{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:C6ULGZH7EWJAKLYIVNRL5OGZY3","short_pith_number":"pith:C6ULGZH7","canonical_record":{"source":{"id":"1308.5314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-24T10:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"2942c95f69dfd312e35976b3b6847822127dd2d368e5b87e4b55408504f9e4c1","abstract_canon_sha256":"0b2aad12f44b29bc07a772baaf0a93e9a6831be32d8d39dc664478dc686ff27f"},"schema_version":"1.0"},"canonical_sha256":"17a8b364ff2592052f08ab62beb8d9c6dde795661eca829d6a4404b0b6e4f120","source":{"kind":"arxiv","id":"1308.5314","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5314","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5314v1","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5314","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"C6ULGZH7EWJA","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C6ULGZH7EWJAKLYI","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C6ULGZH7","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:C6ULGZH7EWJAKLYIVNRL5OGZY3","target":"record","payload":{"canonical_record":{"source":{"id":"1308.5314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-24T10:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"2942c95f69dfd312e35976b3b6847822127dd2d368e5b87e4b55408504f9e4c1","abstract_canon_sha256":"0b2aad12f44b29bc07a772baaf0a93e9a6831be32d8d39dc664478dc686ff27f"},"schema_version":"1.0"},"canonical_sha256":"17a8b364ff2592052f08ab62beb8d9c6dde795661eca829d6a4404b0b6e4f120","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:05.247878Z","signature_b64":"fNaWYpfCvCDEpDBeBe1O/SbvUcvvutXkrRKiXzyznv3rGDg2vlxrtQRt3NhszhzD0Qm4OwL/EPXgiP/FHeKhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a8b364ff2592052f08ab62beb8d9c6dde795661eca829d6a4404b0b6e4f120","last_reissued_at":"2026-05-18T03:15:05.247106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:05.247106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.5314","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":"2026-05-18T03:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Uhis4FWSP+H3mzKrv69nxRQwuncdqLvsQ/WxJdE6GaFdWXX9YRZrcd9GaTQZrn+EWgkzAOctTWVsJT6mWK8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:10:15.786108Z"},"content_sha256":"485f59af4b398b9237c49ddfc6448e6a0b729c43117e29a0c19bec096cf12d31","schema_version":"1.0","event_id":"sha256:485f59af4b398b9237c49ddfc6448e6a0b729c43117e29a0c19bec096cf12d31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:C6ULGZH7EWJAKLYIVNRL5OGZY3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability and spectral convergence of Fourier method for nonlinear problems. On the shortcomings of the 2/3 de-aliasing method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Claude Bardos, Eitan Tadmor","submitted_at":"2013-08-24T10:38:18Z","abstract_excerpt":"The high-order accuracy of Fourier method makes it the method of choice in many large scale simulations. We discuss here the stability of Fourier method for nonlinear evolution problems, focusing on the two prototypical cases of the inviscid Burgers' equation and the multi-dimensional incompressible Euler equations. The Fourier method for such problems with quadratic nonlinearities comes in two main flavors. One is the spectral Fourier method. The other is the 2/3 pseudo-spectral Fourier method, where one removes the highest 1/3 portion of the spectrum; this is often the method of choice to ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5314","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":"2026-05-18T03:15:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lH0M/JK6ZMjvvSpGrQsn4irkPlhrti6OuHHSKY3phEOe09QYhMflLSzWSdL1jp8e65ZUJ9znR/s0hwFD9HxBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:10:15.787021Z"},"content_sha256":"a9e17db893de610cf2cc8e21f6d8332a5cf4afd2633f73b79a6ec88b300f9f7d","schema_version":"1.0","event_id":"sha256:a9e17db893de610cf2cc8e21f6d8332a5cf4afd2633f73b79a6ec88b300f9f7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6ULGZH7EWJAKLYIVNRL5OGZY3/bundle.json","state_url":"https://pith