{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:L4DXNAIIQ4KHP3HB2356VSOPFP","short_pith_number":"pith:L4DXNAII","schema_version":"1.0","canonical_sha256":"5f07768108871477ece1d6fbeac9cf2bf6627b1074ea1b82ded84ef402154d76","source":{"kind":"arxiv","id":"math/0610051","version":1},"attestation_state":"computed","paper":{"title":"Fast Computation of Fourier Integral Operators","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Emmanuel Candes, Laurent Demanet, Lexing Ying","submitted_at":"2006-10-01T19:12:53Z","abstract_excerpt":"We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically a so-called Fourier integral operator (FIO) of the form $\\int e^{2\\pi i \\Phi(x,\\xi)} a(x,\\xi) \\hat{f}(\\xi) \\mathrm{d}\\xi$ at points given on a Cartesian grid. Here, $\\xi$ is a frequency variable, $\\hat f(\\xi)$ is the Fourier transform of the input $f$, $a(x,\\xi)$ is an amplitude and $\\Phi(x,\\xi)$ is a phase function, which is typically as large as $|\\xi|$; h"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0610051","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NA","submitted_at":"2006-10-01T19:12:53Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"547d7ae60b1700d5d869f0efcfb48eed70a732e22eeef79f44fe6647894b62f2","abstract_canon_sha256":"c8e96cf64943cab6e1bc3ff1c6dda9455456afcd3f63c36697eafebb781092f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:20.689552Z","signature_b64":"ka2CRlCeiwyNgDCw7oMM+bN9v7W0bhfkkL2pxXuJgTDO/pb+SHuoUhswliL+GpR74ITl2hzoykoELRDvi00oBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f07768108871477ece1d6fbeac9cf2bf6627b1074ea1b82ded84ef402154d76","last_reissued_at":"2026-06-03T22:06:20.689205Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:20.689205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast Computation of Fourier Integral Operators","license":"","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Emmanuel Candes, Laurent Demanet, Lexing Ying","submitted_at":"2006-10-01T19:12:53Z","abstract_excerpt":"We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically a so-called Fourier integral operator (FIO) of the form $\\int e^{2\\pi i \\Phi(x,\\xi)} a(x,\\xi) \\hat{f}(\\xi) \\mathrm{d}\\xi$ at points given on a Cartesian grid. Here, $\\xi$ is a frequency variable, $\\hat f(\\xi)$ is the Fourier transform of the input $f$, $a(x,\\xi)$ is an amplitude and $\\Phi(x,\\xi)$ is a phase function, which is typically as large as $|\\xi|$; h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610051","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0610051/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0610051","created_at":"2026-06-03T22:06:20.689257+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0610051v1","created_at":"2026-06-03T22:06:20.689257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0610051","created_at":"2026-06-03T22:06:20.689257+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4DXNAIIQ4KH","created_at":"2026-06-03T22:06:20.689257+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4DXNAIIQ4KHP3HB","created_at":"2026-06-03T22:06:20.689257+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4DXNAII","created_at":"2026-06-03T22:06:20.689257+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP","json":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP.json","graph_json":"https://pith.science/api/pith-number/L4DXNAIIQ4KHP3HB2356VSOPFP/graph.json","events_json":"https://pith.science/api/pith-number/L4DXNAIIQ4KHP3HB2356VSOPFP/events.json","paper":"https://pith.science/paper/L4DXNAII"},"agent_actions":{"view_html":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP","download_json":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP.json","view_paper":"https://pith.science/paper/L4DXNAII","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0610051&json=true","fetch_graph":"https://pith.science/api/pith-number/L4DXNAIIQ4KHP3HB2356VSOPFP/graph.json","fetch_events":"https://pith.science/api/pith-number/L4DXNAIIQ4KHP3HB2356VSOPFP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP/action/storage_attestation","attest_author":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP/action/author_attestation","sign_citation":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP/action/citation_signature","submit_replication":"https://pith.science/pith/L4DXNAIIQ4KHP3HB2356VSOPFP/action/replication_record"}},"created_at":"2026-06-03T22:06:20.689257+00:00","updated_at":"2026-06-03T22:06:20.689257+00:00"}