{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VHMMAYN5HG6A7ZUFTUKYQINWT4","short_pith_number":"pith:VHMMAYN5","canonical_record":{"source":{"id":"1601.02361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-11T08:40:52Z","cross_cats_sorted":[],"title_canon_sha256":"9feeecd4fe89cb18d240f6bb7d81f6c50fba080aa506f05303ead31bb68d7698","abstract_canon_sha256":"eb3c76cb133431e5d2adc10e1016fb0333bdb3e744e7f4ceee461b9076639c92"},"schema_version":"1.0"},"canonical_sha256":"a9d8c061bd39bc0fe6859d158821b69f273926f43b556af2db62ae77abf611c8","source":{"kind":"arxiv","id":"1601.02361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02361","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02361v1","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02361","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"pith_short_12","alias_value":"VHMMAYN5HG6A","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VHMMAYN5HG6A7ZUF","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VHMMAYN5","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VHMMAYN5HG6A7ZUFTUKYQINWT4","target":"record","payload":{"canonical_record":{"source":{"id":"1601.02361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-11T08:40:52Z","cross_cats_sorted":[],"title_canon_sha256":"9feeecd4fe89cb18d240f6bb7d81f6c50fba080aa506f05303ead31bb68d7698","abstract_canon_sha256":"eb3c76cb133431e5d2adc10e1016fb0333bdb3e744e7f4ceee461b9076639c92"},"schema_version":"1.0"},"canonical_sha256":"a9d8c061bd39bc0fe6859d158821b69f273926f43b556af2db62ae77abf611c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:06.629718Z","signature_b64":"YD+B04ft4sO1Vp1XpEYDz2aF4C1sf0epFaBn5Lq8jkYi/LCJSowQoZhG0SDej/Of0+kMNfthnb0DPbYmlS4BCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9d8c061bd39bc0fe6859d158821b69f273926f43b556af2db62ae77abf611c8","last_reissued_at":"2026-05-18T01:23:06.629120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:06.629120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.02361","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":"2026-05-18T01:23:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UFvWFcqEoTjoICNY1jqtMFfH6BD3I9iUPmzXustN21ZFw7h8NM7Ta4LwEWE5jpytnBHBlF4wpS21TZpgQowxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:42:40.409786Z"},"content_sha256":"ab3d7c414eed1607beac72459cfb726afd9ebd86de8b51f9f28c157facfa441b","schema_version":"1.0","event_id":"sha256:ab3d7c414eed1607beac72459cfb726afd9ebd86de8b51f9f28c157facfa441b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VHMMAYN5HG6A7ZUFTUKYQINWT4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Multigrid Finite Element Method for the Transmission Eigenvalue Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hai Bi, Jiayu Han, Yidu Yang","submitted_at":"2016-01-11T08:40:52Z","abstract_excerpt":"Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need to solve a series of primal and dual eigenvalue problems on a coarse mesh and the associated boundary value problems on the finer and finer meshes. Theoretical analysis and numerical results show that our method is simple and easy to implement and is efficient for computing real and complex transmission eigenvalues."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02361","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":"2026-05-18T01:23:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DKu6RT0sra/p06dFd216EZzXZEcX51vzmssqfJxyPgFuNG1C1w3rZ4334972W1RMVIXUgniq9BPIqdYy2FdpAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:42:40.410423Z"},"content_sha256":"ae8ef8d1ee0ee9a0944de0afb5258d5493f1b3ab5bd9a82944185285e05ae2f8","schema_version":"1.0","event_id":"sha256:ae8ef8d1ee0ee9a0944de0afb5258d5493f1b3ab5bd9a82944185285e05ae2f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHMMAYN5HG6A7ZUFTUKYQINWT4/bundle.json","state_url":"https://pith.science/pith/VHMMAYN5HG6A7ZUFTUKYQINWT4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHMMAYN5HG6A7ZUFTUKYQINWT4/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":"2026-05-28T01:42:40Z","links":{"resolver":"https://pith.science/pith/VHMMAYN5HG6A7ZUFTUKYQINWT4","bundle":"https://pith.science/pith/VHMMAYN5HG6A7ZUFTUKYQINWT4/bundle.json","state":"https://pith.science/pith/VHMMAYN5HG6A7ZUFTUKYQINWT4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHMMAYN5HG6A7ZUFTUKYQINWT4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VHMMAYN5HG6A7ZUFTUKYQINWT4","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":"eb3c76cb133431e5d2adc10e1016fb0333bdb3e744e7f4ceee461b9076639c92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-11T08:40:52Z","title_canon_sha256":"9feeecd4fe89cb18d240f6bb7d81f6c50fba080aa506f05303ead31bb68d7698"},"schema_version":"1.0","source":{"id":"1601.02361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02361","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02361v1","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02361","created_at":"2026-05-18T01:23:06Z"},{"alias_kind":"pith_short_12","alias_value":"VHMMAYN5HG6A","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VHMMAYN5HG6A7ZUF","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VHMMAYN5","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:ae8ef8d1ee0ee9a0944de0afb5258d5493f1b3ab5bd9a82944185285e05ae2f8","target":"graph","created_at":"2026-05-18T01:23:06Z","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":"Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need to solve a series of primal and dual eigenvalue problems on a coarse mesh and the associated boundary value problems on the finer and finer meshes. Theoretical analysis and numerical results show that our method is simple and easy to implement and is efficient for computing real and complex transmission eigenvalues.","authors_text":"Hai Bi, Jiayu Han, Yidu Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-11T08:40:52Z","title":"A New Multigrid Finite Element Method for the Transmission Eigenvalue Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02361","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:ab3d7c414eed1607beac72459cfb726afd9ebd86de8b51f9f28c157facfa441b","target":"record","created_at":"2026-05-18T01:23:06Z","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":"eb3c76cb133431e5d2adc10e1016fb0333bdb3e744e7f4ceee461b9076639c92","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-11T08:40:52Z","title_canon_sha256":"9feeecd4fe89cb18d240f6bb7d81f6c50fba080aa506f05303ead31bb68d7698"},"schema_version":"1.0","source":{"id":"1601.02361","kind":"arxiv","version":1}},"canonical_sha256":"a9d8c061bd39bc0fe6859d158821b69f273926f43b556af2db62ae77abf611c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9d8c061bd39bc0fe6859d158821b69f273926f43b556af2db62ae77abf611c8","first_computed_at":"2026-05-18T01:23:06.629120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:06.629120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YD+B04ft4sO1Vp1XpEYDz2aF4C1sf0epFaBn5Lq8jkYi/LCJSowQoZhG0SDej/Of0+kMNfthnb0DPbYmlS4BCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:06.629718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab3d7c414eed1607beac72459cfb726afd9ebd86de8b51f9f28c157facfa441b","sha256:ae8ef8d1ee0ee9a0944de0afb5258d5493f1b3ab5bd9a82944185285e05ae2f8"],"state_sha256":"a9e1578abb19cf7e92000de1fad47b00b671603f5aa384cfeeaab52fd7c3ea96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NpXr3GwwX1U06KzDtSRdP7D2//7VyEV6KArA9wM+wvoeIeoCLdsd1MQNVOn7RNGraTRxK8/acNwN59dKA/pLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:42:40.413716Z","bundle_sha256":"f9f0fbb8c3e3b882f7e446fd8a0d6cb19e4abb7c756938f6bb372f11754e8a16"}}