{"as_of":"2026-08-20T06:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:137d547019b4046b6f9769ab2f9594e100d85e6885ede5c91d9662bc83ad4025","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T17:44:49.595953Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2411.12399/citation-record","integrity":"/paper/2411.12399/integrity","json":"/paper/2411.12399/citation-record.json","paper":"/paper/2411.12399"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2303.06738","last_updated":"2023-03-12T19:43:50Z","snapshot_observed_at":"2026-08-20T03:00:13.301635Z","submitted_at":"2023-03-12T19:43:50Z","title":"On sharp isoperimetric inequalities on the hypercube","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.06738","snapshot_observed_at":"2026-08-12T17:44:49.462208Z","title":"Beltran, P","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.462208Z"},"links":{"cited_paper":"/paper/2303.06738","citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:393c5977c0be87cb4fd4cb0d0b273d878da6ebe78811d156443d543da34be29e","observation_id":"c04130da-45a5-4fa8-a89f-8ab8b260c7eb","resolution":{"observed_at":"2026-08-12T17:44:49.462208Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.00224","last_updated":"2024-08-30T19:27:47Z","snapshot_observed_at":"2026-08-19T22:14:34.376622Z","submitted_at":"2024-08-30T19:27:47Z","title":"Geometric influences on quantum Boolean cubes","version":1},"cited_work":{"arxiv_id":"2409.00224","doi":null,"metadata_source":"pith","pith_arxiv_id":"2409.00224","snapshot_observed_at":"2026-08-12T17:44:49.953629Z","title":"Geometric influences on quantum Boolean cubes","venue":"math.FA","work_id":"2385b79d-ba4b-49b9-9100-6f95d25aae4f","year":2024},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.469429Z"},"links":{"cited_paper":"/paper/2409.00224","citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:e7a288918d34b8328095b636fb860b82e87fefe86326eb196d8d6e12aa327a15","observation_id":"5fb29739-ce5c-44f5-9eab-cd873cf7601d","resolution":{"observed_at":"2026-08-12T17:44:49.961688Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.349840Z","title":"Bourgain, J","venue":null,"work_id":"cb7b1f48-52d0-4f2f-81cd-ef58c5d90b19","year":1992},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.476292Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:661254995e21b7d4567b8ffd2316d907daa51f81dd019baee9b14ce16d8f7e53","observation_id":"77463b3b-7641-40e8-8774-050c9cee255f","resolution":{"observed_at":"2026-08-12T17:44:50.354694Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.328636Z","title":"Carlen and H","venue":null,"work_id":"2e15fb97-e0ca-4329-b2a3-20072a9542e0","year":1993},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.482516Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:d20c876c91bdf77ebe33a64154a3e805a1fc0a656808dd8ebc921b111b067da7","observation_id":"369cb150-28b3-40db-af90-4911da5ab6fd","resolution":{"observed_at":"2026-08-12T17:44:50.333758Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.308562Z","title":"Cordero-Erausquin and M","venue":null,"work_id":"c2f8cab4-02f5-4336-9caf-4b059c8e8f38","year":2012},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.487554Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:31240b095786a0e8b213b22b520928df0ec08c7ba97cd55ded67c638118b2ebe","observation_id":"7c4988bf-8cbc-42a4-afbf-6bafdc608dca","resolution":{"observed_at":"2026-08-12T17:44:50.313858Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.292849Z","title":"Eldan and R","venue":null,"work_id":"d41363dc-d6cd-4705-a224-07c372cbd75f","year":2020},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.492501Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:f9716e8fbfb5e8b8f44412cedbb42fb7e0e06dcf799fc0d8c2698ee489863e91","observation_id":"95c3aff5-4f58-49c4-8f11-7b9a76d1292c","resolution":{"observed_at":"2026-08-12T17:44:50.297849Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.277181Z","title":"Eldan and R","venue":null,"work_id":"7f647221-31f9-4969-8041-8eb69d79fce5","year":2022},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.498163Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:a529e06b011990cb7d7dfafb6790cfacd96b2d57f1c6044de5e675865150eeb9","observation_id":"ca5d37db-5d2a-4714-9b83-642637858f63","resolution":{"observed_at":"2026-08-12T17:44:50.282682Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2204.06686","last_updated":"2025-07-21T12:01:37Z","snapshot_observed_at":"2026-08-16T17:07:03.813788Z","submitted_at":"2022-04-14T01:11:05Z","title":"Isoperimetric Inequalities Made