{"as_of":"2026-08-20T20:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:75f5cebdac203975805a777ef909d3288bc2bbf26d6125a2c2d8b271a538747f","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T01:07:40.686676Z","state":"measured"},{"denominator":65,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":65,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T00:18:05.896158Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T23:39:04.788099Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"cited_work":{"arxiv_id":"2508.03961","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.03961","snapshot_observed_at":"2026-07-03T23:39:04.788099Z","title":"Bansal and H","venue":null,"work_id":"5833ce4b-1430-40f7-b2c9-7da8960b7afc","year":2025},"citing_paper":{"arxiv_id":"2604.09806","last_updated":"2026-07-18T18:02:29Z","snapshot_observed_at":"2026-08-18T00:35:42.495473Z","submitted_at":"2026-04-10T18:30:43Z","title":"Algorithms for Standard-form ILP Problems via Koml\\'os' Discrepancy Setting","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-05-10T16:36:12.361308Z"},"links":{"cited_paper":"/paper/2508.03961","citing_paper":"/paper/2604.09806"},"observation_digest":"sha256:16ad7506bce70fc98f1bc21f3b2267a48595729bc23a8a65044b519266141333","observation_id":"7f4fc7a5-eee9-48c6-8b4a-b917ae9f981b","resolution":{"observed_at":"2026-05-11T08:30:57.402649Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.03961","snapshot_observed_at":"2026-08-02T16:43:38.099392Z","title":"Decoupling via affine spectral-independence: Beck-Fiala and Koml\\'os bounds beyond Banaszczyk","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2604.09806","last_updated":"2026-07-18T18:02:29Z","snapshot_observed_at":"2026-08-18T00:35:42.495473Z","submitted_at":"2026-04-10T18:30:43Z","title":"Algorithms for Standard-form ILP Problems via Koml\\'os' Discrepancy Setting","version":3},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-02T16:43:38.099392Z"},"links":{"cited_paper":"/paper/2508.03961","citing_paper":"/paper/2604.09806"},"observation_digest":"sha256:af68b1a0b03615f530ee6bf71efceb68eadb43d1f469dfdc8375638e7f5a73c9","observation_id":"d714cbb7-8430-4c99-aca9-84367ed623e6","resolution":{"observed_at":"2026-08-02T16:43:38.099392Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"cited_work":{"arxiv_id":"2508.03961","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.03961","snapshot_observed_at":"2026-07-03T23:39:04.788099Z","title":"Bansal and H","venue":null,"work_id":"5833ce4b-1430-40f7-b2c9-7da8960b7afc","year":2025},"citing_paper":{"arxiv_id":"2605.23866","last_updated":"2026-05-22T17:25:00Z","snapshot_observed_at":"2026-08-19T08:05:52.950276Z","submitted_at":"2026-05-22T17:25:00Z","title":"Optimal Vector Balancing for Zonotopes","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-05-25T02:16:00.467522Z"},"links":{"cited_paper":"/paper/2508.03961","citing_paper":"/paper/2605.23866"},"observation_digest":"sha256:7a7df3b87453e50eff4568b17cbe95f6d31b51f25f7e1424c0db20df99511215","observation_id":"00fcd006-e8f8-4bd6-a1df-363caef5ff3b","resolution":{"observed_at":"2026-05-25T02:16:32.888098Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"cited_work":{"arxiv_id":"2508.03961","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.03961","snapshot_observed_at":"2026-07-03T23:39:04.788099Z","title":"Bansal and H","venue":null,"work_id":"5833ce4b-1430-40f7-b2c9-7da8960b7afc","year":2025},"citing_paper":{"arxiv_id":"2606.17991","last_updated":"2026-06-16T14:42:12Z","snapshot_observed_at":"2026-08-12T13:52:26.944889Z","submitted_at":"2026-06-16T14:42:12Z","title":"Greedy Vector Balancing","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-06-26T21:50:30.086697Z"},"links":{"cited_paper":"/paper/2508.03961","citing_paper":"/paper/2606.17991"},"observation_digest":"sha256:2a221c4fa7cf52c0f6e11a4f7d037ab5f6dd290fd6e59989dd53009f02949823","observation_id":"0be28816-e7ff-427c-953f-55dfbdadf10f","resolution":{"observed_at":"2026-07-03T23:39:04.790617Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.03961","snapshot_observed_at":"2026-08-02T02:55:26.533794Z","title":"Bansal and H","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.14238","last_updated":"2026-07-15T18:01:43Z","snapshot_observed_at":"2026-08-20T06:27:26.917711Z","submitted_at":"2026-07-15T18:01:43Z","title":"Online Beck--Fiala Down to Logarithmic