{"as_of":"2026-08-16T12:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c5cb3959c4c47dd6e4290b82b0223449f538005c6435d95e3fc2fa1bee14f2ca","coverage":[{"denominator":9,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T12:57:05.645327Z","state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/1908.07154/citation-record","integrity":"/paper/1908.07154/integrity","json":"/paper/1908.07154/citation-record.json","paper":"/paper/1908.07154"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.816234Z","title":"The best of the 20th century: Editors name t op 10 algorithms","venue":null,"work_id":"0c017db4-a4a1-461a-8433-d798367b3892","year":2000},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.601104Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:ab7825f36e32253b4ac946c591c6030d817c246b651d5e5f9bf2f6aa90bda514","observation_id":"4181beec-21e8-4fb3-a2b8-d71e6a9fae40","resolution":{"observed_at":"2026-08-14T12:57:05.821497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.802452Z","title":"An algorithm for the machi ne calculation of complex fourier series","venue":null,"work_id":"a5762040-6385-4e0f-984f-6eec0750a829","year":1965},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.606924Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:7970f666d327ce36ce429ac170617263bffa49ad2bf43194dfb0b908414990ef","observation_id":"b2e02575-336d-4cd9-a4f5-d0a0726886d4","resolution":{"observed_at":"2026-08-14T12:57:05.807192Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.788969Z","title":"Algorithms","venue":null,"work_id":"7ac99d61-3bc2-4714-8aab-bbe62bbe2d7b","year":2008},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.612517Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:0e696270de322f5528ce2b81d05d981aa8dc71449a85ce354fe6d204d39cfdad","observation_id":"65d58345-92d4-44db-8fa9-37b2223b0471","resolution":{"observed_at":"2026-08-14T12:57:05.793218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.771502Z","title":"A brief introduction to fourier analysis on the boolean cube","venue":null,"work_id":"e0f9c18e-1a13-4353-affa-80b76cc3a64e","year":2008},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.617609Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:8a48340fe012b535c7eafa4eaac45917b6a59e66773acbe5fc58c2043db5bc79","observation_id":"ebd26688-2bef-4cff-bf4d-5e48cece2db5","resolution":{"observed_at":"2026-08-14T12:57:05.776970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.752758Z","title":"Mathematics++, volume 75","venue":null,"work_id":"0d05634a-d59f-4997-a1d1-3c619407f163","year":2015},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.622324Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:24e72bf09d847c3e25656defb049f4a253f82796c440d681e7610756706412c7","observation_id":"2a461651-efad-4986-8857-ec54a3f9f1b8","resolution":{"observed_at":"2026-08-14T12:57:05.757735Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.735998Z","title":"Harmonic analysis: from Fourier to wavelets , vol- ume 63","venue":null,"work_id":"07820aa2-4058-4242-bf14-3f74b1f73a42","year":2012},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.627682Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:bdfc4932b422c3a5c33694b5166b760d6b498b1fed6a60dd2726fd2e70023488","observation_id":"ecd8a32d-75ea-4957-af66-80ab7dd8a109","resolution":{"observed_at":"2026-08-14T12:57:05.741271Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.719935Z","title":"An introduction to the theory of groups , volume 148","venue":null,"work_id":"4ef406a3-644c-4a15-9964-c659481acbcb","year":2012},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.633970Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:84892cbf7815b746e323e8a0442056cb903c85fa9cd8ffa7ff46ba2917352f11","observation_id":"12ff8d53-163d-46d4-a12a-1aea7184ce36","resolution":{"observed_at":"2026-08-14T12:57:05.724999Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.703335Z","title":"Introduction to applied mathematics , volume 16","venue":null,"work_id":"82e0b2db-3183-4fbc-9859-bf3036e47faf","year":1986},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.639100Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:a563d85009bb853fc1eb62560fdc4b119daed047cf37b7196394523ef1e4bcdb","observation_id":"33cf0357-6d51-41a8-b0e1-2eb712556a38","resolution":{"observed_at":"2026-08-14T12:57:05.708180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:57:05.684862Z","title":"Fourier analysis on finite groups and applications","venue":null,"work_id":"15ad4d13-c255-4ce2-bce1-ee3a41c2298e","year":1999},"citing_paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T12:57:05.645327Z"},"links":{"citing_paper":"/paper/1908.07154"},"observation_digest":"sha256:1ca654a1a069fd5c171e4bbb67d052122db4fcb62c4a3ee38a886c459a10986e","observation_id":"c16d9cfc-cd59-4b3f-b55e-3ce458fecaa3","resolution":{"observed_at":"2026-08-14T12:57:05.692539Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.07154","last_updated":"2019-08-17T07:59:57Z","latest_version":1,"primary_category":"cs.DS","snapshot_observed_at":"2026-08-16T03:37:04.699942Z","submitted_at":"2019-08-17T07:59:57Z","title":"Discrete and Fast Fourier Transform Made Clear"},"reference_resolution":{"displayed":9,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":9},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:1908.07154."}