{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YFLKYXKYD4HDSJVXENDPRG2FBS","short_pith_number":"pith:YFLKYXKY","canonical_record":{"source":{"id":"1112.5346","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-22T15:13:05Z","cross_cats_sorted":[],"title_canon_sha256":"83b5a743bba674fcca1efd06a9a54b6c9b3d21c5a3de3a04996cd867d9e21725","abstract_canon_sha256":"b63db4381ae69e06fa5981480c4cff93a5a4c4a410d7aa1c90496d330ae79652"},"schema_version":"1.0"},"canonical_sha256":"c156ac5d581f0e3926b72346f89b450cb2ef6dc380b7fdc4ba2bb83a5c595190","source":{"kind":"arxiv","id":"1112.5346","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5346","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5346v3","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5346","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"YFLKYXKYD4HD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YFLKYXKYD4HDSJVX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YFLKYXKY","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YFLKYXKYD4HDSJVXENDPRG2FBS","target":"record","payload":{"canonical_record":{"source":{"id":"1112.5346","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-22T15:13:05Z","cross_cats_sorted":[],"title_canon_sha256":"83b5a743bba674fcca1efd06a9a54b6c9b3d21c5a3de3a04996cd867d9e21725","abstract_canon_sha256":"b63db4381ae69e06fa5981480c4cff93a5a4c4a410d7aa1c90496d330ae79652"},"schema_version":"1.0"},"canonical_sha256":"c156ac5d581f0e3926b72346f89b450cb2ef6dc380b7fdc4ba2bb83a5c595190","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:08.836639Z","signature_b64":"eoX+/yuRVhtvtCb4sv8XMuIDVSQVxEQHQFsiRP/27BYMPEBH9Gaywq3voLx4lOkewXyEQR1BUkMHtk0XJaYxCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c156ac5d581f0e3926b72346f89b450cb2ef6dc380b7fdc4ba2bb83a5c595190","last_reissued_at":"2026-05-18T03:14:08.836127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:08.836127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.5346","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":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vDNet6okbbvp3b1DdI3znpXs3Moqyk/Bju5L7I/w0oJ+DMLNDrjmANidgE5Fred/U7jb43PdDpgJWBk43+ZvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:09:37.467522Z"},"content_sha256":"e3b2f8ee2a8df894d1f1a9e21d9ea273fe7df7af9333755a05da40f4aabe2a60","schema_version":"1.0","event_id":"sha256:e3b2f8ee2a8df894d1f1a9e21d9ea273fe7df7af9333755a05da40f4aabe2a60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YFLKYXKYD4HDSJVXENDPRG2FBS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local Fourier Analysis of the Complex Shifted Laplacian preconditioner for Helmholtz problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Siegfried Cools, Wim Vanroose","submitted_at":"2011-12-22T15:13:05Z","abstract_excerpt":"In this paper we solve the Helmholtz equation with multigrid preconditioned Krylov subspace methods. The class of Shifted Laplacian preconditioners are known to significantly speed-up Krylov convergence. However, these preconditioners have a parameter beta, a measure of the complex shift. Due to contradictory requirements for the multigrid and Krylov convergence, the choice of this shift parameter can be a bottleneck in applying the method. In this paper, we propose a wavenumber-dependent minimal complex shift parameter which is predicted by a rigorous k-grid Local Fourier Analysis (LFA) of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5346","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":"2026-05-18T03:14:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TaPqI68YwWi/zVgiW8J9MoBoM6r5tJBbOvXa/J2ScMzPvi2rQdxqZ+eQQBpKddEs+J1YMiY2bzSAVa0Zvl1PDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:09:37.467929Z"},"content_sha256":"2fa7a0f1e9636bf197ce7b218861c4f4bd6d971cae635f77626a5442f7bb20f1","schema_version":"1.0","event_id":"sha256:2fa7a0f1e9636bf197ce7b218861c4f4bd6d971cae635f77626a5442f7bb20f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFLKYXKYD4HDSJVXENDPRG2FBS/bundle.json","state_url":"https://pith.science/pith/YFLKYXKYD4HDSJVXENDPRG2FBS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFLKYXKYD4HDSJVXENDPRG2FBS/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":"2026-05-27T01:09:37Z","links":{"resolver":"https://pith.science/pith/YFLKYXKYD4HDSJVXENDPRG2FBS","bundle":"https://pith.science/pith/YFLKYXKYD4HDSJVXENDPRG2FBS/bundle.json","state":"https://pith.science/pith/YFLKYXKYD4HDSJVXENDPRG2FBS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFLKYXKYD4HDSJVXENDPRG2FBS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YFLKYXKYD4HDSJVXENDPRG2FBS","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":"b63db4381ae69e06fa5981480c4cff93a5a4c4a410d7aa1c90496d330ae79652","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-22T15:13:05Z","title_canon_sha256":"83b5a743bba674fcca1efd06a9a54b6c9b3d21c5a3de3a04996cd867d9e21725"},"schema_version":"1.0","source":{"id":"1112.5346","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5346","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5346v3","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5346","created_at":"2026-05-18T03:14:08Z"},{"alias_kind":"pith_short_12","alias_value":"YFLKYXKYD4HD","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YFLKYXKYD4HDSJVX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YFLKYXKY","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:2fa7a0f1e9636bf197ce7b218861c4f4bd6d971cae635f77626a5442f7bb20f1","target":"graph","created_at":"2026-05-18T03:14:08Z","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 solve the Helmholtz equation with multigrid preconditioned Krylov subspace methods. The class of Shifted Laplacian preconditioners are known to significantly speed-up Krylov convergence. However, these preconditioners have a parameter beta, a measure of the complex shift. Due to contradictory requirements for the multigrid and Krylov convergence, the choice of this shift parameter can be a bottleneck in applying the method. In this paper, we propose a wavenumber-dependent minimal complex shift parameter which is predicted by a rigorous k-grid Local Fourier Analysis (LFA) of th","authors_text":"Siegfried Cools, Wim Vanroose","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-22T15:13:05Z","title":"Local Fourier Analysis of the Complex Shifted Laplacian preconditioner for Helmholtz problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5346","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:e3b2f8ee2a8df894d1f1a9e21d9ea273fe7df7af9333755a05da40f4aabe2a60","target":"record","created_at":"2026-05-18T03:14:08Z","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":"b63db4381ae69e06fa5981480c4cff93a5a4c4a410d7aa1c90496d330ae79652","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-22T15:13:05Z","title_canon_sha256":"83b5a743bba674fcca1efd06a9a54b6c9b3d21c5a3de3a04996cd867d9e21725"},"schema_version":"1.0","source":{"id":"1112.5346","kind":"arxiv","version":3}},"canonical_sha256":"c156ac5d581f0e3926b72346f89b450cb2ef6dc380b7fdc4ba2bb83a5c595190","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c156ac5d581f0e3926b72346f89b450cb2ef6dc380b7fdc4ba2bb83a5c595190","first_computed_at":"2026-05-18T03:14:08.836127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:08.836127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eoX+/yuRVhtvtCb4sv8XMuIDVSQVxEQHQFsiRP/27BYMPEBH9Gaywq3voLx4lOkewXyEQR1BUkMHtk0XJaYxCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:08.836639Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5346","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3b2f8ee2a8df894d1f1a9e21d9ea273fe7df7af9333755a05da40f4aabe2a60","sha256:2fa7a0f1e9636bf197ce7b218861c4f4bd6d971cae635f77626a5442f7bb20f1"],"state_sha256":"24ee7abd003eecbf9048e22e50de3ed497906e5cd2d698f681d5524bd71c2872"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1kr/jPaNcp412gYIPw8B50EbyKJDT1JinnpexbDAoRbPilUgGA+1RlOoisJRmMqWmE/ELGFeLWWcSzF8Lk+sDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:09:37.470765Z","bundle_sha256":"7f7f7b9408c65399d8b42afbd6cd559b2acb08cec6e39dc03a00f3e37e39e5bd"}}