{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NZQATE3HOBZJQDOXRAUZFQTPFD","short_pith_number":"pith:NZQATE3H","canonical_record":{"source":{"id":"1811.12449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-29T19:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"698b5eab7859a6dcc7ad224f1f6e5e9d10105364256f4ffeadd92f9d5f912df0","abstract_canon_sha256":"feaf51e308575bbd6097b79647b3b8e9d52cd033e847e3834c152ea4a47a4766"},"schema_version":"1.0"},"canonical_sha256":"6e600993677072980dd7882992c26f28debcc34253fae2e87b94044f49491f9e","source":{"kind":"arxiv","id":"1811.12449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12449","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12449v1","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12449","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"pith_short_12","alias_value":"NZQATE3HOBZJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NZQATE3HOBZJQDOX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NZQATE3H","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NZQATE3HOBZJQDOXRAUZFQTPFD","target":"record","payload":{"canonical_record":{"source":{"id":"1811.12449","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-29T19:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"698b5eab7859a6dcc7ad224f1f6e5e9d10105364256f4ffeadd92f9d5f912df0","abstract_canon_sha256":"feaf51e308575bbd6097b79647b3b8e9d52cd033e847e3834c152ea4a47a4766"},"schema_version":"1.0"},"canonical_sha256":"6e600993677072980dd7882992c26f28debcc34253fae2e87b94044f49491f9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:31.639066Z","signature_b64":"tNVSu9GyRuIUOI8Rbdqy5V7SbV89WQNRvCaVdsMLiUk7ddNQTV0Ltop7/paWD8W49mnxsIiiRrIb+TSzcxN6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e600993677072980dd7882992c26f28debcc34253fae2e87b94044f49491f9e","last_reissued_at":"2026-05-17T23:59:31.638483Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:31.638483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.12449","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":"2026-05-17T23:59:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rC1Kp6nYT+WFv3+5n5pyogKKXD2chEtznRRwnW+LZl6xS+8Obfj9djE0Y2U704R6Xtpq4IrBnTY6SCyglWQjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:37:12.308211Z"},"content_sha256":"10289a595e4185c7cb586bfa739c81644c7b941e22fa04f10424e018d9df4f27","schema_version":"1.0","event_id":"sha256:10289a595e4185c7cb586bfa739c81644c7b941e22fa04f10424e018d9df4f27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NZQATE3HOBZJQDOXRAUZFQTPFD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Adaptive Finite Element DtN Method for Maxwell's Equations in Biperiodic Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Haijun Wu, Junliang Lv, Peijun Li, Weiying Zheng, Xue Jiang, Zhoufeng Wang","submitted_at":"2018-11-29T19:40:01Z","abstract_excerpt":"Consider the diffraction of an electromagnetic plane wave by a biperiodic structure where the wave propagation is governed by the three-dimensional Maxwell equations. Based on transparent boundary condition, the grating problem is formulated into a boundary value problem in a bounded domain. Using a duality argument technique, we derive an a posteriori error estimate for the finite element method with the truncation of the nonlocal Dirichlet-to-Neumann (DtN) boundary operator. The a posteriori error consists of both the finite element approximation error and the truncation error of boundary op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12449","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":"2026-05-17T23:59:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdkzRicSjqTU6C4ix327J0ZVNnnUfi9kz3t9YcN9oU0TpKHQ9xFr2RidG8gpFagLJpJ/I5NwDua8Pb+8rcn7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T05:37:12.308829Z"},"content_sha256":"1b5da2cfad6ab45a4c2b0ca534976c3d21c467328f3211387dfac0f6eb9908a3","schema_version":"1.0","event_id":"sha256:1b5da2cfad6ab45a4c2b0ca534976c3d21c467328f3211387dfac0f6eb9908a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZQATE3HOBZJQDOXRAUZFQTPFD/bundle.json","state_url":"https://pith.science/pith