{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:X24WFAWVTG7TZPFE7YZ45JBQDN","short_pith_number":"pith:X24WFAWV","canonical_record":{"source":{"id":"2210.12495","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-22T16:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"9f35e2d8a9604e9ca4ef7b8630c26df0c21bcbfe534155a4d14f9a25570617e1","abstract_canon_sha256":"d5f67d4dcf26adbf50a6b91f92655b0d43390e382571a4acac48e2e457e2f035"},"schema_version":"1.0"},"canonical_sha256":"beb96282d599bf3cbca4fe33cea4301b522b060de42d18093fca2644c06c3c0c","source":{"kind":"arxiv","id":"2210.12495","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.12495","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"2210.12495v3","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.12495","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"X24WFAWVTG7T","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"pith_short_16","alias_value":"X24WFAWVTG7TZPFE","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"pith_short_8","alias_value":"X24WFAWV","created_at":"2026-07-05T05:39:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:X24WFAWVTG7TZPFE7YZ45JBQDN","target":"record","payload":{"canonical_record":{"source":{"id":"2210.12495","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-22T16:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"9f35e2d8a9604e9ca4ef7b8630c26df0c21bcbfe534155a4d14f9a25570617e1","abstract_canon_sha256":"d5f67d4dcf26adbf50a6b91f92655b0d43390e382571a4acac48e2e457e2f035"},"schema_version":"1.0"},"canonical_sha256":"beb96282d599bf3cbca4fe33cea4301b522b060de42d18093fca2644c06c3c0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:39:53.949515Z","signature_b64":"F4pGfeypX9pJgqSbJme/7dlAnlHlb0i3hBpZoDlH5p5lYGMYDskqE94mcwMKvX5jfRccqYXAcFgkAqNpNFaGDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beb96282d599bf3cbca4fe33cea4301b522b060de42d18093fca2644c06c3c0c","last_reissued_at":"2026-07-05T05:39:53.949004Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:39:53.949004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.12495","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QcjVZ/o2nDwwgHRk8PsYE66jERDO8QKE9D+3T/bbf9HHL3GrfL+sJnqHUk+acMsACE8eXU2Rs6D1AQaTrnMCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:20:41.564982Z"},"content_sha256":"f3318166cbce8c9ad9e744e13120652bf53b5a95452e3760ce92b816953ceafb","schema_version":"1.0","event_id":"sha256:f3318166cbce8c9ad9e744e13120652bf53b5a95452e3760ce92b816953ceafb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:X24WFAWVTG7TZPFE7YZ45JBQDN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quartic Samples Suffice for Fourier Interpolation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Baocheng Sun, Omri Weinstein, Ruizhe Zhang, Zhao Song","submitted_at":"2022-10-22T16:54:49Z","abstract_excerpt":"We study the problem of interpolating a noisy Fourier-sparse signal in the time duration $[0, T]$ from noisy samples in the same range, where the ground truth signal can be any $k$-Fourier-sparse signal with band-limit $[-F, F]$. Our main result is an efficient Fourier Interpolation algorithm that improves the previous best algorithm by [Chen, Kane, Price, and Song, FOCS 2016] in the following three aspects:\n  $\\bullet$ The sample complexity is improved from $\\widetilde{O}(k^{51})$ to $\\widetilde{O}(k^{4})$.\n  $\\bullet$ The time complexity is improved from $ \\widetilde{O}(k^{10\\omega+40})$ to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.12495","kind":"arxiv","version":3},"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/2210.12495/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zoZ6QVTCgPe8XPbIQ4ARJB0LqMwu0d9zncVX/d3SgO59pWLJ3nidma+dTuaefHfz4RbXOc7xP4XbQ84H3D09CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T07:20:41.565471Z"},"content_sha256":"2a6f6904e7e1cefbdb559a4e640ee0afa5667467d17bd8bbdd27e9c4ba405ace","schema_version":"1.0","event_id":"sha256:2a6f6904e7e1cefbdb559a4e640ee0afa5667467d17bd8bbdd27e9c4ba405ace"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X24WFAWVTG7TZPFE7YZ45JBQDN/bundle.json","state_url":"https://pith.science/pith/X24WFAWVTG7TZPFE7YZ45JBQDN