{"as_of":"2026-08-13T05:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0e2e28933d797c8267a357128548487414f6ee28506104f9bcdd092d8d8a5992","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T14:43:35.189214Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-09T14:12:36.583629Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-09T14:12:36.685633Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"cited_work":{"arxiv_id":"2411.15136","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.15136","snapshot_observed_at":"2026-08-09T14:12:36.685633Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","venue":"cs.CC","work_id":"08483920-868e-4f26-a0e0-51bda9718ef2","year":2024},"citing_paper":{"arxiv_id":"2502.01900","last_updated":"2025-02-04T00:16:23Z","snapshot_observed_at":"2026-08-09T14:01:05.679191Z","submitted_at":"2025-02-04T00:16:23Z","title":"Biased Linearity Testing in the 1% Regime","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-09T14:12:36.583629Z"},"links":{"cited_paper":"/paper/2411.15136","citing_paper":"/paper/2502.01900"},"observation_digest":"sha256:bdf557ff54d017999420843a070d57d8cc75fd5170adbc42b2d3e13d93c46077","observation_id":"54ec36a3-3023-45b6-b081-df8235c1c7cc","resolution":{"observed_at":"2026-08-09T14:12:36.691015Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.15136/citation-record","integrity":"/paper/2411.15136/integrity","json":"/paper/2411.15136/citation-record.json","paper":"/paper/2411.15136"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:43:35.805456Z","title":"[BK21] Amey Bhangale and Subhash Khot","venue":null,"work_id":"81b205d2-0780-4eca-97ee-19f0c5895fd0","year":1992},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:34.881947Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:54c44203bfa5072f59426683fe3acef1077f3c48e9c7dd6363eb1cc42a27673b","observation_id":"3e07c58c-4884-4e18-9d7e-7b1801e1a672","resolution":{"observed_at":"2026-08-12T14:43:35.842151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T14:43:35.586030Z","title":"On appr oximability of satisfiable k -csps: I","venue":null,"work_id":"39951b01-a389-4f53-8215-bcfeaa3c73b4","year":2022},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.017780Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:c2b814f7e3bb5d3d32d721aa3299454e0d32de61e0d0003f618063deff8110e9","observation_id":"521d6310-6117-4a27-b7dc-27888e94a3c9","resolution":{"observed_at":"2026-08-12T14:43:35.619218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T14:43:35.498711Z","title":"On app roximability of satisfiable k-csps: II","venue":null,"work_id":"9694cd30-78d8-4d4f-a2b2-da2839caf9e3","year":2023},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.040271Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:2663c81cbf488edf54ef64250b3085c162d534f25c4a56f01b2686b9a642de46","observation_id":"8c467ddd-d7d4-42e4-a042-c202a14459cc","resolution":{"observed_at":"2026-08-12T14:43:35.530265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T14:43:35.368003Z","title":"On app roximability of satisfiable k-csps: IV","venue":null,"work_id":"5ea1958f-cc3b-418a-a56c-a20f1dfce72d","year":2024},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.094741Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:a50fc8c78389647b7765e1b62407eeb98e39735b0ee57157775c364e89cd0570","observation_id":"4c9d5501-49c0-4032-93ac-f2a7a329b5a3","resolution":{"observed_at":"2026-08-12T14:43:35.398468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1712.00241","last_updated":"2017-12-01T09:13:12Z","snapshot_observed_at":"2026-08-05T04:07:00.784434Z","submitted_at":"2017-12-01T09:13:12Z","title":"A quantitative inverse theorem for the $U^4$ norm over finite fields","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1712.00241","snapshot_observed_at":"2026-08-12T14:43:35.171957Z","title":"A quantitative inverse theorem for the U 4 norm over finite