Sparsity","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T02:55:26.533794Z"},"links":{"cited_paper":"/paper/2508.03961","citing_paper":"/paper/2607.14238"},"observation_digest":"sha256:a08d6a2b2394dc49e8928e329d947898488a003b8c2ff2aa21bbc85d5d94c3f6","observation_id":"86eb93b7-3032-4d07-bd4f-65c1115633cb","resolution":{"observed_at":"2026-08-02T02:55:26.533794Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.03961","snapshot_observed_at":"2026-08-16T00:18:05.896158Z","title":"Bansal and H","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2608.12490","last_updated":"2026-08-12T18:10:45Z","snapshot_observed_at":"2026-08-19T11:35:32.091779Z","submitted_at":"2026-08-12T18:10:45Z","title":"Online balancing of vectors with small coordinates","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T00:18:05.896158Z"},"links":{"cited_paper":"/paper/2508.03961","citing_paper":"/paper/2608.12490"},"observation_digest":"sha256:8f67fd8a342c2260588747bb5009377895a04b035b5a49ce819aab33e2be2b0f","observation_id":"708fe371-2a20-432d-be73-26eac1d8a3bc","resolution":{"observed_at":"2026-08-16T00:18:05.896158Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2508.03961/citation-record","integrity":"/paper/2508.03961/integrity","json":"/paper/2508.03961/citation-record.json","paper":"/paper/2508.03961"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T01:07:50.818132Z","title":"Spectral independence in high-dimensional expanders and applications to the hardcore model","venue":null,"work_id":"b7e9075e-a7c9-4efc-a0be-e7daee4af55d","year":2020},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:35.952093Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:877d109391687ac11a4f54fa6a07637f65480211c791e2427582307727510997","observation_id":"6f6699a5-6702-42ca-95f0-8a610f3372bd","resolution":{"observed_at":"2026-08-06T01:07:50.880832Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:50.638926Z","title":"Liu, and Mehtaab Sawhney","venue":null,"work_id":"5c4fdbba-87e6-48b7-be9e-8634c9edaef3","year":2021},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.031543Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:2dce07b2634f1f99dd8ec443e248984f7f69835c9cebdf77932589aa64ca2b1e","observation_id":"940b9dba-2041-4850-b1bf-4a3ba6d02ac0","resolution":{"observed_at":"2026-08-06T01:07:50.735261Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:50.465858Z","title":"The discrepancy of random rectangular matrices","venue":null,"work_id":"10ff6dee-28ac-49be-9f61-3c6480d9899c","year":2022},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.076792Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:d96845e54950c2c108df912702a1386b8796534619a6840b1c502d8a3df3f67a","observation_id":"2e5576bb-454d-484e-bb2a-8c08236e4819","resolution":{"observed_at":"2026-08-06T01:07:50.561019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:50.257356Z","title":"Balancing vectors and G aussian measures of n-dimensional convex bodies","venue":null,"work_id":"e3339efc-6e41-4fd8-aae8-dc037ead7170","year":1998},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.116216Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:9d06cf28de28cec04dcbc1dec48647485216207d884cd240b47144c92b3f560e","observation_id":"2ec3adc6-d591-4dec-ba26-6e2cb164a4bd","resolution":{"observed_at":"2026-08-06T01:07:50.359620Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:50.105427Z","title":"Constructive algorithms for discrepancy minimization","venue":null,"work_id":"10b74f25-11a1-41b8-8c8f-ff045d515735","year":2010},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.188088Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:06159fc75eeb18982dbae351933a56cd1799fc8510fff18b12048b6be08b4ce6","observation_id":"ab014e59-a013-42c3-936a-de07ddcb1437","resolution":{"observed_at":"2026-08-06T01:07:50.153688Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:49.917616Z","title":"On series of signed vectors and their rearrangements","venue":null,"work_id":"7da00c64-0024-46fb-819f-3ca344b458e0","year":2012},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.259848Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:5227ddeffc5ca6069b9b1541db9d46b40e59a57148026f044dcf0f5b70da9921","observation_id":"57bc454c-949e-47ba-b48d-b15cea2eb55d","resolution":{"observed_at":"2026-08-06T01:07:50.022151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:49.734546Z","title":"Discrepancy theory and related