/NZQATE3HOBZJQDOXRAUZFQTPFD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZQATE3HOBZJQDOXRAUZFQTPFD/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":"2026-06-07T05:37:12Z","links":{"resolver":"https://pith.science/pith/NZQATE3HOBZJQDOXRAUZFQTPFD","bundle":"https://pith.science/pith/NZQATE3HOBZJQDOXRAUZFQTPFD/bundle.json","state":"https://pith.science/pith/NZQATE3HOBZJQDOXRAUZFQTPFD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZQATE3HOBZJQDOXRAUZFQTPFD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NZQATE3HOBZJQDOXRAUZFQTPFD","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":"feaf51e308575bbd6097b79647b3b8e9d52cd033e847e3834c152ea4a47a4766","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-29T19:40:01Z","title_canon_sha256":"698b5eab7859a6dcc7ad224f1f6e5e9d10105364256f4ffeadd92f9d5f912df0"},"schema_version":"1.0","source":{"id":"1811.12449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.12449","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.12449v1","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.12449","created_at":"2026-05-17T23:59:31Z"},{"alias_kind":"pith_short_12","alias_value":"NZQATE3HOBZJ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NZQATE3HOBZJQDOX","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NZQATE3H","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:1b5da2cfad6ab45a4c2b0ca534976c3d21c467328f3211387dfac0f6eb9908a3","target":"graph","created_at":"2026-05-17T23:59:31Z","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":"Consider the diffraction of an electromagnetic plane wave by a biperiodic structure where the wave propagation is governed by the three-dimensional Maxwell equations. Based on transparent boundary condition, the grating problem is formulated into a boundary value problem in a bounded domain. Using a duality argument technique, we derive an a posteriori error estimate for the finite element method with the truncation of the nonlocal Dirichlet-to-Neumann (DtN) boundary operator. The a posteriori error consists of both the finite element approximation error and the truncation error of boundary op","authors_text":"Haijun Wu, Junliang Lv, Peijun Li, Weiying Zheng, Xue Jiang, Zhoufeng Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-29T19:40:01Z","title":"An Adaptive Finite Element DtN Method for Maxwell's Equations in Biperiodic Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12449","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":"sha256:10289a595e4185c7cb586bfa739c81644c7b941e22fa04f10424e018d9df4f27","target":"record","created_at":"2026-05-17T23:59:31Z","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":"feaf51e308575bbd6097b79647b3b8e9d52cd033e847e3834c152ea4a47a4766","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-11-29T19:40:01Z","title_canon_sha256":"698b5eab7859a6dcc7ad224f1f6e5e9d10105364256f4ffeadd92f9d5f912df0"},"schema_version":"1.0","source":{"id":"1811.12449","kind":"arxiv","version":1}},"canonical_sha256":"6e600993677072980dd7882992c26f28debcc34253fae2e87b94044f49491f9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e600993677072980dd7882992c26f28debcc34253fae2e87b94044f49491f9e","first_computed_at":"2026-05-17T23:59:31.638483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:31.638483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tNVSu9GyRuIUOI8Rbdqy5V7SbV89WQNRvCaVdsMLiUk7ddNQTV0Ltop7/paWD8W49mnxsIiiRrIb+TSzcxN6AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:31.639066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.12449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10289a595e4185c7cb586bfa739c81644c7b941e22fa04f10424e018d9df4f27","sha256:1b5da2cfad6ab45a4c2b0ca534976c3d21c467328f3211387dfac0f6eb9908a3"],"state_sha256":"aced86cacbe5bc560080826d96a55d0c3d89c767b35f7d93a59038df4426ea2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PalgXafvjz69jw6yuPAwZu/T42hBC0W8fczE8n9CpiMmvINbmDvs2CdFuNUHABGZd/1MEV8OW58z3ftY2AiiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T05:37:12.312042Z","bundle_sha256":"fb33fdc1cee4ed5406fa5ba5f9cf8e0ffa227e09de8e996a6fccfebaed61dba8"}}