2017-08-09T05:25:07Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.03219","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":"2026-05-18T00:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QKARG7ykTls1bDNqkVBY7mUcEqm+/JRXFyTkshrqVkMa6pl4S9qO7ahGsYG9HrI2So2SfX9iDa6Ee+dXuNx0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T21:05:58.572670Z"},"content_sha256":"7347ab9a3bc1ca9a58ec9926c35803bcef026dd9c6aa0f81aa1c31f0f2a18964","schema_version":"1.0","event_id":"sha256:7347ab9a3bc1ca9a58ec9926c35803bcef026dd9c6aa0f81aa1c31f0f2a18964"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWDMYLIISYCRUZM2QI6X5IXA3Z/bundle.json","state_url":"https://pith.science/pith/EWDMYLIISYCRUZM2QI6X5IXA3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWDMYLIISYCRUZM2QI6X5IXA3Z/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":"2026-05-22T21:05:58Z","links":{"resolver":"https://pith.science/pith/EWDMYLIISYCRUZM2QI6X5IXA3Z","bundle":"https://pith.science/pith/EWDMYLIISYCRUZM2QI6X5IXA3Z/bundle.json","state":"https://pith.science/pith/EWDMYLIISYCRUZM2QI6X5IXA3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWDMYLIISYCRUZM2QI6X5IXA3Z/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ph1OLPD7ysFxpc+og0cgSCCXS1TF7RFxDdJJBKG6Hn9wZ0yLD/HoyUEZ9+c0CTR2+dfTWs+4NtjF0OlJQongDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T21:05:58.575718Z","bundle_sha256":"1e1560f4f83121f3e621c7d45323280fd9769e3aca9c8340a8c09edd63ca7e6c"}}