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X24WFAWVTG7TZPFE7YZ45JBQDN/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":"2026-08-08T07:20:41Z","links":{"resolver":"https://pith.science/pith/X24WFAWVTG7TZPFE7YZ45JBQDN","bundle":"https://pith.science/pith/X24WFAWVTG7TZPFE7YZ45JBQDN/bundle.json","state":"https://pith.science/pith/X24WFAWVTG7TZPFE7YZ45JBQDN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X24WFAWVTG7TZPFE7YZ45JBQDN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:X24WFAWVTG7TZPFE7YZ45JBQDN","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":"d5f67d4dcf26adbf50a6b91f92655b0d43390e382571a4acac48e2e457e2f035","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-22T16:54:49Z","title_canon_sha256":"9f35e2d8a9604e9ca4ef7b8630c26df0c21bcbfe534155a4d14f9a25570617e1"},"schema_version":"1.0","source":{"id":"2210.12495","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.12495","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"2210.12495v3","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.12495","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"X24WFAWVTG7T","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"pith_short_16","alias_value":"X24WFAWVTG7TZPFE","created_at":"2026-07-05T05:39:53Z"},{"alias_kind":"pith_short_8","alias_value":"X24WFAWV","created_at":"2026-07-05T05:39:53Z"}],"graph_snapshots":[{"event_id":"sha256:2a6f6904e7e1cefbdb559a4e640ee0afa5667467d17bd8bbdd27e9c4ba405ace","target":"graph","created_at":"2026-07-05T05:39:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.12495/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of interpolating a noisy Fourier-sparse signal in the time duration $[0, T]$ from noisy samples in the same range, where the ground truth signal can be any $k$-Fourier-sparse signal with band-limit $[-F, F]$. Our main result is an efficient Fourier Interpolation algorithm that improves the previous best algorithm by [Chen, Kane, Price, and Song, FOCS 2016] in the following three aspects:\n  $\\bullet$ The sample complexity is improved from $\\widetilde{O}(k^{51})$ to $\\widetilde{O}(k^{4})$.\n  $\\bullet$ The time complexity is improved from $ \\widetilde{O}(k^{10\\omega+40})$ to ","authors_text":"Baocheng Sun, Omri Weinstein, Ruizhe Zhang, Zhao Song","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-22T16:54:49Z","title":"Quartic Samples Suffice for Fourier Interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.12495","kind":"arxiv","version":3},"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:f3318166cbce8c9ad9e744e13120652bf53b5a95452e3760ce92b816953ceafb","target":"record","created_at":"2026-07-05T05:39:53Z","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":"d5f67d4dcf26adbf50a6b91f92655b0d43390e382571a4acac48e2e457e2f035","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-10-22T16:54:49Z","title_canon_sha256":"9f35e2d8a9604e9ca4ef7b8630c26df0c21bcbfe534155a4d14f9a25570617e1"},"schema_version":"1.0","source":{"id":"2210.12495","kind":"arxiv","version":3}},"canonical_sha256":"beb96282d599bf3cbca4fe33cea4301b522b060de42d18093fca2644c06c3c0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"beb96282d599bf3cbca4fe33cea4301b522b060de42d18093fca2644c06c3c0c","first_computed_at":"2026-07-05T05:39:53.949004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:39:53.949004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F4pGfeypX9pJgqSbJme/7dlAnlHlb0i3hBpZoDlH5p5lYGMYDskqE94mcwMKvX5jfRccqYXAcFgkAqNpNFaGDw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:39:53.949515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.12495","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3318166cbce8c9ad9e744e13120652bf53b5a95452e3760ce92b816953ceafb","sha256:2a6f6904e7e1cefbdb559a4e640ee0afa5667467d17bd8bbdd27e9c4ba405ace"],"state_sha256":"d0149f2de11824e6c6974e0f8739b37e6d46fefe37a049b300b0349807b971bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DaY6sF7b4k/5stWa5yVa0zt/spEipbu+4wzbgXpOH3GQa3sa+InV/SNJVS+Foo80Nopzfh4F4fWuzPZjyqeGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T07:20:41.570362Z","bundle_sha256":"6906a9fb6a5327783a5eb7ed85563fe0957a3ea2d3ec88039a06c1e9b5b6acc8"}}