algorithms","venue":null,"work_id":"82778c49-aaca-4279-a36f-c939917074ef","year":2022},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.300833Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:8d773777a039e4463bdecac9e60359f65fea5d7bb36be5f4bc993004ac9c0a03","observation_id":"142071ab-f478-4c7f-818b-20f6382337cc","resolution":{"observed_at":"2026-08-06T01:07:49.805597Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:49.499581Z","title":"On a generalization of iterated and randomized rounding","venue":null,"work_id":"19e8b67c-c34e-43a2-b8cd-3200f7759711","year":2024},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.374785Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:ee42b74dbdf62f96188b98fb11368a47e72d471301168f3c2277af7eed9ad156","observation_id":"1f77b336-af4a-4f42-a3d1-a121e96e82ee","resolution":{"observed_at":"2026-08-06T01:07:49.617519Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:49.180451Z","title":"An algorithm for K oml \\'o s conjecture matching banaszczyk's bound","venue":null,"work_id":"a0fce466-5431-4794-a14b-33fe1edb3665","year":2019},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.431766Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:51fa035b6834ef6ecaa66430b0d49aad3e3cc30c6468da7c3a950c05851ddb97","observation_id":"c2cd1441-9252-4b2a-9f31-c61fe41dc077","resolution":{"observed_at":"2026-08-06T01:07:49.336072Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:48.862278Z","title":"The Gram-Schmidt walk: a cure for the Banaszczyk blues","venue":null,"work_id":"b0512b22-3ea1-462e-b3c5-6ec69b260cd5","year":2018},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.493940Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:486a31f1969143fb8a9438ea19e08565cbbea83426d5333eefa9bde43fc08ff7","observation_id":"67a3d905-0583-458e-9d04-1adb58df9865","resolution":{"observed_at":"2026-08-06T01:07:49.014355Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:48.682912Z","title":"Roth’s estimate of the discrepancy of integer sequences is nearly sharp","venue":null,"work_id":"e41dc4c1-db54-4e5c-8217-c8700915ba52","year":1981},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.552785Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:6c2514c4a1e94ea5148fa65f0b79119c6daaffad3ae7c0409a94c94bdd03187c","observation_id":"ec7082de-15a2-4207-8a66-e06992127f55","resolution":{"observed_at":"2026-08-06T01:07:48.750757Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:48.599014Z","title":"I nteger-making","venue":null,"work_id":"e091c4fe-a6f0-4ce0-b6ea-90f8d0c9c6ec","year":1981},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.606977Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:657003148dbbbe53483bee1cb778fa830f3822d32574d74155e252a5603b774a","observation_id":"f5f4cab7-44b1-48c3-8069-e1b77415efed","resolution":{"observed_at":"2026-08-06T01:07:48.671816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:48.424194Z","title":"Algorithmic discrepancy beyond partial coloring","venue":null,"work_id":"cfb22101-4774-44e2-b2db-be9be56b157e","year":2017},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.675295Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:d7bfe658d58cb51e87cdbd501b1c79f247817489d9dc3ace83500a76fc735560","observation_id":"6095ec0c-8d88-4236-b6a6-2dc03ca83ac7","resolution":{"observed_at":"2026-08-06T01:07:48.488258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:48.312499Z","title":"A note on the beck-fiala theorem","venue":null,"work_id":"7f306374-f213-45a1-8a2a-d2c57ea8e77c","year":1997},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.729489Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:83f8bc272fc61c2a1cc550b7236f2da8845e288acee984cdc8e02aa5708574a3","observation_id":"4798c925-99a9-4004-8e8f-216e1ed1fb94","resolution":{"observed_at":"2026-08-06T01:07:48.356296Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:48.169422Z","title":"An improved bound for the Beck-Fiala conjecture","venue":null,"work_id":"17e81d75-8d4e-4d8c-a024-7c32a97a1fe4","year":2025},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.769329Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:92fb1ab06b7b8f7680b9935380a9d5a3f7f059306682f9bc6284f9be132e6d4c","observation_id":"8e2e52ef-cd1b-4a06-82ad-bfd28001dd5f","resolution":{"observed_at":"2026-08-06T01:07:48.249193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:48.024782Z","title":"Quasi-Monte Carlo Beyond Hardy-Krause","venue":null,"work_id":"45a1ce5e-0afc-414a-b6dd-6d3014dbbfb3","year":2051},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.846425Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:d8e72680fd7baf6be8c822608797aac10ebe5784b54478f7e494f12e2f91f4a6","observation_id":"9ab6aaab-a7b7-45ce-a16a-3f07bb277add","resolution":{"observed_at":"2026-08-06T01:07:48.068026Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:47.922841Z","title":"Smoothed