{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BQ5JFE437M22HAYW6ZFIQ3QDLF","short_pith_number":"pith:BQ5JFE43","canonical_record":{"source":{"id":"1206.0002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-05-31T09:59:52Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"8c8d25b2907e3a8e8e418feac8f9ea70e5dc6b0935e4016453db2ed014edcf18","abstract_canon_sha256":"ec5ced562daa226ff2bc417eaae5309a70d6249cabdc6a0c4bbfba91eb2dee62"},"schema_version":"1.0"},"canonical_sha256":"0c3a92939bfb35a38316f64a886e03594ffa8cb6f3e8640ff0d0000faa38e02c","source":{"kind":"arxiv","id":"1206.0002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0002","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0002v1","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0002","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"BQ5JFE437M22","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BQ5JFE437M22HAYW","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BQ5JFE43","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BQ5JFE437M22HAYW6ZFIQ3QDLF","target":"record","payload":{"canonical_record":{"source":{"id":"1206.0002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-05-31T09:59:52Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"8c8d25b2907e3a8e8e418feac8f9ea70e5dc6b0935e4016453db2ed014edcf18","abstract_canon_sha256":"ec5ced562daa226ff2bc417eaae5309a70d6249cabdc6a0c4bbfba91eb2dee62"},"schema_version":"1.0"},"canonical_sha256":"0c3a92939bfb35a38316f64a886e03594ffa8cb6f3e8640ff0d0000faa38e02c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:27.262490Z","signature_b64":"0GMrQrFROQnFsnbV7HY4njCx+sS+3LkZ9P0NGRxroip/nNHDIYhM5VnDek7L5qpfWGmlU3UrLjvRD+HEbXbADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c3a92939bfb35a38316f64a886e03594ffa8cb6f3e8640ff0d0000faa38e02c","last_reissued_at":"2026-05-18T03:54:27.262032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:27.262032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.0002","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":"2026-05-18T03:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5XRgpsNd4PN0oY/hP4p2cV6TuBmFI42q17jtSX+P8yHImuxo9hl0xXPgPH3itRSWfd/XCJlHfRaSQwm+GJKoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:33:01.573706Z"},"content_sha256":"9892a03a80d02b4cc228b18ee7cd411ba294db1650f3b70952005425eebc556a","schema_version":"1.0","event_id":"sha256:9892a03a80d02b4cc228b18ee7cd411ba294db1650f3b70952005425eebc556a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BQ5JFE437M22HAYW6ZFIQ3QDLF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"physics.flu-dyn","authors_text":"Dmitry Kolomenskiy, Kai Schneider, Romain Nguyen van yen","submitted_at":"2012-05-31T09:59:52Z","abstract_excerpt":"We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $\\eta$, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of $\\eta$, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed $\\eta$, we find that only the part of the spectrum corresponding to eigenvalues $\\lambda \\lesssim \\eta^{-1}$ approaches Dirich"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0002","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":"2026-05-18T03:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fa7d5mkFt1hpkDUr4SErTi5+L19/hBiRhqA0dJ8wC5d3H3xZox79cuoOgBkfmYzq4hHfWFrl0EawUQrLihHNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:33:01.574216Z"},"content_sha256":"380cb936ace98358ac6b76a905816984e6ab646595164f124b7244074b9f6dbc","schema_version":"1.0","event_id":"sha256:380cb936ace98358ac6b76a905816984e6ab646595164f124b7244074b9f6dbc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQ5JFE437M22HAYW6ZFIQ3QDLF/bundle.json","state_url":"https://pith.science/pith/BQ5JFE437M22HAYW6ZFIQ3QDLF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQ5JFE437M22HAYW6ZFIQ3QDLF/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":"2026-05-27T04:33:01Z","links":{"resolver":"https://pith.science/pith/BQ5JFE437M22HAYW6ZFIQ3QDLF","bundle":"https://pith.science/pith/BQ5JFE437M22HAYW6ZFIQ3QDLF/bundle.json","state":"https://pith.science/pith/BQ5JFE437M22HAYW6ZFIQ3QDLF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQ5JFE437M22HAYW6ZFIQ3QDLF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BQ5JFE437M22HAYW6ZFIQ3QDLF","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":"ec5ced562daa226ff2bc417eaae5309a70d6249cabdc6a0c4bbfba91eb2dee62","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-05-31T09:59:52Z","title_canon_sha256":"8c8d25b2907e3a8e8e418feac8f9ea70e5dc6b0935e4016453db2ed014edcf18"},"schema_version":"1.0","source":{"id":"1206.0002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0002","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0002v1","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0002","created_at":"2026-05-18T03:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"BQ5JFE437M22","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BQ5JFE437M22HAYW","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BQ5JFE43","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:380cb936ace98358ac6b76a905816984e6ab646595164f124b7244074b9f6dbc","target":"graph","created_at":"2026-05-18T03:54:27Z","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":"We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, $\\eta$, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of $\\eta$, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed $\\eta$, we find that only the part of the spectrum corresponding to eigenvalues $\\lambda \\lesssim \\eta^{-1}$ approaches Dirich","authors_text":"Dmitry Kolomenskiy, Kai Schneider, Romain Nguyen van yen","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-05-31T09:59:52Z","title":"Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0002","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":"sha256:9892a03a80d02b4cc228b18ee7cd411ba294db1650f3b70952005425eebc556a","target":"record","created_at":"2026-05-18T03:54:27Z","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":"ec5ced562daa226ff2bc417eaae5309a70d6249cabdc6a0c4bbfba91eb2dee62","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2012-05-31T09:59:52Z","title_canon_sha256":"8c8d25b2907e3a8e8e418feac8f9ea70e5dc6b0935e4016453db2ed014edcf18"},"schema_version":"1.0","source":{"id":"1206.0002","kind":"arxiv","version":1}},"canonical_sha256":"0c3a92939bfb35a38316f64a886e03594ffa8cb6f3e8640ff0d0000faa38e02c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c3a92939bfb35a38316f64a886e03594ffa8cb6f3e8640ff0d0000faa38e02c","first_computed_at":"2026-05-18T03:54:27.262032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:27.262032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0GMrQrFROQnFsnbV7HY4njCx+sS+3LkZ9P0NGRxroip/nNHDIYhM5VnDek7L5qpfWGmlU3UrLjvRD+HEbXbADg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:27.262490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9892a03a80d02b4cc228b18ee7cd411ba294db1650f3b70952005425eebc556a","sha256:380cb936ace98358ac6b76a905816984e6ab646595164f124b7244074b9f6dbc"],"state_sha256":"a4be44a0b2297fbf249ba72d9359c0fb41a189dc38fe3fdc88f3dbf435d313b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPUuQL7B75Ta2g4tp6TpZhXmIcyHB2pEpAumnp80/G9XDJNyaeMlrPEfVrgEkTxlmWy0TGcjYhjVlNRQR/XmDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:33:01.577503Z","bundle_sha256":"7ed66f58867063048fa9b2ce45749151f96706cce0e218ea2d5a48a13d32e424"}}