{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IK4FH3TE76YLUJL6267DIKHQOD","short_pith_number":"pith:IK4FH3TE","canonical_record":{"source":{"id":"1209.0617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-09-04T11:55:09Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"84f5a38b721ab6ded4763720ff437f20ed8819771da0a737620479362bcf0e76","abstract_canon_sha256":"f3adad24a8905c809add4ef359b0c4b2faa2320fee4e4a8effcfab8b69500cdb"},"schema_version":"1.0"},"canonical_sha256":"42b853ee64ffb0ba257ed7be3428f070c88d7a15ee0cdce3292b0c139006040f","source":{"kind":"arxiv","id":"1209.0617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0617","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0617v1","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0617","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"IK4FH3TE76YL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IK4FH3TE76YLUJL6","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IK4FH3TE","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IK4FH3TE76YLUJL6267DIKHQOD","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-09-04T11:55:09Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"84f5a38b721ab6ded4763720ff437f20ed8819771da0a737620479362bcf0e76","abstract_canon_sha256":"f3adad24a8905c809add4ef359b0c4b2faa2320fee4e4a8effcfab8b69500cdb"},"schema_version":"1.0"},"canonical_sha256":"42b853ee64ffb0ba257ed7be3428f070c88d7a15ee0cdce3292b0c139006040f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:17.664294Z","signature_b64":"/FPHxOyADZ1bczaf5lOS9D7w6vIEfGjOkGY8NigCw2ZJYHzPzgValGo0DrTcsQDUnBFNx4r5xHUzK7gtudaRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42b853ee64ffb0ba257ed7be3428f070c88d7a15ee0cdce3292b0c139006040f","last_reissued_at":"2026-05-18T03:46:17.663609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:17.663609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0617","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":"2026-05-18T03:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0LxVc64UxGYHAh+/Y995F1ZLNCVBneyRoNqC8lkJI6lWXzrsWjmEoUrUTJxk1H0VNvaeIGpgdiHY6jkADg7uDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:34:49.698176Z"},"content_sha256":"3c2c0be7ac4bb2a62d2a0ccfd47cea53ab697fc994b5e6518ab143b5c0a4b3ef","schema_version":"1.0","event_id":"sha256:3c2c0be7ac4bb2a62d2a0ccfd47cea53ab697fc994b5e6518ab143b5c0a4b3ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IK4FH3TE76YLUJL6267DIKHQOD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Fourier Optimization: Sparsity Matters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.OC","authors_text":"Robert J. Vanderbei","submitted_at":"2012-09-04T11:55:09Z","abstract_excerpt":"Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\\em fast Fourier transform} (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it enc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0617","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":"2026-05-18T03:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgOXJq+GcFPFsDmx3D4pUnlQa9H7AJDY3qtZsV7HIMAMFKu/ksmkchSv7v2jgIsWTf4gNxlnfWAuMvPvG+ofAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:34:49.698556Z"},"content_sha256":"502f40bba9551515b24610d48a2a99363a47425b0e4607f9e046b438a7592ced","schema_version":"1.0","event_id":"sha256:502f40bba9551515b24610d48a2a99363a47425b0e4607f9e046b438a7592ced"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IK4FH3TE76YLUJL6267DIKHQOD/bundle.json","state_url":"https://pith.science/pith/IK4FH3TE76YLUJL6267DIKHQOD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IK4FH3TE76YLUJL6267DIKHQOD/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":"2026-06-02T02:34:49Z","links":{"resolver":"https://pith.science/pith/IK4FH3TE76YLUJL6267DIKHQOD","bundle":"https://pith.science/pith/IK4FH3TE76YLUJL6267DIKHQOD/bundle.json","state":"https://pith.science/pith/IK4FH3TE76YLUJL6267DIKHQOD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IK4FH3TE76YLUJL6267DIKHQOD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IK4FH3TE76YLUJL6267DIKHQOD","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":"f3adad24a8905c809add4ef359b0c4b2faa2320fee4e4a8effcfab8b69500cdb","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-09-04T11:55:09Z","title_canon_sha256":"84f5a38b721ab6ded4763720ff437f20ed8819771da0a737620479362bcf0e76"},"schema_version":"1.0","source":{"id":"1209.0617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0617","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0617v1","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0617","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"IK4FH3TE76YL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IK4FH3TE76YLUJL6","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IK4FH3TE","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:502f40bba9551515b24610d48a2a99363a47425b0e4607f9e046b438a7592ced","target":"graph","created_at":"2026-05-18T03:46:17Z","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":"Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\\em fast Fourier transform} (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it enc","authors_text":"Robert J. Vanderbei","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-09-04T11:55:09Z","title":"Fast Fourier Optimization: Sparsity Matters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0617","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":"sha256:3c2c0be7ac4bb2a62d2a0ccfd47cea53ab697fc994b5e6518ab143b5c0a4b3ef","target":"record","created_at":"2026-05-18T03:46:17Z","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":"f3adad24a8905c809add4ef359b0c4b2faa2320fee4e4a8effcfab8b69500cdb","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-09-04T11:55:09Z","title_canon_sha256":"84f5a38b721ab6ded4763720ff437f20ed8819771da0a737620479362bcf0e76"},"schema_version":"1.0","source":{"id":"1209.0617","kind":"arxiv","version":1}},"canonical_sha256":"42b853ee64ffb0ba257ed7be3428f070c88d7a15ee0cdce3292b0c139006040f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42b853ee64ffb0ba257ed7be3428f070c88d7a15ee0cdce3292b0c139006040f","first_computed_at":"2026-05-18T03:46:17.663609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:17.663609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/FPHxOyADZ1bczaf5lOS9D7w6vIEfGjOkGY8NigCw2ZJYHzPzgValGo0DrTcsQDUnBFNx4r5xHUzK7gtudaRBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:17.664294Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c2c0be7ac4bb2a62d2a0ccfd47cea53ab697fc994b5e6518ab143b5c0a4b3ef","sha256:502f40bba9551515b24610d48a2a99363a47425b0e4607f9e046b438a7592ced"],"state_sha256":"8c0fd80b89239b70e80e6d691a90c932520113d42f1b598f3279ec2974434d81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RpaxdCnGNU+CcRvonITculYGgNLUrWouS4OsE8m92nMXfObRcX9f6y6ki3StDXoNYeS1cG4iYUwWEjhYvnVEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:34:49.700469Z","bundle_sha256":"7d8a72dfd06ce0c2b769be338a7bbb0cfe52d28b964ed22d92920c9969933d4c"}}