analysis of the Koml \\'o s conjecture","venue":null,"work_id":"11613950-7602-4d26-b1b1-d9f7afd1ac4e","year":2022},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:36.962691Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:858e4697622b58c074906fc3fcd5b78ad449b97b879f534c22a0f1a625854f69","observation_id":"395bb557-3624-49c6-9030-5ea61d738f0a","resolution":{"observed_at":"2026-08-06T01:07:47.971936Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:47.808571Z","title":"A unified approach to discrepancy minimization","venue":null,"work_id":"7e2e8fdf-5166-42c5-b3dc-617f019e008f","year":2022},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.048570Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:e66296b0f4ced7115581915baecc6b4f097e4a2166cfaa2fac78523db8951a6f","observation_id":"4d9da518-0312-48fa-b26b-c488a36b2bfe","resolution":{"observed_at":"2026-08-06T01:07:47.870130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:47.710708Z","title":"On the discrepancy of random low degree set systems","venue":null,"work_id":"f0fa36f4-182e-4fbe-98d9-e2959f0bb7eb","year":2020},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.141193Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:9ccf1ff8e90ea109f6f61d773a875b5cd8c71cd829cd119bf45b1424e03df340","observation_id":"6069641a-9fa7-46a8-9223-72da0d295979","resolution":{"observed_at":"2026-08-06T01:07:47.740421Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:47.582933Z","title":"Cover-decomposition and polychromatic numbers","venue":null,"work_id":"5a3b867b-0950-4cbe-9d34-1ad4a8ca32b5","year":2013},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.223185Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:a1b05f08e1ba1e65af8e120fdeae8b1649167f04ae8108c02fadc369368f5065","observation_id":"081da856-be2b-4dbc-a5a6-f93cd1746e76","resolution":{"observed_at":"2026-08-06T01:07:47.637879Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:47.428494Z","title":"Flow time scheduling and prefix Beck-Fiala","venue":null,"work_id":"10209b1a-0906-4d7b-b3ec-b00335bb86f2","year":2022},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.315901Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:4f6b86ac5beaaede044d47b5659d4ef9c39fc1d975be0296c4c9270dbfe12585","observation_id":"a3020aa7-8e6c-40c0-ba65-26787552306b","resolution":{"observed_at":"2026-08-06T01:07:47.484722Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:47.183301Z","title":"Deterministic discrepancy minimization","venue":null,"work_id":"0a8e2e44-ca27-4406-9be0-ebbe203085b0","year":2013},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.366184Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:4facb63cfedeac18645aa5f1074cf38940e88c2a86b8f77892b2c0abd75c02c7","observation_id":"387d490a-cb26-4513-b806-b01f00b021d3","resolution":{"observed_at":"2026-08-06T01:07:47.285928Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:46.993090Z","title":"An improvement of the beck--fiala theorem","venue":null,"work_id":"27c87c60-38fc-4ba9-9dd1-74717381c808","year":2016},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.423875Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:1b7555e271b94e8a53a9c2bcdc15a222f036585014265d58f4ca5de7a98bcd3b","observation_id":"9b4f6994-b37a-4795-b9ca-eb98b1f3082a","resolution":{"observed_at":"2026-08-06T01:07:47.070862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T01:07:37.504656Z","title":"The Discrepancy Method: Randomness and Complexity","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.504656Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:9aa6bc6aeb531de64fa7b11983fec2b7f44df1d325fa78f6399c6ed464471725","observation_id":"fff6fd37-5291-44d8-9454-0258f1d40377","resolution":{"observed_at":"2026-08-06T01:07:37.504656Z","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":"2026-08-06T01:07:46.846216Z","title":"A quasi-monte carlo data structure for smooth kernel evaluations","venue":null,"work_id":"10110fb8-cb9d-4759-9939-95f13f5dc3d3","year":2024},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.591828Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:4d04f7da878039dfbc486a6d0f6acf4e3c1c00e62088a19c3830bdd66f5eb71e","observation_id":"e86710e1-9616-40f3-ab23-960594c80f48","resolution":{"observed_at":"2026-08-06T01:07:46.896916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:46.737053Z","title":"A