{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QH7W4QAMQPZPIELEER5PZTN6GJ","short_pith_number":"pith:QH7W4QAM","canonical_record":{"source":{"id":"1201.5648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-26T21:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"870faa17f9dadb6cd1a70d3bedaf5e58511e977dc6ff33cb4ad0bf75b9476fe9","abstract_canon_sha256":"3ae308b6d9df0031f22a5aafba49d1f238e531c944e7219c51a02608da0df471"},"schema_version":"1.0"},"canonical_sha256":"81ff6e400c83f2f41164247afccdbe324179c6287c7aab10cbb9254e2083bf85","source":{"kind":"arxiv","id":"1201.5648","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5648","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5648v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5648","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"QH7W4QAMQPZP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QH7W4QAMQPZPIELE","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QH7W4QAM","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QH7W4QAMQPZPIELEER5PZTN6GJ","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5648","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-26T21:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"870faa17f9dadb6cd1a70d3bedaf5e58511e977dc6ff33cb4ad0bf75b9476fe9","abstract_canon_sha256":"3ae308b6d9df0031f22a5aafba49d1f238e531c944e7219c51a02608da0df471"},"schema_version":"1.0"},"canonical_sha256":"81ff6e400c83f2f41164247afccdbe324179c6287c7aab10cbb9254e2083bf85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:44.852436Z","signature_b64":"KYzAS7bFVt+6CF1QL3fY6UDZoEhgdlCwNEMVoj9xCiMw6jWaULTZ0FBH4KSlhYAH9lPwvdKTDcGHdI2rrkN9CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ff6e400c83f2f41164247afccdbe324179c6287c7aab10cbb9254e2083bf85","last_reissued_at":"2026-05-18T04:03:44.851960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:44.851960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5648","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":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKQSRaWAPraqvswF/1w9xGl83/+KrNEPdrsB88i/BKGCsLwaCeJSLBKy+M9w4tKJkoOIVy7nRcXtRp3X+KzbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:17:07.722735Z"},"content_sha256":"48c0d7327c251855a9be0b8059513d9667a6f30c120ef2f31f01a6d81809035c","schema_version":"1.0","event_id":"sha256:48c0d7327c251855a9be0b8059513d9667a6f30c120ef2f31f01a6d81809035c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QH7W4QAMQPZPIELEER5PZTN6GJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive Fourier-Galerkin Methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claudio Canuto, Marco Verani, Ricardo H. Nochetto","submitted_at":"2012-01-26T21:04:24Z","abstract_excerpt":"We study the performance of adaptive Fourier-Galerkin methods in a periodic box in $\\mathbb{R}^d$ with dimension $d\\ge 1$. These methods offer unlimited approximation power only restricted by solution and data regularity. They are of intrinsic interest but are also a first step towards understanding adaptivity for the $hp$-FEM. We examine two nonlinear approximation classes, one classical corresponding to algebraic decay of Fourier coefficients and another associated with exponential decay. We study the sparsity classes of the residual and show that they are the same as the solution for the al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5648","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":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ONzR6AkJm98J5wYHkbY8KcK5lVqp9YvXBzUYyDQI2x5zOAsua93VNkjTc81B+tRL+NQQuA5MHohieMZKhsK2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:17:07.723085Z"},"content_sha256":"64e456234b05fb14f062e5bd0fd60a57b8c843fe69d80c4fd542cd348a3010b2","schema_version":"1.0","event_id":"sha256:64e456234b05fb14f062e5bd0fd60a57b8c843fe69d80c4fd542cd348a3010b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QH7W4QAMQPZPIELEER5PZTN6GJ/bundle.json","state_url":"https://pith.science/pith/QH7W4QAMQPZPIELEER5PZTN6GJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QH7W4QAMQPZPIELEER5PZTN6GJ/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":"2026-06-20T14:17:07Z","links":{"resolver":"https://pith.science/pith/QH7W4QAMQPZPIELEER5PZTN6GJ","bundle":"https://pith.science/pith/QH7W4QAMQPZPIELEER5PZTN6GJ/bundle.json","state":"https://pith.science/pith/QH7W4QAMQPZPIELEER5PZTN6GJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QH7W4QAMQPZPIELEER5PZTN6GJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QH7W4QAMQPZPIELEER5PZTN6GJ","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":"3ae308b6d9df0031f22a5aafba49d1f238e531c944e7219c51a02608da0df471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-26T21:04:24Z","title_canon_sha256":"870faa17f9dadb6cd1a70d3bedaf5e58511e977dc6ff33cb4ad0bf75b9476fe9"},"schema_version":"1.0","source":{"id":"1201.5648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5648","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5648v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5648","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"QH7W4QAMQPZP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QH7W4QAMQPZPIELE","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QH7W4QAM","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:64e456234b05fb14f062e5bd0fd60a57b8c843fe69d80c4fd542cd348a3010b2","target":"graph","created_at":"2026-05-18T04:03:44Z","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 study the performance of adaptive Fourier-Galerkin methods in a periodic box in $\\mathbb{R}^d$ with dimension $d\\ge 1$. These methods offer unlimited approximation power only restricted by solution and data regularity. They are of intrinsic interest but are also a first step towards understanding adaptivity for the $hp$-FEM. We examine two nonlinear approximation classes, one classical corresponding to algebraic decay of Fourier coefficients and another associated with exponential decay. We study the sparsity classes of the residual and show that they are the same as the solution for the al","authors_text":"Claudio Canuto, Marco Verani, Ricardo H. Nochetto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-26T21:04:24Z","title":"Adaptive Fourier-Galerkin Methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5648","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":"sha256:48c0d7327c251855a9be0b8059513d9667a6f30c120ef2f31f01a6d81809035c","target":"record","created_at":"2026-05-18T04:03:44Z","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":"3ae308b6d9df0031f22a5aafba49d1f238e531c944e7219c51a02608da0df471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-26T21:04:24Z","title_canon_sha256":"870faa17f9dadb6cd1a70d3bedaf5e58511e977dc6ff33cb4ad0bf75b9476fe9"},"schema_version":"1.0","source":{"id":"1201.5648","kind":"arxiv","version":1}},"canonical_sha256":"81ff6e400c83f2f41164247afccdbe324179c6287c7aab10cbb9254e2083bf85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81ff6e400c83f2f41164247afccdbe324179c6287c7aab10cbb9254e2083bf85","first_computed_at":"2026-05-18T04:03:44.851960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:44.851960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KYzAS7bFVt+6CF1QL3fY6UDZoEhgdlCwNEMVoj9xCiMw6jWaULTZ0FBH4KSlhYAH9lPwvdKTDcGHdI2rrkN9CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:44.852436Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48c0d7327c251855a9be0b8059513d9667a6f30c120ef2f31f01a6d81809035c","sha256:64e456234b05fb14f062e5bd0fd60a57b8c843fe69d80c4fd542cd348a3010b2"],"state_sha256":"e7d694bf894cac2aa11d36cb84ca838fedd4d3d5d288c153daa773c4a8a393a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"asMnAB140UWeYbyrjqB8roHvyDxNNbvZohMH3uXMJOuM64/JYVGfEgLU/uHj153ZesdOOEV16r0dj6kUqfsnBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:17:07.725269Z","bundle_sha256":"13f647cd78b76c4e47ddcce153fb18493fa7639d3d783231eb6e20565df62cde"}}