{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AFRKVE4R3LDVCMPTTIBVYCAUJ3","short_pith_number":"pith:AFRKVE4R","canonical_record":{"source":{"id":"1803.04510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-12T20:17:40Z","cross_cats_sorted":[],"title_canon_sha256":"d0f099b0faa318bcdaba8b4e6761368bc4060e3a9a19496370bc1e2a071e38ca","abstract_canon_sha256":"15ba59b59bc18113e609fa519ddb2b4ddba3e21e14ea5b2111513d7fa5e0e30a"},"schema_version":"1.0"},"canonical_sha256":"0162aa9391dac75131f39a035c08144ef83a094a67685c150942bea65d134112","source":{"kind":"arxiv","id":"1803.04510","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04510","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04510v1","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04510","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"AFRKVE4R3LDV","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AFRKVE4R3LDVCMPT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AFRKVE4R","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AFRKVE4R3LDVCMPTTIBVYCAUJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1803.04510","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-12T20:17:40Z","cross_cats_sorted":[],"title_canon_sha256":"d0f099b0faa318bcdaba8b4e6761368bc4060e3a9a19496370bc1e2a071e38ca","abstract_canon_sha256":"15ba59b59bc18113e609fa519ddb2b4ddba3e21e14ea5b2111513d7fa5e0e30a"},"schema_version":"1.0"},"canonical_sha256":"0162aa9391dac75131f39a035c08144ef83a094a67685c150942bea65d134112","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:53.212362Z","signature_b64":"sj2MNVX7yBBFjMNsS+O85Jxo+yRvyyLGZAG1DuV2XMRUzLe1BILxGnraI4xZ8+CBxPtvIsOj8uymagNDjebhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0162aa9391dac75131f39a035c08144ef83a094a67685c150942bea65d134112","last_reissued_at":"2026-05-17T23:45:53.211742Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:53.211742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.04510","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":"2026-05-17T23:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qb3/NvBedS50XH+aQF9gZwiaXpGcJX0gmWpdBxa0UNmfnFS1rIrmxNvbY7eQBU6LmcoDHntSQrvyHi/mJ7EBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:27:53.564832Z"},"content_sha256":"00ba9aa9dd8d59bf2818033dfa07a165a35c8c42f1160fdb84997821e076aaef","schema_version":"1.0","event_id":"sha256:00ba9aa9dd8d59bf2818033dfa07a165a35c8c42f1160fdb84997821e076aaef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AFRKVE4R3LDVCMPTTIBVYCAUJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discontinuity propagation in delay differential-algebraic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benjamin Unger","submitted_at":"2018-03-12T20:17:40Z","abstract_excerpt":"The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\\ss} form for regular matrix pencil, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as the worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE. The new classification for DDAE"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04510","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":"2026-05-17T23:45:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K5WgJwP7n6Gqe8EXw0g8vJ0oDasCu0oAFtFN4TsUFsVNzeEz8xOLvJzepXtvukvTVN9A4MdlQ+aZWTCGVGT6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:27:53.565219Z"},"content_sha256":"ff67bca0bb4adc60c179068dc738e18451a2e03d7bab136abe870b9e23e01d39","schema_version":"1.0","event_id":"sha256:ff67bca0bb4adc60c179068dc738e18451a2e03d7bab136abe870b9e23e01d39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AFRKVE4R3LDVCMPTTIBVYCAUJ3/bundle.json","state_url":"https://pith.science/pith/AFRKVE4R3LDVCMPTTIBVYCAUJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AFRKVE4R3LDVCMPTTIBVYCAUJ3/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":"2026-05-28T11:27:53Z","links":{"resolver":"https://pith.science/pith/AFRKVE4R3LDVCMPTTIBVYCAUJ3","bundle":"https://pith.science/pith/AFRKVE4R3LDVCMPTTIBVYCAUJ3/bundle.json","state":"https://pith.science/pith/AFRKVE4R3LDVCMPTTIBVYCAUJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AFRKVE4R3LDVCMPTTIBVYCAUJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AFRKVE4R3LDVCMPTTIBVYCAUJ3","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":"15ba59b59bc18113e609fa519ddb2b4ddba3e21e14ea5b2111513d7fa5e0e30a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-12T20:17:40Z","title_canon_sha256":"d0f099b0faa318bcdaba8b4e6761368bc4060e3a9a19496370bc1e2a071e38ca"},"schema_version":"1.0","source":{"id":"1803.04510","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04510","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04510v1","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04510","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"AFRKVE4R3LDV","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AFRKVE4R3LDVCMPT","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AFRKVE4R","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:ff67bca0bb4adc60c179068dc738e18451a2e03d7bab136abe870b9e23e01d39","target":"graph","created_at":"2026-05-17T23:45:53Z","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":"The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\\ss} form for regular matrix pencil, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as the worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE. The new classification for DDAE","authors_text":"Benjamin Unger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-12T20:17:40Z","title":"Discontinuity propagation in delay differential-algebraic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04510","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":"sha256:00ba9aa9dd8d59bf2818033dfa07a165a35c8c42f1160fdb84997821e076aaef","target":"record","created_at":"2026-05-17T23:45:53Z","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":"15ba59b59bc18113e609fa519ddb2b4ddba3e21e14ea5b2111513d7fa5e0e30a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-03-12T20:17:40Z","title_canon_sha256":"d0f099b0faa318bcdaba8b4e6761368bc4060e3a9a19496370bc1e2a071e38ca"},"schema_version":"1.0","source":{"id":"1803.04510","kind":"arxiv","version":1}},"canonical_sha256":"0162aa9391dac75131f39a035c08144ef83a094a67685c150942bea65d134112","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0162aa9391dac75131f39a035c08144ef83a094a67685c150942bea65d134112","first_computed_at":"2026-05-17T23:45:53.211742Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:53.211742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sj2MNVX7yBBFjMNsS+O85Jxo+yRvyyLGZAG1DuV2XMRUzLe1BILxGnraI4xZ8+CBxPtvIsOj8uymagNDjebhDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:53.212362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04510","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00ba9aa9dd8d59bf2818033dfa07a165a35c8c42f1160fdb84997821e076aaef","sha256:ff67bca0bb4adc60c179068dc738e18451a2e03d7bab136abe870b9e23e01d39"],"state_sha256":"01e028208bb88df0437856a5540798485db0406af698633bfe4662b5565ea881"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O/Ch54S1Kqy7DgeS1V7jotcPfRs6134vyb+iao0Rm947PjcA5IybD8jnT5p6JH8dn2o4gCD5iVs1xCo4G9/gAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:27:53.567243Z","bundle_sha256":"e5b9e05994890f2715fc4c3f1c02c5f8c736eeb7e89180848d353c973d71a44d"}}