note on norms of signed sums of vectors","venue":null,"work_id":"f8c44725-b4f7-4325-9652-905575426a9e","year":2021},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.649077Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:11474f7c6dfe0ba1b7b1c55756c83442e8bf33f2636e4febd687966256bae996","observation_id":"2a34f47a-311e-4c49-b0ba-89155e4a91cc","resolution":{"observed_at":"2026-08-06T01:07:46.776032Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:46.570947Z","title":"A panorama of discrepancy theory , volume 2107","venue":null,"work_id":"6f1797d1-254d-48dd-85e2-132376cad6dc","year":2014},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.787403Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:28a4e4c860892460c85b5a7cc343f66ed59be4bea2989131b4c449ae6f7a704f","observation_id":"546e1384-d3c2-43af-b054-f75ef75d5372","resolution":{"observed_at":"2026-08-06T01:07:46.672166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:46.359920Z","title":"Towards a constructive version of B anaszczyk's vector balancing theorem","venue":null,"work_id":"f0145ed9-fd87-469c-8de0-80a6bd734840","year":2016},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.873513Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:ded81d9fdd6e7b2564ec1ad4c02e0b7bf50981effb7950ceadf7264630e75e3d","observation_id":"7b89c9f6-cc53-4222-a9ff-bddc8d4c8e1c","resolution":{"observed_at":"2026-08-06T01:07:46.464391Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:46.086977Z","title":"On the beck-fiala conjecture for random set systems","venue":null,"work_id":"d140417e-3e30-4132-81a1-626138fc7405","year":2019},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:37.946505Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:050eb8d3348914e384e85785e5d13b70687748de1342f66faa19370d0b76503a","observation_id":"40d9f025-c165-4aad-aa85-f3e99026356d","resolution":{"observed_at":"2026-08-06T01:07:46.235188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:45.912494Z","title":"Efficient algorithms for discrepancy minimization in convex sets","venue":null,"work_id":"b8b0425e-9d84-44b1-aa27-d524e16e279e","year":2018},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.029357Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:5111e4fcd5eb358b550597a81b66b3b69ec61cc1fb6aa8e8557eefc9c662c45f","observation_id":"a73e657b-a652-4fa3-9658-57d4483dcaa3","resolution":{"observed_at":"2026-08-06T01:07:45.998574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:45.678062Z","title":"On the discrepancy of random matrices with many columns","venue":null,"work_id":"4f92b735-ec58-4064-81d0-33b8da786679","year":2020},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.126037Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:87302fdda9e1b5338784689ec0dd184345f3406031c58ea9168b3794772c78b5","observation_id":"9708f37a-5cc7-49a5-b1bc-31b81821145f","resolution":{"observed_at":"2026-08-06T01:07:45.782449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T01:07:38.199829Z","title":"Extremal properties of orthogonal parallelepipeds and their applications to the geometry of banach spaces","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.199829Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:dc7185ca8a24520020cb8b243919ffc1833eaa99144dce079d5a353e65113b47","observation_id":"b6594846-09af-43f9-a00a-4cab25bfe17b","resolution":{"observed_at":"2026-08-06T01:07:38.199829Z","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":"2026-08-06T01:07:45.505023Z","title":"On a conjecture of k \\\"o mlos about signed sums of vectors inside the sphere","venue":null,"work_id":"15074c21-bb8f-4d0b-b8ae-1567cdb3660d","year":1988},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.252909Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:adc57fdd61486d1a7cbc370703a08ab1bdbf64509e16920a1fa551af46f5a49b","observation_id":"e57ba9c7-3ce3-4530-b242-cc148fc02d22","resolution":{"observed_at":"2026-08-06T01:07:45.584119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:45.322887Z","title":"A note on the discrepancy of matrices with bounded row and column sums","venue":null,"work_id":"1d3227ee-7992-480b-86c2-0b062eee3463","year":2015},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.368755Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:4058db1dc8852f0bb8c6738915bd285446a4e4454860cf7355182580a428763e","observation_id":"3f6adbd2-3136-4331-abb4-a2de296694c6","resolution":{"observed_at":"2026-08-06T01:07:45.410545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:45.072949Z","title":"On