{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:4GJYTTSHVGS5IRCQIADOELBCUQ","short_pith_number":"pith:4GJYTTSH","canonical_record":{"source":{"id":"0905.2321","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-14T16:06:17Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"742eae794e5de5008fd94f8190d30d591a59756e6dd5cf81b0ccd9934161cc51","abstract_canon_sha256":"5a82b60c58756c32f238d50ae9e75f2ac32c30a404679bf0665c28a1d119e9cc"},"schema_version":"1.0"},"canonical_sha256":"e19389ce47a9a5d444504006e22c22a4074ecc404b0805520dabac6dece0f3c0","source":{"kind":"arxiv","id":"0905.2321","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.2321","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"0905.2321v3","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2321","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"4GJYTTSHVGS5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4GJYTTSHVGS5IRCQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4GJYTTSH","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:4GJYTTSHVGS5IRCQIADOELBCUQ","target":"record","payload":{"canonical_record":{"source":{"id":"0905.2321","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-14T16:06:17Z","cross_cats_sorted":["nlin.PS"],"title_canon_sha256":"742eae794e5de5008fd94f8190d30d591a59756e6dd5cf81b0ccd9934161cc51","abstract_canon_sha256":"5a82b60c58756c32f238d50ae9e75f2ac32c30a404679bf0665c28a1d119e9cc"},"schema_version":"1.0"},"canonical_sha256":"e19389ce47a9a5d444504006e22c22a4074ecc404b0805520dabac6dece0f3c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:39.410007Z","signature_b64":"WsfIM4oiGg06CAyEyUFd5sDbD/a/XMq25DZLrqDxpY1wm4TB+PKyUECYUh46vSckRrWsq1eTv0Ji8DtuP1B8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e19389ce47a9a5d444504006e22c22a4074ecc404b0805520dabac6dece0f3c0","last_reissued_at":"2026-05-18T02:13:39.409636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:39.409636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.2321","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V5mqpCIOApg8Q+F7aMnm1hKdbTZqIsba3ZZVFqv4iejzMW5tfzoY9bp8rHLuJjDeRxaV91k+XIiZleDIYNJgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:39:41.651943Z"},"content_sha256":"2a9511b5e243da9aa194d983651b843b8c04a5212539d1c7a43dfa5236409824","schema_version":"1.0","event_id":"sha256:2a9511b5e243da9aa194d983651b843b8c04a5212539d1c7a43dfa5236409824"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:4GJYTTSHVGS5IRCQIADOELBCUQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfectly Matched Layers for Coupled Nonlinear Schr\\\"{o}dinger Equations with Mixed Derivatives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"math.NA","authors_text":"Tom\\'a\\v{s} Dohnal","submitted_at":"2009-05-14T16:06:17Z","abstract_excerpt":"This paper constructs perfectly matched layers (PML) for a system of 2D Coupled Nonlinear Schr\\\"odinger equations with mixed derivatives which arises in the modeling of gap solitons in nonlinear periodic structures with a non-separable linear part. The PML construction is performed in Laplace Fourier space via a modal analysis and can be viewed as a complex change of variables. The mixed derivatives cause the presence of waves with opposite phase and group velocities, which has previously been shown to cause instability of layer equations in certain types of hyperbolic problems. Nevertheless, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2321","kind":"arxiv","version":3},"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":"2026-05-18T02:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rfa2Zcu+U6kVHLpmjcjBtnYqlv5mc/OG0+zOWBXdK/0tDAg9Ew649tyOCxI9mk/uRtuUQ9qOPWT/LSt0DVaEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:39:41.652519Z"},"content_sha256":"b6b21383b3a2c18897cbcd3603422b4737f53631369639f0eaa85db363aa18cf","schema_version":"1.0","event_id":"sha256:b6b21383b3a2c18897cbcd3603422b4737f53631369639f0eaa85db363aa18cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GJYTTSHVGS5IRCQIADOELBCUQ/bundle.json","state_url":"https://pith.science/pith/4GJYTTSHVGS5IRCQIADOELBCUQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GJYTTSHVGS5IRCQIADOELBCUQ/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":"2026-06-07T02:39:41Z","links":{"resolver":"https://pith.science/pith/4GJYTTSHVGS5IRCQIADOELBCUQ","bundle":"https://pith.science/pith/4GJYTTSHVGS5IRCQIADOELBCUQ/bundle.json","state":"https://pith.science/pith/4GJYTTSHVGS5IRCQIADOELBCUQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GJYTTSHVGS5IRCQIADOELBCUQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4GJYTTSHVGS5IRCQIADOELBCUQ","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":"5a82b60c58756c32f238d50ae9e75f2ac32c30a404679bf0665c28a1d119e9cc","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-14T16:06:17Z","title_canon_sha256":"742eae794e5de5008fd94f8190d30d591a59756e6dd5cf81b0ccd9934161cc51"},"schema_version":"1.0","source":{"id":"0905.2321","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.2321","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"0905.2321v3","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.2321","created_at":"2026-05-18T02:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"4GJYTTSHVGS5","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4GJYTTSHVGS5IRCQ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4GJYTTSH","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:b6b21383b3a2c18897cbcd3603422b4737f53631369639f0eaa85db363aa18cf","target":"graph","created_at":"2026-05-18T02:13:39Z","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":"This paper constructs perfectly matched layers (PML) for a system of 2D Coupled Nonlinear Schr\\\"odinger equations with mixed derivatives which arises in the modeling of gap solitons in nonlinear periodic structures with a non-separable linear part. The PML construction is performed in Laplace Fourier space via a modal analysis and can be viewed as a complex change of variables. The mixed derivatives cause the presence of waves with opposite phase and group velocities, which has previously been shown to cause instability of layer equations in certain types of hyperbolic problems. Nevertheless, ","authors_text":"Tom\\'a\\v{s} Dohnal","cross_cats":["nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-14T16:06:17Z","title":"Perfectly Matched Layers for Coupled Nonlinear Schr\\\"{o}dinger Equations with Mixed Derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.2321","kind":"arxiv","version":3},"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":"sha256:2a9511b5e243da9aa194d983651b843b8c04a5212539d1c7a43dfa5236409824","target":"record","created_at":"2026-05-18T02:13:39Z","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":"5a82b60c58756c32f238d50ae9e75f2ac32c30a404679bf0665c28a1d119e9cc","cross_cats_sorted":["nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-05-14T16:06:17Z","title_canon_sha256":"742eae794e5de5008fd94f8190d30d591a59756e6dd5cf81b0ccd9934161cc51"},"schema_version":"1.0","source":{"id":"0905.2321","kind":"arxiv","version":3}},"canonical_sha256":"e19389ce47a9a5d444504006e22c22a4074ecc404b0805520dabac6dece0f3c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e19389ce47a9a5d444504006e22c22a4074ecc404b0805520dabac6dece0f3c0","first_computed_at":"2026-05-18T02:13:39.409636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:39.409636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WsfIM4oiGg06CAyEyUFd5sDbD/a/XMq25DZLrqDxpY1wm4TB+PKyUECYUh46vSckRrWsq1eTv0Ji8DtuP1B8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:39.410007Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.2321","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a9511b5e243da9aa194d983651b843b8c04a5212539d1c7a43dfa5236409824","sha256:b6b21383b3a2c18897cbcd3603422b4737f53631369639f0eaa85db363aa18cf"],"state_sha256":"c0f94eed09625adfb906f4f208c2d5af43c4d8aff4eae9ffd5e63feec053a981"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4joVGWOiJdIuTOejo4NMfcswD7U73cqeHFhWUuwD2K1sGBsHCUfrkXdFv6uR+hzjz/DF32vEeGtfT5qlh0RBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:39:41.655479Z","bundle_sha256":"2e7be85e74a8654a3146f64814d63e4638660395bc5fab425e0d843ae64cb8ba"}}