{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7AL7RVCWNURIR7XSFD64M27224","short_pith_number":"pith:7AL7RVCW","canonical_record":{"source":{"id":"1112.5665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-23T21:55:19Z","cross_cats_sorted":[],"title_canon_sha256":"8cc87a0f8755d5133f1cf3a7ce7bc9d71187d363d7ed17b53bc667eb263c23c4","abstract_canon_sha256":"b9c3e483dbe2a03a93b5395a8a832d82c0a5fb731029ae06339fe2a270743951"},"schema_version":"1.0"},"canonical_sha256":"f817f8d4566d2288fef228fdc66bfad71f74f6400107af12abf2af8d7c5454a3","source":{"kind":"arxiv","id":"1112.5665","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5665","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5665v1","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5665","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"7AL7RVCWNURI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7AL7RVCWNURIR7XS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7AL7RVCW","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7AL7RVCWNURIR7XSFD64M27224","target":"record","payload":{"canonical_record":{"source":{"id":"1112.5665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-23T21:55:19Z","cross_cats_sorted":[],"title_canon_sha256":"8cc87a0f8755d5133f1cf3a7ce7bc9d71187d363d7ed17b53bc667eb263c23c4","abstract_canon_sha256":"b9c3e483dbe2a03a93b5395a8a832d82c0a5fb731029ae06339fe2a270743951"},"schema_version":"1.0"},"canonical_sha256":"f817f8d4566d2288fef228fdc66bfad71f74f6400107af12abf2af8d7c5454a3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:37.850406Z","signature_b64":"cc03OhRSL65owm8YAnM02wHTdQQ4L0b6YPOAHyOInSJMO4FflqbkkmSDiJTi+AAiQrjZQy+NF4heRxDoQ2ShCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f817f8d4566d2288fef228fdc66bfad71f74f6400107af12abf2af8d7c5454a3","last_reissued_at":"2026-05-18T04:05:37.850042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:37.850042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.5665","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":"2026-05-18T04:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xjHO5D2CBL5OzEOlUcc6drfzHSKRAyUlDkpgBfZFn7aBEEtBHXPGK7tIFCxGduyhySya2d2/xcDusVX9U8fHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:55:00.307036Z"},"content_sha256":"c22b3b4ce1d903d2de7f200b5ef29f81c4de7cc50b90bbf6fafd5c46fe5fdf1d","schema_version":"1.0","event_id":"sha256:c22b3b4ce1d903d2de7f200b5ef29f81c4de7cc50b90bbf6fafd5c46fe5fdf1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7AL7RVCWNURIR7XSFD64M27224","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast computation of high frequency Dirichlet eigenmodes via the spectral flow of the interior Neumann-to-Dirichlet map","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Alex H. Barnett, Andrew Hassell","submitted_at":"2011-12-23T21:55:19Z","abstract_excerpt":"We present a new algorithm for numerical computation of large eigenvalues and associated eigenfunctions of the Dirichlet Laplacian in a smooth, star-shaped domain in $\\mathbb{R}^d$, $d\\ge 2$. Conventional boundary-based methods require a root-search in eigenfrequency $k$, hence take $O(N^3)$ effort per eigenpair found, using dense linear algebra, where $N=O(k^{d-1})$ is the number of unknowns required to discretize the boundary. Our method is O(N) faster, achieved by linearizing with respect to $k$ the spectrum of a weighted interior Neumann-to-Dirichlet (NtD) operator for the Helmholtz equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5665","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":"2026-05-18T04:05:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rmoes33HN5OyTxMn4Ob30eGRm/o1rd/pIhJh/NW6uDj0mY+ePtaglTKz/NZlu9puxHDAsgDHtGMBG5J0hNP9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:55:00.307706Z"},"content_sha256":"7610886c58e6808de8c562deef53ae7522b95649490e91917c3434914ab0b197","schema_version":"1.0","event_id":"sha256:7610886c58e6808de8c562deef53ae7522b95649490e91917c3434914ab0b197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AL7RVCWNURIR7XSFD64M27224/bundle.json","state_url":"https://pith.science/pith/7AL7RVCWNURIR7XSFD64M27224/