the beck-fiala theorem","venue":null,"work_id":"374f21e5-5557-480c-85fe-bead827f0162","year":1999},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.448316Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:efb06bf91c9d36ccf113f56afee0a44d985bf5718921bc9c0c1badd421d3fcd0","observation_id":"1bd3b042-3873-4053-a4af-5b8b23723fd8","resolution":{"observed_at":"2026-08-06T01:07:45.197461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:44.921589Z","title":"A fourier-analytic approach for the discrepancy of random set systems","venue":null,"work_id":"2e0d8eed-29a8-40d0-9d44-4aef54fe01f2","year":2019},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.525155Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:0b3f83ceef1dc5f7bafb5ce625da300b49ac8afe86f70c73d97601b36ee1db74","observation_id":"b3f39b44-a166-4951-9016-6055dafd5a2f","resolution":{"observed_at":"2026-08-06T01:07:44.981048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:44.726185Z","title":"Discrepancy without partial colorings","venue":null,"work_id":"8d9d29e4-9533-40a1-9a49-4f3d1b0453fd","year":2014},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.603977Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:83e73427e46c7d2179070cc31223e9f2089019e7a26b744f0a772817599d5237","observation_id":"0acc5435-46e9-47b5-8564-891c92917785","resolution":{"observed_at":"2026-08-06T01:07:44.807949Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:44.598057Z","title":"Balancing covariates in randomized experiments with the G ram-- S chmidt walk design","venue":null,"work_id":"816ae3f6-ff41-4750-952b-36c518b9aee8","year":2024},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.718187Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:5900abccf923934f35280046a3d1f920b200b5331e65e7469b7855904b0a5093","observation_id":"1386a9fd-2abc-4a06-924a-7312044b9a81","resolution":{"observed_at":"2026-08-06T01:07:44.655079Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:44.457723Z","title":"Spencer's theorem in nearly input-sparsity time","venue":null,"work_id":"599e7d0a-0b6c-41a7-b421-f4f539d0f55c","year":2023},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.809861Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:62f3d88ca7732fd4adcc0de693c57fdf8e85fbf145c7c4801410a99edd6f0392","observation_id":"1eb7668d-aa42-4edf-8e38-4eded344cb8a","resolution":{"observed_at":"2026-08-06T01:07:44.518035Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:44.277222Z","title":"Personal Communication","venue":null,"work_id":"9416ac97-f563-4396-a5ce-7e0230bb2f9c","year":null},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:38.908867Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:d0f63998fc67c5b19fcf3f7b477355efcdfa25906e7c9f69e2910a7c8bfac9b6","observation_id":"8feed8cc-665b-471e-ac05-82076f953329","resolution":{"observed_at":"2026-08-06T01:07:44.340267Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:44.120300Z","title":"The discrepancy of unsatisfiable matrices and a lower bound for the koml \\'o s conjecture constant","venue":null,"work_id":"67f60c44-9895-4182-b594-4242913f5c90","year":2023},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.001298Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:d81be4448f64e3dacfaf94e43a76b5551bb248a3800e6563f0e993be8d3c955f","observation_id":"a50fa6b1-8087-4cd8-a759-49301512f168","resolution":{"observed_at":"2026-08-06T01:07:44.176183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T01:07:39.093172Z","title":"Constructive discrepancy minimization by walking on the edges","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.093172Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:79237362bbf342600cdf4f9e91ee379ae79f348b3e58371327bec51440ba4b0b","observation_id":"15326b82-aca0-4e60-a008-a66758554387","resolution":{"observed_at":"2026-08-06T01:07:39.093172Z","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":"2026-08-06T01:07:43.950276Z","title":"Deterministic discrepancy minimization via the multiplicative weight update method","venue":null,"work_id":"373f76c4-2635-44a9-96ec-bf792b4eea27","year":2017},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.167933Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:0978301152cd070c81ac18ae04e439420ff234bbafe3ade6e560095a870b36f9","observation_id":"c9c75080-e64f-4879-8b3e-aa140f166827","resolution":{"observed_at":"2026-08-06T01:07:44.043550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:43.796273Z","title":"Geometric