Simpler","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2204.06686","snapshot_observed_at":"2026-08-12T17:44:49.503582Z","title":"Eldan, G","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.503582Z"},"links":{"cited_paper":"/paper/2204.06686","citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:9a2bb4adf9052c436803a0f2f6e71693b41bdf0c23420c8c62c1b91a741a52b2","observation_id":"fae65dff-682f-40e7-8868-97cdaef0b6c3","resolution":{"observed_at":"2026-08-12T17:44:49.503582Z","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":"2026-08-12T17:44:50.260077Z","title":"Gross, Logarithmic Sobolev inequalities , Amer","venue":null,"work_id":"66efaede-4336-4122-9b96-c957c623d22d","year":1975},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.512909Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:2ab75c5a0dd0753f9e247b83a4d51f9658f4baf53e02e1262834f079c9ced46e","observation_id":"240123d6-2543-4248-b7f8-04f6187f1e19","resolution":{"observed_at":"2026-08-12T17:44:50.266202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:49.518900Z","title":"Ivanisvili and H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.518900Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:79e7fe3980811c2c4e39a35da5337aa2fdd6c16e94fd6320c3607abd04843695","observation_id":"4aab387f-8625-4c98-9caf-b41a0ddd2f5a","resolution":{"observed_at":"2026-08-12T17:44:49.518900Z","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":"2026-08-12T17:44:50.241493Z","title":null,"venue":null,"work_id":"4e171b1a-1c9b-46b4-90e7-d592752808f3","year":2025},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.523189Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:96963ea98a2e2942f991697f4cdf6e4e3a474293804f5a3845e0b6b6de97839e","observation_id":"2c4ddac9-7cca-4dd2-b0f0-9158babac40f","resolution":{"observed_at":"2026-08-12T17:44:50.247713Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.216622Z","title":null,"venue":null,"work_id":"cad4ff94-bdfc-40d6-97c0-8ea5e6b9e0db","year":1988},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.528904Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:c56db053a326ded1bb0a2a3b78caae9666565b77ea02219ee2a98c14e4b0ea05","observation_id":"f99bb754-f5ce-4884-a47c-49b6a7148fd2","resolution":{"observed_at":"2026-08-12T17:44:50.220931Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.201827Z","title":"Keller and G","venue":null,"work_id":"9edbea8a-f071-454a-8767-17a5bab50dc8","year":2013},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.533346Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:8113d4d737b1a768007b9670cb8054be27b323b525fbab574e1be917ad734e43","observation_id":"5cc3303d-feaa-4789-a688-eb0e1b84acd9","resolution":{"observed_at":"2026-08-12T17:44:50.205870Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.187881Z","title":"Kelman, S","venue":null,"work_id":"13446d80-981e-4a89-bf58-b881b2ec36ab","year":2021},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.537893Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:80ca73f79d92293dcbec3053047dac71ee45034f224ed7c02c95b315010e5202","observation_id":"d83d8264-4d08-404e-9399-2822ccc67d7c","resolution":{"observed_at":"2026-08-12T17:44:50.192888Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.171146Z","title":"Kelman, G","venue":null,"work_id":"3836bb75-8b5e-492d-b59c-4aa690700bf5","year":2020},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.544099Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:92a692ea82809dfffe2876b8898de227b15e34396470141a83292ab63d8e0f0a","observation_id":"7ba91380-64f5-4970-9153-14687bcf411e","resolution":{"observed_at":"2026-08-12T17:44:50.176834Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.151842Z","title":"Kindler, N","venue":null,"work_id":"30bc9546-722c-433a-ad1a-38075314f54f","year":2018},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.550477Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:00355fc17f6ca96094bfd60ac58138ce58c7bff2d69063ac62db1b4d38e5e280","observation_id":"97beb547-4a4c-49d4-942d-17d9dfeb3f31","resolution":{"observed_at":"2026-08-12T17:44:50.157000Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.137677Z","title":"King, Hypercontractivity for semigroups of unital qubit channel s, Comm","venue":null,"work_id":"04e8fe96-8e36-4e97-9448-9835a67e15ff","year":2014},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.555027Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:9da409835e3263ada6f3b7d3679d1b8a0da93fc94e9f3b0d2c939de3adac2331","observation_id":"77d96f99-6c33-4b20-9c28-f232573688d7","resolution":{"observed_at":"2026-08-12T17:44:50.142992Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.117636Z","title":"Montanaro