{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:T5F3KNTTOVENR77235NVZWPMWV","short_pith_number":"pith:T5F3KNTT","canonical_record":{"source":{"id":"1704.01816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-06T13:04:44Z","cross_cats_sorted":[],"title_canon_sha256":"6c5a815ecc6ca3c67d1797926807c055f47112dfbb5f7257c4ba387a227591cb","abstract_canon_sha256":"1c1c2d8f708f3a44daf97ef206b7495af59f71403cd90e1fe76d023378a97d22"},"schema_version":"1.0"},"canonical_sha256":"9f4bb536737548d8fffadf5b5cd9ecb555921ed0f27b5e3a2cd89bef7092a458","source":{"kind":"arxiv","id":"1704.01816","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01816","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01816v1","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01816","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"pith_short_12","alias_value":"T5F3KNTTOVEN","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T5F3KNTTOVENR772","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T5F3KNTT","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:T5F3KNTTOVENR77235NVZWPMWV","target":"record","payload":{"canonical_record":{"source":{"id":"1704.01816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-06T13:04:44Z","cross_cats_sorted":[],"title_canon_sha256":"6c5a815ecc6ca3c67d1797926807c055f47112dfbb5f7257c4ba387a227591cb","abstract_canon_sha256":"1c1c2d8f708f3a44daf97ef206b7495af59f71403cd90e1fe76d023378a97d22"},"schema_version":"1.0"},"canonical_sha256":"9f4bb536737548d8fffadf5b5cd9ecb555921ed0f27b5e3a2cd89bef7092a458","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:54.282355Z","signature_b64":"7LHj4Kem8rOq5yFzJDWWWbFgkzq64pp4Xjvlp+d8YyPwLST0KacL8CZjH873I2jd7yfaEhctWqCefO1rDMKmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f4bb536737548d8fffadf5b5cd9ecb555921ed0f27b5e3a2cd89bef7092a458","last_reissued_at":"2026-05-18T00:46:54.281899Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:54.281899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.01816","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":"2026-05-18T00:46:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mU38YSM7pzKpOA6VCG6uv7djMQ1c3QTPiTxx/DRO+sriK9HgDTQpXpgI0qkcTLRnFoRvkaPBswCi6CmywlSECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:30:56.469789Z"},"content_sha256":"ad9f41a281caa6e1cbecbdde86bf7409a2d96d732f9eb3cba02968e6549bc32f","schema_version":"1.0","event_id":"sha256:ad9f41a281caa6e1cbecbdde86bf7409a2d96d732f9eb3cba02968e6549bc32f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:T5F3KNTTOVENR77235NVZWPMWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Well-Posedness for a Piezo-Electromagnetic Coupling Model with Boundary Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rainer Picard","submitted_at":"2017-04-06T13:04:44Z","abstract_excerpt":"We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces coupled to the partial differential equations. Evolutionary well-posedness, i.e. Hadamard well-posedness and causal dependence on the data, is shown for the resulting model system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01816","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":"2026-05-18T00:46:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pyd+G7Y4c29xfbYkqLSwH0UPyMOe2q5Bz9qJST+RE5DS6MxJvij2Swe80bgN1uEw9/KkQoEB9ul4MCVctqHHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:30:56.470240Z"},"content_sha256":"8567fa787d1474b0bec0eaa5510dd264e1623e6b362a2afecefad08d41ac6fd3","schema_version":"1.0","event_id":"sha256:8567fa787d1474b0bec0eaa5510dd264e1623e6b362a2afecefad08d41ac6fd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T5F3KNTTOVENR77235NVZWPMWV/bundle.json","state_url":"https://pith.science/pith/T5F3KNTTOVENR77235NVZWPMWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T5F3KNTTOVENR77235NVZWPMWV/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":"2026-06-05T00:30:56Z","links":{"resolver":"https://pith.science/pith/T5F3KNTTOVENR77235NVZWPMWV","bundle":"https://pith.science/pith/T5F3KNTTOVENR77235NVZWPMWV/bundle.json","state":"https://pith.science/pith/T5F3KNTTOVENR77235NVZWPMWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T5F3KNTTOVENR77235NVZWPMWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T5F3KNTTOVENR77235NVZWPMWV","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":"1c1c2d8f708f3a44daf97ef206b7495af59f71403cd90e1fe76d023378a97d22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-06T13:04:44Z","title_canon_sha256":"6c5a815ecc6ca3c67d1797926807c055f47112dfbb5f7257c4ba387a227591cb"},"schema_version":"1.0","source":{"id":"1704.01816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01816","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01816v1","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01816","created_at":"2026-05-18T00:46:54Z"},{"alias_kind":"pith_short_12","alias_value":"T5F3KNTTOVEN","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T5F3KNTTOVENR772","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T5F3KNTT","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:8567fa787d1474b0bec0eaa5510dd264e1623e6b362a2afecefad08d41ac6fd3","target":"graph","created_at":"2026-05-18T00:46:54Z","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 consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces coupled to the partial differential equations. Evolutionary well-posedness, i.e. Hadamard well-posedness and causal dependence on the data, is shown for the resulting model system.","authors_text":"Rainer Picard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-06T13:04:44Z","title":"On Well-Posedness for a Piezo-Electromagnetic Coupling Model with Boundary Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01816","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:ad9f41a281caa6e1cbecbdde86bf7409a2d96d732f9eb3cba02968e6549bc32f","target":"record","created_at":"2026-05-18T00:46:54Z","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":"1c1c2d8f708f3a44daf97ef206b7495af59f71403cd90e1fe76d023378a97d22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-04-06T13:04:44Z","title_canon_sha256":"6c5a815ecc6ca3c67d1797926807c055f47112dfbb5f7257c4ba387a227591cb"},"schema_version":"1.0","source":{"id":"1704.01816","kind":"arxiv","version":1}},"canonical_sha256":"9f4bb536737548d8fffadf5b5cd9ecb555921ed0f27b5e3a2cd89bef7092a458","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f4bb536737548d8fffadf5b5cd9ecb555921ed0f27b5e3a2cd89bef7092a458","first_computed_at":"2026-05-18T00:46:54.281899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:54.281899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7LHj4Kem8rOq5yFzJDWWWbFgkzq64pp4Xjvlp+d8YyPwLST0KacL8CZjH873I2jd7yfaEhctWqCefO1rDMKmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:54.282355Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad9f41a281caa6e1cbecbdde86bf7409a2d96d732f9eb3cba02968e6549bc32f","sha256:8567fa787d1474b0bec0eaa5510dd264e1623e6b362a2afecefad08d41ac6fd3"],"state_sha256":"38896633fd18f3f4adc0a7c9c434dba55a551ea4bf158b0cc400aa23316a9198"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QbBNIRHL1Z4qnc0LAZun2HPyki5OQoYDXhAdAGY+mvoBnOrd93DGgDp0E8XCFGnQy4jgqJBQYrrKLodUFvgJCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:30:56.472824Z","bundle_sha256":"a54cfb3a44cd37e389783eb512d8e7c5ec1db218384192d3b78dd0cb83663b92"}}