{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MCAWRYJOOLMNAE23SXZFZBUYQA","short_pith_number":"pith:MCAWRYJO","canonical_record":{"source":{"id":"1402.6297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-25T20:08:16Z","cross_cats_sorted":[],"title_canon_sha256":"ed29a91d34050dba4a1cea373c64c60f6fe995b110514ccebff6aeaf3b04cdc3","abstract_canon_sha256":"6947767522402fc3498e385527341dca0d2fe88c99432206f35c55d4e5617c75"},"schema_version":"1.0"},"canonical_sha256":"608168e12e72d8d0135b95f25c8698802faf5d4d9e937b3abd3102c890ac51ee","source":{"kind":"arxiv","id":"1402.6297","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6297","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6297v1","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6297","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"MCAWRYJOOLMN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MCAWRYJOOLMNAE23","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MCAWRYJO","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MCAWRYJOOLMNAE23SXZFZBUYQA","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-25T20:08:16Z","cross_cats_sorted":[],"title_canon_sha256":"ed29a91d34050dba4a1cea373c64c60f6fe995b110514ccebff6aeaf3b04cdc3","abstract_canon_sha256":"6947767522402fc3498e385527341dca0d2fe88c99432206f35c55d4e5617c75"},"schema_version":"1.0"},"canonical_sha256":"608168e12e72d8d0135b95f25c8698802faf5d4d9e937b3abd3102c890ac51ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:51.224278Z","signature_b64":"r9tQZ2kTk3qJkXRQrts73UgoFNB9eKJmG96ITnuw2S4uNv67R8WrviI/cmazLc2Q9YdBF4i7nl1Hs+BBEPZRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"608168e12e72d8d0135b95f25c8698802faf5d4d9e937b3abd3102c890ac51ee","last_reissued_at":"2026-05-18T02:57:51.223797Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:51.223797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6297","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":"2026-05-18T02:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tdxWUAUlclz5SemY2pbBja2Xt+Nvvj6h+q1AphwNiTDD9V4A8DgMpSuCI3GQeQ4/CnJhNBXJ6AN3oUD17piTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:16:06.601652Z"},"content_sha256":"30c339b3c87c037336e138b87999820b33f2842dd2c253bd963c3b39c46f8c45","schema_version":"1.0","event_id":"sha256:30c339b3c87c037336e138b87999820b33f2842dd2c253bd963c3b39c46f8c45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MCAWRYJOOLMNAE23SXZFZBUYQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular Value Decompositions for Single-Curl Operators in Three-Dimensional Maxwell's Equations for Complex Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Han-En Hsieh, Ruey-Lin Chern, Tsung-Ming Huang, Weichung Wang, Wen-Wei Lin","submitted_at":"2014-02-25T20:08:16Z","abstract_excerpt":"This article focuses on solving the generalized eigenvalue problems (GEP) arising in the source-free Maxwell equation with magnetoelectric coupling effects that models three-dimensional complex media. The goal is to compute the smallest positive eigenvalues, and the main challenge is that the coefficient matrix in the discrete Maxwell equation is indefinite and degenerate. To overcome this difficulty, we derive a singular value decomposition (SVD) of the discrete single-curl operator and then explicitly express the basis of the invariant subspace corresponding to the nonzero eigenvalues of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6297","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":"2026-05-18T02:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ErMSYQ0KSloiPVH+JCJvaHOikbJJyFPQ+/8Q75LPVIn+Y+4NqM1qpLA+P5LmDNeYR8loWzkq8bb7FpvjmMDJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:16:06.602017Z"},"content_sha256":"f43fdc9803fb6d3684f975f01fce63fe1cc43dc25e325e979f4909325ca34f9d","schema_version":"1.0","event_id":"sha256:f43fdc9803fb6d3684f975f01fce63fe1cc43dc25e325e979f4909325ca34f9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MCAWRYJOOLMNAE23SXZFZBUYQA/bundle.json","state_url":"https://pith.science/pith/MCAWRYJOOLMNAE23SXZFZBUYQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MCAWRYJOOLMNAE23SXZFZBUYQA/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":"2026-05-28T22:16:06Z","links":{"resolver":"https://pith.science/pith/MCAWRYJOOLMNAE23SXZFZBUYQA","bundle":"https://pith.science/pith/MCAWRYJOOLMNAE23SXZFZBUYQA/bundle.json","state":"https://pith.science/pith/MCAWRYJOOLMNAE23SXZFZBUYQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MCAWRYJOOLMNAE23SXZFZBUYQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MCAWRYJOOLMNAE23SXZFZBUYQA","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":"6947767522402fc3498e385527341dca0d2fe88c99432206f35c55d4e5617c75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-25T20:08:16Z","title_canon_sha256":"ed29a91d34050dba4a1cea373c64c60f6fe995b110514ccebff6aeaf3b04cdc3"},"schema_version":"1.0","source":{"id":"1402.6297","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6297","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6297v1","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6297","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"MCAWRYJOOLMN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MCAWRYJOOLMNAE23","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MCAWRYJO","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:f43fdc9803fb6d3684f975f01fce63fe1cc43dc25e325e979f4909325ca34f9d","target":"graph","created_at":"2026-05-18T02:57:51Z","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 article focuses on solving the generalized eigenvalue problems (GEP) arising in the source-free Maxwell equation with magnetoelectric coupling effects that models three-dimensional complex media. The goal is to compute the smallest positive eigenvalues, and the main challenge is that the coefficient matrix in the discrete Maxwell equation is indefinite and degenerate. To overcome this difficulty, we derive a singular value decomposition (SVD) of the discrete single-curl operator and then explicitly express the basis of the invariant subspace corresponding to the nonzero eigenvalues of the","authors_text":"Han-En Hsieh, Ruey-Lin Chern, Tsung-Ming Huang, Weichung Wang, Wen-Wei Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-25T20:08:16Z","title":"Singular Value Decompositions for Single-Curl Operators in Three-Dimensional Maxwell's Equations for Complex Media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6297","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":"sha256:30c339b3c87c037336e138b87999820b33f2842dd2c253bd963c3b39c46f8c45","target":"record","created_at":"2026-05-18T02:57:51Z","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":"6947767522402fc3498e385527341dca0d2fe88c99432206f35c55d4e5617c75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-02-25T20:08:16Z","title_canon_sha256":"ed29a91d34050dba4a1cea373c64c60f6fe995b110514ccebff6aeaf3b04cdc3"},"schema_version":"1.0","source":{"id":"1402.6297","kind":"arxiv","version":1}},"canonical_sha256":"608168e12e72d8d0135b95f25c8698802faf5d4d9e937b3abd3102c890ac51ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"608168e12e72d8d0135b95f25c8698802faf5d4d9e937b3abd3102c890ac51ee","first_computed_at":"2026-05-18T02:57:51.223797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:51.223797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r9tQZ2kTk3qJkXRQrts73UgoFNB9eKJmG96ITnuw2S4uNv67R8WrviI/cmazLc2Q9YdBF4i7nl1Hs+BBEPZRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:51.224278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6297","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30c339b3c87c037336e138b87999820b33f2842dd2c253bd963c3b39c46f8c45","sha256:f43fdc9803fb6d3684f975f01fce63fe1cc43dc25e325e979f4909325ca34f9d"],"state_sha256":"c8e1b14067e2caa9bace5cbf72c0f7d694534a00237dc640af72760bb3a30b2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nFKV5TeYQMTO83p2/d8mvREuNuRWBdRghd2agviikNPZsN/bc7Df5JF3TTtj+ep089owVHzp7f657RumkXVrBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:16:06.604449Z","bundle_sha256":"20bc16874774a836022b9478cef0d0469bc1f7a8108a4f1de8ed658c2eaaefc7"}}