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AL7RVCWNURIR7XSFD64M27224/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":"2026-05-27T09:55:00Z","links":{"resolver":"https://pith.science/pith/7AL7RVCWNURIR7XSFD64M27224","bundle":"https://pith.science/pith/7AL7RVCWNURIR7XSFD64M27224/bundle.json","state":"https://pith.science/pith/7AL7RVCWNURIR7XSFD64M27224/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AL7RVCWNURIR7XSFD64M27224/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7AL7RVCWNURIR7XSFD64M27224","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":"b9c3e483dbe2a03a93b5395a8a832d82c0a5fb731029ae06339fe2a270743951","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-23T21:55:19Z","title_canon_sha256":"8cc87a0f8755d5133f1cf3a7ce7bc9d71187d363d7ed17b53bc667eb263c23c4"},"schema_version":"1.0","source":{"id":"1112.5665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.5665","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"arxiv_version","alias_value":"1112.5665v1","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.5665","created_at":"2026-05-18T04:05:37Z"},{"alias_kind":"pith_short_12","alias_value":"7AL7RVCWNURI","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7AL7RVCWNURIR7XS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7AL7RVCW","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:7610886c58e6808de8c562deef53ae7522b95649490e91917c3434914ab0b197","target":"graph","created_at":"2026-05-18T04:05:37Z","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 present a new algorithm for numerical computation of large eigenvalues and associated eigenfunctions of the Dirichlet Laplacian in a smooth, star-shaped domain in $\\mathbb{R}^d$, $d\\ge 2$. Conventional boundary-based methods require a root-search in eigenfrequency $k$, hence take $O(N^3)$ effort per eigenpair found, using dense linear algebra, where $N=O(k^{d-1})$ is the number of unknowns required to discretize the boundary. Our method is O(N) faster, achieved by linearizing with respect to $k$ the spectrum of a weighted interior Neumann-to-Dirichlet (NtD) operator for the Helmholtz equati","authors_text":"Alex H. Barnett, Andrew Hassell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-23T21:55:19Z","title":"Fast computation of high frequency Dirichlet eigenmodes via the spectral flow of the interior Neumann-to-Dirichlet map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.5665","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:c22b3b4ce1d903d2de7f200b5ef29f81c4de7cc50b90bbf6fafd5c46fe5fdf1d","target":"record","created_at":"2026-05-18T04:05:37Z","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":"b9c3e483dbe2a03a93b5395a8a832d82c0a5fb731029ae06339fe2a270743951","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-12-23T21:55:19Z","title_canon_sha256":"8cc87a0f8755d5133f1cf3a7ce7bc9d71187d363d7ed17b53bc667eb263c23c4"},"schema_version":"1.0","source":{"id":"1112.5665","kind":"arxiv","version":1}},"canonical_sha256":"f817f8d4566d2288fef228fdc66bfad71f74f6400107af12abf2af8d7c5454a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f817f8d4566d2288fef228fdc66bfad71f74f6400107af12abf2af8d7c5454a3","first_computed_at":"2026-05-18T04:05:37.850042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:37.850042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cc03OhRSL65owm8YAnM02wHTdQQ4L0b6YPOAHyOInSJMO4FflqbkkmSDiJTi+AAiQrjZQy+NF4heRxDoQ2ShCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:37.850406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.5665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c22b3b4ce1d903d2de7f200b5ef29f81c4de7cc50b90bbf6fafd5c46fe5fdf1d","sha256:7610886c58e6808de8c562deef53ae7522b95649490e91917c3434914ab0b197"],"state_sha256":"e4c9bc02a5d75dd25b802d16ad3c3559ddb5b43a760086031c81f95ea182c276"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/TEzLALs/93PaDCDO+lGoGmRitLY7cJuTvfcsDEYFwW2nDwPZ8C5wcE5aQVsGPe9aj1ioMF2p7x4GfQ8rueAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:55:00.310882Z","bundle_sha256":"4dfe00d767a9fe4606920be19091176ce9e49840afc57efd563769e74351d16a"}}