{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PP6XPB3QIELDR6HA6WAEZ2UIUY","short_pith_number":"pith:PP6XPB3Q","canonical_record":{"source":{"id":"1812.03803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-10T14:13:38Z","cross_cats_sorted":[],"title_canon_sha256":"e840b6984717996872c35dd9821072b2505db4c096b9d0fcfa8b1bb162636d09","abstract_canon_sha256":"2c7b74c93061a6fffb2f7eedaf667d0b5064cbe7220ed7e0af4ede4787d1360f"},"schema_version":"1.0"},"canonical_sha256":"7bfd778770411638f8e0f5804cea88a61215e8cb4fa3a2c3ab96f462a6fddfd9","source":{"kind":"arxiv","id":"1812.03803","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03803","created_at":"2026-05-17T23:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03803v1","created_at":"2026-05-17T23:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03803","created_at":"2026-05-17T23:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"PP6XPB3QIELD","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PP6XPB3QIELDR6HA","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PP6XPB3Q","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PP6XPB3QIELDR6HA6WAEZ2UIUY","target":"record","payload":{"canonical_record":{"source":{"id":"1812.03803","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-10T14:13:38Z","cross_cats_sorted":[],"title_canon_sha256":"e840b6984717996872c35dd9821072b2505db4c096b9d0fcfa8b1bb162636d09","abstract_canon_sha256":"2c7b74c93061a6fffb2f7eedaf667d0b5064cbe7220ed7e0af4ede4787d1360f"},"schema_version":"1.0"},"canonical_sha256":"7bfd778770411638f8e0f5804cea88a61215e8cb4fa3a2c3ab96f462a6fddfd9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:43.834177Z","signature_b64":"r8kgSo5KfFbu7x6bta3rH3ZnDtVbq3Ew46WTV5jdjMbM6bcafPop2U0D3nZKUxeKS7e5OO5fxMKt2YfkD9IXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bfd778770411638f8e0f5804cea88a61215e8cb4fa3a2c3ab96f462a6fddfd9","last_reissued_at":"2026-05-17T23:58:43.833744Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:43.833744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.03803","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":"2026-05-17T23:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MscD9GivuTxg1DaAbrspGriOr43VMpoacH3SAuYbbLxwGappkqY05iKy+Lh46x7J3VGSOCWvBWKMXuKAqzTmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:20:40.454999Z"},"content_sha256":"8d258029382596354685d3f862718c0f472e9fa0a1bb4cba937af9d913a4ce40","schema_version":"1.0","event_id":"sha256:8d258029382596354685d3f862718c0f472e9fa0a1bb4cba937af9d913a4ce40"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PP6XPB3QIELDR6HA6WAEZ2UIUY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Martin Spitz, Roland Schnaubelt","submitted_at":"2018-12-10T14:13:38Z","abstract_excerpt":"In this article we provide a local wellposedness theory for quasilinear Maxwell equations with absorbing boundary conditions in $\\mathcal{H}^m$ for $m \\geq 3$. The Maxwell equations are equipped with instantaneous nonlinear material laws leading to a quasilinear symmetric hyperbolic first order system. We consider both linear and nonlinear absorbing boundary conditions. We show existence and uniqueness of a local solution, provide a blow-up criterion in the Lipschitz norm, and prove the continuous dependence on the data. In the case of nonlinear boundary conditions we need a smallness assumpti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03803","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":"2026-05-17T23:58:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dlZHoUARCbZec3r/kHf8az7QIHkQ1DaF79eIPvCRkw25WZ7c9Qn/UJrmGA0AGS5WBoPPf/BC6xp5fuFiM27ZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:20:40.455356Z"},"content_sha256":"c8aa6b0f4c2fc852b1727a527d8096fc325c8b52a884becec7f35bb17a0fd381","schema_version":"1.0","event_id":"sha256:c8aa6b0f4c2fc852b1727a527d8096fc325c8b52a884becec7f35bb17a0fd381"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PP6XPB3QIELDR6HA6WAEZ2UIUY/bundle.json","state_url":"https://pith.science/pith/PP6XPB3QIELDR6HA6WAEZ2UIUY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PP6XPB3QIELDR6HA6WAEZ2UIUY/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":"2026-06-27T01:20:40Z","links":{"resolver":"https://pith.science/pith/PP6XPB3QIELDR6HA6WAEZ2UIUY","bundle":"https://pith.science/pith/PP6XPB3QIELDR6HA6WAEZ2UIUY/bundle.json","state":"https://pith.science/pith/PP6XPB3QIELDR6HA6WAEZ2UIUY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PP6XPB3QIELDR6HA6WAEZ2UIUY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PP6XPB3QIELDR6HA6WAEZ2UIUY","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":"2c7b74c93061a6fffb2f7eedaf667d0b5064cbe7220ed7e0af4ede4787d1360f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-10T14:13:38Z","title_canon_sha256":"e840b6984717996872c35dd9821072b2505db4c096b9d0fcfa8b1bb162636d09"},"schema_version":"1.0","source":{"id":"1812.03803","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.03803","created_at":"2026-05-17T23:58:43Z"},{"alias_kind":"arxiv_version","alias_value":"1812.03803v1","created_at":"2026-05-17T23:58:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.03803","created_at":"2026-05-17T23:58:43Z"},{"alias_kind":"pith_short_12","alias_value":"PP6XPB3QIELD","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PP6XPB3QIELDR6HA","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PP6XPB3Q","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:c8aa6b0f4c2fc852b1727a527d8096fc325c8b52a884becec7f35bb17a0fd381","target":"graph","created_at":"2026-05-17T23:58:43Z","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":"In this article we provide a local wellposedness theory for quasilinear Maxwell equations with absorbing boundary conditions in $\\mathcal{H}^m$ for $m \\geq 3$. The Maxwell equations are equipped with instantaneous nonlinear material laws leading to a quasilinear symmetric hyperbolic first order system. We consider both linear and nonlinear absorbing boundary conditions. We show existence and uniqueness of a local solution, provide a blow-up criterion in the Lipschitz norm, and prove the continuous dependence on the data. In the case of nonlinear boundary conditions we need a smallness assumpti","authors_text":"Martin Spitz, Roland Schnaubelt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-10T14:13:38Z","title":"Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03803","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":"sha256:8d258029382596354685d3f862718c0f472e9fa0a1bb4cba937af9d913a4ce40","target":"record","created_at":"2026-05-17T23:58:43Z","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":"2c7b74c93061a6fffb2f7eedaf667d0b5064cbe7220ed7e0af4ede4787d1360f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-10T14:13:38Z","title_canon_sha256":"e840b6984717996872c35dd9821072b2505db4c096b9d0fcfa8b1bb162636d09"},"schema_version":"1.0","source":{"id":"1812.03803","kind":"arxiv","version":1}},"canonical_sha256":"7bfd778770411638f8e0f5804cea88a61215e8cb4fa3a2c3ab96f462a6fddfd9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bfd778770411638f8e0f5804cea88a61215e8cb4fa3a2c3ab96f462a6fddfd9","first_computed_at":"2026-05-17T23:58:43.833744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:43.833744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r8kgSo5KfFbu7x6bta3rH3ZnDtVbq3Ew46WTV5jdjMbM6bcafPop2U0D3nZKUxeKS7e5OO5fxMKt2YfkD9IXDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:43.834177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.03803","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d258029382596354685d3f862718c0f472e9fa0a1bb4cba937af9d913a4ce40","sha256:c8aa6b0f4c2fc852b1727a527d8096fc325c8b52a884becec7f35bb17a0fd381"],"state_sha256":"ddf00bd26300b77af18260237bc6d8b49a2a3c14c986092f5fa2e19ae53847b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FgOLbvhfw1Fj+E1xggclRS5xzqq2LKzIj1YOgVsxjdW2Nm1M01XH8SsGBjQJKCrIjIKpRpGaYEBG74QS04BVAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:20:40.457127Z","bundle_sha256":"8092078fe65dc840c071b9c4f7093636e1e4ed615021522a1e5c08c4fec6f30e"}}