discrepancy: An illustrated guide , volume 18","venue":null,"work_id":"e4dd5a8f-1bba-4129-b969-e4e89f570e9e","year":2009},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.266852Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:708dd389da4788312a4bf02b7acd1ee4cd5ea597d773a10f68d3464565740d57","observation_id":"1069e23a-7b7f-47e8-87d4-d3d58a2bfd3e","resolution":{"observed_at":"2026-08-06T01:07:43.864071Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:43.616959Z","title":"Combinatorial discrepancy for boxes via the _2 norm","venue":null,"work_id":"eb11e54e-4224-44b1-a758-3a502c74bbd9","year":2015},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.377122Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:c612a0dd95390f3001c52845cb46ea8b6197c3e16a0819fe505c5e670feccceb","observation_id":"1c2109ef-82f3-42e5-b9cf-8d029ac73ef2","resolution":{"observed_at":"2026-08-06T01:07:43.709610Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1301.4039","last_updated":"2013-08-01T20:57:05Z","snapshot_observed_at":"2026-08-15T00:32:17.451666Z","submitted_at":"2013-01-17T10:42:53Z","title":"The Komlos Conjecture Holds for Vector Colorings","version":2},"cited_work":{"arxiv_id":"1301.4039","doi":null,"metadata_source":"pith","pith_arxiv_id":"1301.4039","snapshot_observed_at":"2026-08-06T01:07:40.804724Z","title":"The Komlos Conjecture Holds for Vector Colorings","venue":"math.CO","work_id":"7ed2a1b9-1cdb-4cfc-b18e-ba28fb12eb29","year":2013},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.478362Z"},"links":{"cited_paper":"/paper/1301.4039","citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:62149870076c7364abde99403d7f562073034b3bf6778b4f1facd35d2b32225c","observation_id":"ec45244d-c043-4484-b9fc-67e91bee7986","resolution":{"observed_at":"2026-08-06T01:07:40.854869Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:43.478398Z","title":"Tighter bounds for the discrepancy of boxes and polytopes","venue":null,"work_id":"562c27ab-8442-4e89-8c3b-af94e4f71135","year":2017},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.571956Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:ecfc1af70e69624506f66c674b773d4e0e2ffbffec887566362507fbccc16bdd","observation_id":"4d482b9e-9236-463a-be24-ebafa40fb9d1","resolution":{"observed_at":"2026-08-06T01:07:43.549626Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:43.327402Z","title":"Beck's three permutations conjecture: A counterexample and some consequences","venue":null,"work_id":"bcdf4610-2796-4880-a6f5-c6ea4b297dde","year":2012},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.639287Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:f402a7101448548e6b0fb2640abd9f993e671b8277125cae967f88e59b7273e0","observation_id":"e7fd8d8d-df1a-49eb-91d9-730c2a1475fe","resolution":{"observed_at":"2026-08-06T01:07:43.377151Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:43.147045Z","title":"The geometry of differential privacy: the sparse and approximate cases","venue":null,"work_id":"4d35ca40-e0fa-4c1e-a3cf-6c5e8e0a0b49","year":2013},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.748454Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:28945e39f178bacb81316d1ca5f2401d9a3ee6519b3ee6d31b56fb67e505c4e8","observation_id":"ff9e0311-5e1d-4b91-abe6-d6c221ae2e5c","resolution":{"observed_at":"2026-08-06T01:07:43.238874Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:42.851571Z","title":"A spectral bound on hypergraph discrepancy","venue":null,"work_id":"83c75429-4107-40d8-8c12-4e6f008fcf76","year":2020},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.849491Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:d3b43759925d0e5f2def438086ef6494af3b6a6c152332b9196cc442118f5a83","observation_id":"a8785d33-b19a-4ef9-8e74-155af6ac5eca","resolution":{"observed_at":"2026-08-06T01:07:43.010544Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:42.573718Z","title":"Near-optimal coresets of kernel density estimates","venue":null,"work_id":"8c3d7167-808d-4e45-9c26-e61d282d5df0","year":2020},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:39.922419Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:12c630e06dc5e7e462d68660630c954ffd554dd9f1e2abbb480ccfb5082d4de8","observation_id":"12a6c73e-a76d-4a5a-b5e9-73ee99740cc9","resolution":{"observed_at":"2026-08-06T01:07:42.703941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:42.321594Z","title":"Discrepancy minimization via