.science/pith/C6ULGZH7EWJAKLYIVNRL5OGZY3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6ULGZH7EWJAKLYIVNRL5OGZY3/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":"2026-06-05T19:10:15Z","links":{"resolver":"https://pith.science/pith/C6ULGZH7EWJAKLYIVNRL5OGZY3","bundle":"https://pith.science/pith/C6ULGZH7EWJAKLYIVNRL5OGZY3/bundle.json","state":"https://pith.science/pith/C6ULGZH7EWJAKLYIVNRL5OGZY3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6ULGZH7EWJAKLYIVNRL5OGZY3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C6ULGZH7EWJAKLYIVNRL5OGZY3","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":"0b2aad12f44b29bc07a772baaf0a93e9a6831be32d8d39dc664478dc686ff27f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-24T10:38:18Z","title_canon_sha256":"2942c95f69dfd312e35976b3b6847822127dd2d368e5b87e4b55408504f9e4c1"},"schema_version":"1.0","source":{"id":"1308.5314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5314","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5314v1","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5314","created_at":"2026-05-18T03:15:05Z"},{"alias_kind":"pith_short_12","alias_value":"C6ULGZH7EWJA","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C6ULGZH7EWJAKLYI","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C6ULGZH7","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:a9e17db893de610cf2cc8e21f6d8332a5cf4afd2633f73b79a6ec88b300f9f7d","target":"graph","created_at":"2026-05-18T03:15:05Z","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":"The high-order accuracy of Fourier method makes it the method of choice in many large scale simulations. We discuss here the stability of Fourier method for nonlinear evolution problems, focusing on the two prototypical cases of the inviscid Burgers' equation and the multi-dimensional incompressible Euler equations. The Fourier method for such problems with quadratic nonlinearities comes in two main flavors. One is the spectral Fourier method. The other is the 2/3 pseudo-spectral Fourier method, where one removes the highest 1/3 portion of the spectrum; this is often the method of choice to ma","authors_text":"Claude Bardos, Eitan Tadmor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-24T10:38:18Z","title":"Stability and spectral convergence of Fourier method for nonlinear problems. On the shortcomings of the 2/3 de-aliasing method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5314","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":"sha256:485f59af4b398b9237c49ddfc6448e6a0b729c43117e29a0c19bec096cf12d31","target":"record","created_at":"2026-05-18T03:15:05Z","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":"0b2aad12f44b29bc07a772baaf0a93e9a6831be32d8d39dc664478dc686ff27f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-08-24T10:38:18Z","title_canon_sha256":"2942c95f69dfd312e35976b3b6847822127dd2d368e5b87e4b55408504f9e4c1"},"schema_version":"1.0","source":{"id":"1308.5314","kind":"arxiv","version":1}},"canonical_sha256":"17a8b364ff2592052f08ab62beb8d9c6dde795661eca829d6a4404b0b6e4f120","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17a8b364ff2592052f08ab62beb8d9c6dde795661eca829d6a4404b0b6e4f120","first_computed_at":"2026-05-18T03:15:05.247106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:05.247106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fNaWYpfCvCDEpDBeBe1O/SbvUcvvutXkrRKiXzyznv3rGDg2vlxrtQRt3NhszhzD0Qm4OwL/EPXgiP/FHeKhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:05.247878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:485f59af4b398b9237c49ddfc6448e6a0b729c43117e29a0c19bec096cf12d31","sha256:a9e17db893de610cf2cc8e21f6d8332a5cf4afd2633f73b79a6ec88b300f9f7d"],"state_sha256":"078b228900489dfe2a851022f6fc99fada5e3d733f9d13d3d3658f55bdeaf931"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Mvqm4XJ4GFiFqMzJqt5qvqPSzrnY6G22dB/Zaup45amUqY6nugaDLkONYXNcr3+Y1HkQGG4qN7Sy/qGDPesDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:10:15.790961Z","bundle_sha256":"cd8210e827fd980cec8eee979695440e9cf512df3c84769dddf24776329d987d"}}