fields","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.171957Z"},"links":{"cited_paper":"/paper/1712.00241","citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:4f84885848ace724ee82a3f88e5fdeffe353355c7208a5b09385d114ab5c77d4","observation_id":"9cf0f3ea-fc59-4176-805e-8f2d1afdb0f3","resolution":{"observed_at":"2026-08-12T14:43:35.171957Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:43:35.152439Z","title":"[FK91] H","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":1989,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.152439Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:24ce5f1ef0687d8189c260fe0ade1f6a4c9295e190cce41043cbea26c54e55f9","observation_id":"34a383f0-f2aa-476e-8317-d41bc9c78d5a","resolution":{"observed_at":"2026-08-12T14:43:35.152439Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T14:43:35.905965Z","title":"[AS98] Sanjeev Arora and Shmuel Safra","venue":null,"work_id":"403b5cee-f8c2-4d01-a1c3-69fe7aa866a6","year":1992},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":1998,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:34.834372Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:91083bbe16a58300c07a4549d2b0c98acdbd9b72a2e7ba6dfecc079a49219096","observation_id":"3db0cb26-67ff-4958-8ef2-707989549a22","resolution":{"observed_at":"2026-08-12T14:43:35.936971Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T14:43:35.270820Z","title":"[Kho02] Subhash Khot","venue":null,"work_id":"912bb439-2bac-466b-9f1c-83a897b1dbf4","year":1997},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":2001,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.189214Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:186b9a2522e0e73bd50276b1db6c5ad72f690a64c585a2a0d6c8c1e7f226a456","observation_id":"3438a139-042d-459b-90cc-b2537080fb9e","resolution":{"observed_at":"2026-08-12T14:43:35.297276Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T14:43:35.731125Z","title":"An invariance principle for the multi-slice, with applications","venue":null,"work_id":"eec5ac01-cd13-4c55-b4ff-744fc7f205c8","year":2022},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:34.927243Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:ccaa78d8c7457fce9d5fcdc419dfe1c94a003e44c996a3c5f5cbada1b501ad22","observation_id":"477c5dd2-3d14-4d1a-8924-13e85006b4cb","resolution":{"observed_at":"2026-08-12T14:43:35.750685Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T14:43:35.656777Z","title":"Liu, and Dor M inzer","venue":null,"work_id":"722b0d21-6076-494b-9802-c61532b9c669","year":2024},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:34.968620Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:1730e71a7e6a4cb453bda32be37c82c2a96dc1f5018c1f060c3d3cca541f6c37","observation_id":"11af1fca-292a-4c7b-a94c-70c66b334747","resolution":{"observed_at":"2026-08-12T14:43:35.688921Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-12T14:43:35.433279Z","title":"On app roximability of satisfiable k-csps: III","venue":null,"work_id":"37173fbd-9748-4a8c-a69c-0a6f07f23e32","year":2023},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.060675Z"},"links":{"citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:1cff3bf277aed70ddb358c91899a3bcab2eddcaed3a851d795af7f6c56e843d9","observation_id":"9d6bafd4-65f5-4134-9bec-14c9c0374379","resolution":{"observed_at":"2026-08-12T14:43:35.467845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.15377","last_updated":"2026-05-19T08:17:47Z","snapshot_observed_at":"2026-08-02T18:01:35.083275Z","submitted_at":"2024-08-27T19:30:26Z","title":"On Approximability of Satisfiable k-CSPs: V","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.15377","snapshot_observed_at":"2026-08-12T14:43:35.129877Z","title":"On app roximability of satisfiable k-csps: V","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-12T14:43:35.129877Z"},"links":{"cited_paper":"/paper/2408.15377","citing_paper":"/paper/2411.15136"},"observation_digest":"sha256:a0ce23953df71d2a1c223655c2c04a9b1a2f88ffcda7f594d3e821f458a52957","observation_id":"125a0665-7abb-48ab-b6b6-f09d82f76ca3","resolution":{"observed_at":"2026-08-12T14:43:35.129877Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2411.15136","last_updated":"2024-11-22T18:58:08Z","latest_version":1,"primary_category":"cs.CC","snapshot_observed_at":"2026-08-12T14:25:11.953024Z","submitted_at":"2024-11-22T18:58:08Z","title":"On Approximability of Satisfiable $k$-CSPs: VII"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":12},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2411.15136."}