{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:P52SX5DIIIZZWUL755ANGU73YA","short_pith_number":"pith:P52SX5DI","canonical_record":{"source":{"id":"1608.03987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-13T14:27:58Z","cross_cats_sorted":[],"title_canon_sha256":"7bf6042fdb4f9cea38a7f78b0d112d01990700024dd3709b4f65f901fcfd680c","abstract_canon_sha256":"d3bfa1894820c17ad701a1295592e293679bbeca8774a8bd072fca578ab606da"},"schema_version":"1.0"},"canonical_sha256":"7f752bf46842339b517fef40d353fbc039c9e998be2c837ffd58b34884e33a97","source":{"kind":"arxiv","id":"1608.03987","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03987","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03987v1","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03987","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"P52SX5DIIIZZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P52SX5DIIIZZWUL7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P52SX5DI","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:P52SX5DIIIZZWUL755ANGU73YA","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03987","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-13T14:27:58Z","cross_cats_sorted":[],"title_canon_sha256":"7bf6042fdb4f9cea38a7f78b0d112d01990700024dd3709b4f65f901fcfd680c","abstract_canon_sha256":"d3bfa1894820c17ad701a1295592e293679bbeca8774a8bd072fca578ab606da"},"schema_version":"1.0"},"canonical_sha256":"7f752bf46842339b517fef40d353fbc039c9e998be2c837ffd58b34884e33a97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:04.503834Z","signature_b64":"H9J22/VxW7EYomz/HUgqPL7oLrDjgWjKh+6FrJg3fjx/8KuGnfDs6arlFgL+6BdM753EogJXL0Fh2QGzskmuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f752bf46842339b517fef40d353fbc039c9e998be2c837ffd58b34884e33a97","last_reissued_at":"2026-05-18T01:09:04.503392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:04.503392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03987","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":"2026-05-18T01:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kD/q0WmuOdrOU0f9s5stXXzPzPEzHjPbp2v4xr9zwjv84JAukX6cKdAH7bsYPnJGbk7Kx2FRnEYdf7izjcF+Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:22:17.705137Z"},"content_sha256":"3efa0cd57bb34c2b398a84b2990b57d9379832638ac8e1253cfad34bbe089ee6","schema_version":"1.0","event_id":"sha256:3efa0cd57bb34c2b398a84b2990b57d9379832638ac8e1253cfad34bbe089ee6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:P52SX5DIIIZZWUL755ANGU73YA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Penalized Crouzeix-Raviart Element Method for Second Order Elliptic Eigenvalue Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jun Hu, Limin Ma","submitted_at":"2016-08-13T14:27:58Z","abstract_excerpt":"In this paper we propose a penalized Crouzeix-Raviart element method for eigenvalue problems of second order elliptic operators. The key idea is to add a penalty term to tune the local approximation property and the global continuity property of the discrete eigenfunctions. The feature of this method is that by adjusting the penalty parameter, the resulted discrete eigenvalues can be in a state of \"chaos\", and consequently a large portion of them can be reliable and approximate the exact ones with high accuracy. Furthermore, we design an algorithm to select such a quasi-optimal penalty paramet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03987","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":"2026-05-18T01:09:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LmHxPAOGRHM6UED9odKMak+j0CdhwEpTpMJbxJSg7jPNQFTa8jJ4GunPXPPkb8/heB1gxFqAP6jBBkup/NZ+Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:22:17.705507Z"},"content_sha256":"3bf87e0634de8a6be5c764e959f6862be40fe6bc32a46c0241c5a03b5eef9da2","schema_version":"1.0","event_id":"sha256:3bf87e0634de8a6be5c764e959f6862be40fe6bc32a46c0241c5a03b5eef9da2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P52SX5DIIIZZWUL755ANGU73YA/bundle.json","state_url":"https://pith.science/pith/P52SX5DIIIZZWUL755ANGU73YA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P52SX5DIIIZZWUL755ANGU73YA/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":"2026-06-11T09:22:17Z","links":{"resolver":"https://pith.science/pith/P52SX5DIIIZZWUL755ANGU73YA","bundle":"https://pith.science/pith/P52SX5DIIIZZWUL755ANGU73YA/bundle.json","state":"https://pith.science/pith/P52SX5DIIIZZWUL755ANGU73YA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P52SX5DIIIZZWUL755ANGU73YA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P52SX5DIIIZZWUL755ANGU73YA","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":"d3bfa1894820c17ad701a1295592e293679bbeca8774a8bd072fca578ab606da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-13T14:27:58Z","title_canon_sha256":"7bf6042fdb4f9cea38a7f78b0d112d01990700024dd3709b4f65f901fcfd680c"},"schema_version":"1.0","source":{"id":"1608.03987","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03987","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03987v1","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03987","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"P52SX5DIIIZZ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P52SX5DIIIZZWUL7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P52SX5DI","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:3bf87e0634de8a6be5c764e959f6862be40fe6bc32a46c0241c5a03b5eef9da2","target":"graph","created_at":"2026-05-18T01:09:04Z","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 paper we propose a penalized Crouzeix-Raviart element method for eigenvalue problems of second order elliptic operators. The key idea is to add a penalty term to tune the local approximation property and the global continuity property of the discrete eigenfunctions. The feature of this method is that by adjusting the penalty parameter, the resulted discrete eigenvalues can be in a state of \"chaos\", and consequently a large portion of them can be reliable and approximate the exact ones with high accuracy. Furthermore, we design an algorithm to select such a quasi-optimal penalty paramet","authors_text":"Jun Hu, Limin Ma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-13T14:27:58Z","title":"A Penalized Crouzeix-Raviart Element Method for Second Order Elliptic Eigenvalue Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03987","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":"sha256:3efa0cd57bb34c2b398a84b2990b57d9379832638ac8e1253cfad34bbe089ee6","target":"record","created_at":"2026-05-18T01:09:04Z","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":"d3bfa1894820c17ad701a1295592e293679bbeca8774a8bd072fca578ab606da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-13T14:27:58Z","title_canon_sha256":"7bf6042fdb4f9cea38a7f78b0d112d01990700024dd3709b4f65f901fcfd680c"},"schema_version":"1.0","source":{"id":"1608.03987","kind":"arxiv","version":1}},"canonical_sha256":"7f752bf46842339b517fef40d353fbc039c9e998be2c837ffd58b34884e33a97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f752bf46842339b517fef40d353fbc039c9e998be2c837ffd58b34884e33a97","first_computed_at":"2026-05-18T01:09:04.503392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:04.503392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H9J22/VxW7EYomz/HUgqPL7oLrDjgWjKh+6FrJg3fjx/8KuGnfDs6arlFgL+6BdM753EogJXL0Fh2QGzskmuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:04.503834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03987","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3efa0cd57bb34c2b398a84b2990b57d9379832638ac8e1253cfad34bbe089ee6","sha256:3bf87e0634de8a6be5c764e959f6862be40fe6bc32a46c0241c5a03b5eef9da2"],"state_sha256":"5305f4638a78a1455054abe1ab1afc365b6429520dfdbbc680a03a493b2b4197"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ywlYKXKmAHNQqZKuMdYSJx80TzM9bJXFq4/SGZKz9kDfhCLbGxgE31OF2ghS/kPTMiN0XXoUZvLdT76/dpaEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:22:17.707442Z","bundle_sha256":"1ba644166a651add0d615099b0b8b59a8a87bc8db5186f43d3ba14efab4ab4d9"}}