{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JFVWBDPAJAVGMCU5HR4L4XFDTK","short_pith_number":"pith:JFVWBDPA","canonical_record":{"source":{"id":"1009.1925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-10T02:33:15Z","cross_cats_sorted":[],"title_canon_sha256":"4abcfb788d1946c423314f4edb9fa51ec98e39d0870e93fb08d404707c0fe2f7","abstract_canon_sha256":"deed7e1d09b0f0fbf97b44ea6b79f39f8f609444638831ae70128de44bd40e61"},"schema_version":"1.0"},"canonical_sha256":"496b608de0482a660a9d3c78be5ca39abc4dd8e0eba7ad72aaf8bff092aa3d46","source":{"kind":"arxiv","id":"1009.1925","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1925","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1925v1","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1925","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"JFVWBDPAJAVG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JFVWBDPAJAVGMCU5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JFVWBDPA","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JFVWBDPAJAVGMCU5HR4L4XFDTK","target":"record","payload":{"canonical_record":{"source":{"id":"1009.1925","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-10T02:33:15Z","cross_cats_sorted":[],"title_canon_sha256":"4abcfb788d1946c423314f4edb9fa51ec98e39d0870e93fb08d404707c0fe2f7","abstract_canon_sha256":"deed7e1d09b0f0fbf97b44ea6b79f39f8f609444638831ae70128de44bd40e61"},"schema_version":"1.0"},"canonical_sha256":"496b608de0482a660a9d3c78be5ca39abc4dd8e0eba7ad72aaf8bff092aa3d46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:05.686756Z","signature_b64":"ywd0Ag0Bx3ME1dcwOgxG3D4SrFGFB3DzVxQWh7b9Eb3dxwHRcsrWARxWk8rOmiNlpuGhfRMsHOmhVFQujtNwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"496b608de0482a660a9d3c78be5ca39abc4dd8e0eba7ad72aaf8bff092aa3d46","last_reissued_at":"2026-05-18T04:41:05.686341Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:05.686341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.1925","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":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i10f++FXjljX3lfRbovmnIDwiyeNnvDF7mH/9NLRMWvxJFX0jOz4JAY1+D+FWvSoz5ouzT8aAWUeP2RqSxE8BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:40:01.464059Z"},"content_sha256":"92ac573b529445af477c29bd7437aeeb9acabd333b54ff27f6695e91ca1fc71f","schema_version":"1.0","event_id":"sha256:92ac573b529445af477c29bd7437aeeb9acabd333b54ff27f6695e91ca1fc71f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JFVWBDPAJAVGMCU5HR4L4XFDTK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Preconditioners based on Windowed Fourier Frames Applied to Elliptic Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christiaan C. Stolk, Samir K. Bhowmik","submitted_at":"2010-09-10T02:33:15Z","abstract_excerpt":"We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given by the symbol of the PDO evaluated at the wave number and central position of the windowed plane wave. This can be exploited in a preconditioning method for use in iterative inversion. For domains with periodic boundary conditions we find that the condition number with the preconditioning bec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1925","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":"2026-05-18T04:41:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3aP3TSTA8Hj7gmPcNItCYzaFBHn2dYKKVfev+yQQQkfhg7EQ6pVdSgiL+TAXMX8tRB0uYZE2KddHeE2pLOwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:40:01.464410Z"},"content_sha256":"1dba94d52db15c4e39957ab4c6814d608d0f3b1894d5063a553783a7edcda05e","schema_version":"1.0","event_id":"sha256:1dba94d52db15c4e39957ab4c6814d608d0f3b1894d5063a553783a7edcda05e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JFVWBDPAJAVGMCU5HR4L4XFDTK/bundle.json","state_url":"https://pith.science/pith/JFVWBDPAJAVGMCU5HR4L4XFDTK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JFVWBDPAJAVGMCU5HR4L4XFDTK/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":"2026-06-24T04:40:01Z","links":{"resolver":"https://pith.science/pith/JFVWBDPAJAVGMCU5HR4L4XFDTK","bundle":"https://pith.science/pith/JFVWBDPAJAVGMCU5HR4L4XFDTK/bundle.json","state":"https://pith.science/pith/JFVWBDPAJAVGMCU5HR4L4XFDTK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JFVWBDPAJAVGMCU5HR4L4XFDTK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JFVWBDPAJAVGMCU5HR4L4XFDTK","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":"deed7e1d09b0f0fbf97b44ea6b79f39f8f609444638831ae70128de44bd40e61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-10T02:33:15Z","title_canon_sha256":"4abcfb788d1946c423314f4edb9fa51ec98e39d0870e93fb08d404707c0fe2f7"},"schema_version":"1.0","source":{"id":"1009.1925","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1925","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1925v1","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1925","created_at":"2026-05-18T04:41:05Z"},{"alias_kind":"pith_short_12","alias_value":"JFVWBDPAJAVG","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JFVWBDPAJAVGMCU5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JFVWBDPA","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:1dba94d52db15c4e39957ab4c6814d608d0f3b1894d5063a553783a7edcda05e","target":"graph","created_at":"2026-05-18T04:41:05Z","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 investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given by the symbol of the PDO evaluated at the wave number and central position of the windowed plane wave. This can be exploited in a preconditioning method for use in iterative inversion. For domains with periodic boundary conditions we find that the condition number with the preconditioning bec","authors_text":"Christiaan C. Stolk, Samir K. Bhowmik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-10T02:33:15Z","title":"Preconditioners based on Windowed Fourier Frames Applied to Elliptic Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1925","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":"sha256:92ac573b529445af477c29bd7437aeeb9acabd333b54ff27f6695e91ca1fc71f","target":"record","created_at":"2026-05-18T04:41:05Z","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":"deed7e1d09b0f0fbf97b44ea6b79f39f8f609444638831ae70128de44bd40e61","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-10T02:33:15Z","title_canon_sha256":"4abcfb788d1946c423314f4edb9fa51ec98e39d0870e93fb08d404707c0fe2f7"},"schema_version":"1.0","source":{"id":"1009.1925","kind":"arxiv","version":1}},"canonical_sha256":"496b608de0482a660a9d3c78be5ca39abc4dd8e0eba7ad72aaf8bff092aa3d46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"496b608de0482a660a9d3c78be5ca39abc4dd8e0eba7ad72aaf8bff092aa3d46","first_computed_at":"2026-05-18T04:41:05.686341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:05.686341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywd0Ag0Bx3ME1dcwOgxG3D4SrFGFB3DzVxQWh7b9Eb3dxwHRcsrWARxWk8rOmiNlpuGhfRMsHOmhVFQujtNwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:05.686756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1925","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92ac573b529445af477c29bd7437aeeb9acabd333b54ff27f6695e91ca1fc71f","sha256:1dba94d52db15c4e39957ab4c6814d608d0f3b1894d5063a553783a7edcda05e"],"state_sha256":"f3dd6b48205525aa2459fdea42372bbefd2d8a34b525b48e7554d7aac19ab32d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Ua0c5UMk3lFv01WRese5MGxXQaTLc7sDaOu0kL+GcxvuMWQIlnsnTFq81zplI7aX1XjbqkGCl50Yt9Xc/SdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:40:01.466460Z","bundle_sha256":"37a5328c2ea0f1db14063105397d1944f556bd31ea5e3abe9e5ee97b5451e769"}}