regularization","venue":null,"work_id":"0178caa8-6684-4af6-a655-0538ebbf34db","year":2023},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.029449Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:b357742ad1ec62226b073661d9a91e08bd3532c51625079372e26526bb03b53a","observation_id":"fcc60386-68f0-4e1c-a9d8-27ca128e96e9","resolution":{"observed_at":"2026-08-06T01:07:42.434977Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:42.072094Z","title":"Better bin packing approximations via discrepancy theory","venue":null,"work_id":"e722913c-23a6-43a6-8279-bd29f2531a2f","year":2016},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.120326Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:ff2e7d175d7031fb1e42771485a93149830bc063bceb94e8e2cb3d9d178400e4","observation_id":"91afb779-7d82-471e-9a66-b4f947749914","resolution":{"observed_at":"2026-08-06T01:07:42.168017Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T01:07:40.223583Z","title":"Constructive discrepancy minimization for convex sets","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.223583Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:ac03954cb882927b9af779350e02bed77747f74d4a33e3b5969f398db29ad102","observation_id":"f4d7b2c2-a592-4ace-a4d3-2d9ea59eac0b","resolution":{"observed_at":"2026-08-06T01:07:40.223583Z","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":"2026-08-06T01:07:41.860644Z","title":"Linear size sparsifier and the geometry of the operator norm ball","venue":null,"work_id":"33c605cd-3e98-4ef7-92b1-343540962a74","year":2020},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.321968Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:9455ef3a48341b7527e8960f90bba742ee1b895b08a9c77272319b5a68e3cd1b","observation_id":"c3aad13c-33b0-45d9-b102-92c7fa17baef","resolution":{"observed_at":"2026-08-06T01:07:41.939631Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:41.667718Z","title":"Six standard deviations suffice","venue":null,"work_id":"5efd8b32-7be4-43b1-90d0-33779b48c7e3","year":1985},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.435617Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:1faa19ccfad07dde7363c564a8ee401f4e7a21412b6502f159ac9c2dd2f1c5cc","observation_id":"e588fe5d-b5fd-42d2-8946-a77dc0c6247d","resolution":{"observed_at":"2026-08-06T01:07:41.770932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:41.431587Z","title":"Improving the discrepancy bound for sparse matrices: Better approximations for sparse lattice approximation problems","venue":null,"work_id":"9100061b-ba13-4f79-8ff1-2770b7833304","year":1997},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.525611Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:268efe0e221a9e0ea8e8198b34a49a5a539747530af3af7ec18a08b3979de0a4","observation_id":"6809d514-01d8-4ab1-9268-b595f84456f2","resolution":{"observed_at":"2026-08-06T01:07:41.554746Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:41.210970Z","title":"The E rd\\\"os discrepancy problem","venue":null,"work_id":"51884db8-19cd-4a0b-88f4-e51f6369d478","year":2016},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.581758Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:32e65d73612a2b82256130f90fdd02c387e00000d6402f7f5b5908cb982e30fc","observation_id":"c9f1a975-fbcb-492d-a49a-70a76e109453","resolution":{"observed_at":"2026-08-06T01:07:41.299336Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-06T01:07:40.979717Z","title":"Balancing gaussian vectors in high dimension","venue":null,"work_id":"5c324859-c260-4235-8a58-90b766cda282","year":2020},"citing_paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk","version":2},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-06T01:07:40.686676Z"},"links":{"citing_paper":"/paper/2508.03961"},"observation_digest":"sha256:7719209f2c031d3cfe4607ad195367f3433da5bbe6a8dcfba935e81706f6a8d5","observation_id":"215f4539-d44d-4b1c-bb51-2ac0606b4087","resolution":{"observed_at":"2026-08-06T01:07:41.114114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.03961","last_updated":"2025-09-09T16:50:49Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-06T01:07:28.179814Z","submitted_at":"2025-08-05T22:54:28Z","title":"Decoupling via Affine Spectral-Independence: Beck-Fiala and Koml\\'os Bounds Beyond Banaszczyk"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":1,"verified_fuzzy":54},"total_outbound_references":59},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 6 inbound Pith citation observations for arXiv:2508.03961."}