and T","venue":null,"work_id":"62217c33-0dbb-4b47-a018-5119a97038bf","year":2010},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.559441Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:4a7dae4f28c2020ed17a9709677ec41ee7a240c5657d66028dc34b42678d6591","observation_id":"f1037743-ba69-479f-9ae5-ea7dda379f39","resolution":{"observed_at":"2026-08-12T17:44:50.123214Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.098327Z","title":"O’Donnell, Analysis of Boolean functions , Cambridge University Press, New York, 2014","venue":null,"work_id":"28bcde57-8415-4ffe-906a-108a04797b5e","year":2014},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.563980Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:3fca1d2ca232fbbff124f41b6e94ee2b8041388d0cab3dae94fa41970729444b","observation_id":"6d8df59d-93c1-4e5b-8ade-dd6bfe0c852f","resolution":{"observed_at":"2026-08-12T17:44:50.106144Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.076516Z","title":"O’Donnell and K","venue":null,"work_id":"edc89300-2ff2-452d-aa9b-2ae23a05bd15","year":2013},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.568600Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:0c14b403b445798f2979a43042288ec7f9a82deeea695c24e46d261b7cedb783","observation_id":"c73978ce-a3b7-4ff3-9abb-ceb7ff9a2967","resolution":{"observed_at":"2026-08-12T17:44:50.084272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.061801Z","title":"Rosenthal, Ramon van Handel’s remarks on the Discrete cube , (2020)","venue":null,"work_id":"51e93b41-28cd-45b2-a04b-faaaea7150fe","year":2020},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.575073Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:4e33a22a5fad8610dfc39dedc6fb2945da3e9c440b26bf07f2005c51c05e5529","observation_id":"1c1aa46f-fc5e-4b1c-9a27-b50afdd69403","resolution":{"observed_at":"2026-08-12T17:44:50.066201Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.044745Z","title":"Rouz´ e, M","venue":null,"work_id":"0ad84b00-0074-4422-b27b-37f945f417fe","year":2024},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.580974Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:9d5098c42f02ae41b876e2e9cb19176842bef83d692c8197b449933370d9ba4f","observation_id":"7ca3ea35-cffa-4156-9cd7-9731a47bb3fd","resolution":{"observed_at":"2026-08-12T17:44:50.052709Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.026502Z","title":"Talagrand, Isoperimetry, logarithmic Sobolev inequalities on the dis crete cube, and Mar- gulis’ graph connectivity theorem, Geom","venue":null,"work_id":"dae559ae-be36-4b5f-873b-0177a44a61bd","year":1993},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.586322Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:2860931dac1680834abf47e6976cd7f449bc649e69c245a5c44cc2e4c7ad8669","observation_id":"5109036b-d269-4eb3-bce6-768ccdbeef56","resolution":{"observed_at":"2026-08-12T17:44:50.033906Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:50.011148Z","title":"Talagrand, On Russo’s approximate zero-one law , Ann","venue":null,"work_id":"5062fd63-43af-40ba-8936-14865a43307d","year":1994},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.591438Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:4ba973b478fcfa3fe7a0d1da069c954692e0b8fe88e558265b7958215dba910a","observation_id":"c9143cac-c1e5-47c7-b85b-72a5ac6044dc","resolution":{"observed_at":"2026-08-12T17:44:50.015527Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-12T17:44:49.994248Z","title":"Talagrand, On boundaries and influences , Combinatorica 17 (1997), no","venue":null,"work_id":"266c7219-3932-4300-97ef-c89a90906082","year":1997},"citing_paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-12T17:44:49.595953Z"},"links":{"citing_paper":"/paper/2411.12399"},"observation_digest":"sha256:2ec60be85e0d70aba15ab3d48ae70c1997f327983b4ba819ecb1759216e72913","observation_id":"524a8a33-6c92-4cd6-bc9d-8db82b82e837","resolution":{"observed_at":"2026-08-12T17:44:50.000184Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.12399","last_updated":"2024-11-19T10:35:19Z","latest_version":1,"primary_category":"math.FA","snapshot_observed_at":"2026-08-19T23:19:33.585766Z","submitted_at":"2024-11-19T10:35:19Z","title":"Quantum KKL-type Inequalities Revisited"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":1,"verified_fuzzy":19},"total_outbound_references":25},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2411.12399."}