{"as_of":"2026-08-11T11:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:821f4aa7cdd2fbf80c1f45130f1029b1abf487d4b4b55210ccfe171428d90bf0","coverage":[{"denominator":68,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":68,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T09:27:14.693975Z","state":"measured"},{"denominator":70,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":70,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T07:49:51.266776Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.03561","snapshot_observed_at":"2026-08-01T07:49:51.266776Z","title":"On the saturated cases of the distillability conjecture","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.21367","last_updated":"2026-07-27T03:28:09Z","snapshot_observed_at":"2026-08-08T05:25:08.555193Z","submitted_at":"2026-07-23T14:31:25Z","title":"A solution to 2-copy distillability of Werner states","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-01T07:49:51.266776Z"},"links":{"cited_paper":"/paper/2606.03561","citing_paper":"/paper/2607.21367"},"observation_digest":"sha256:1e602e6dc255dc5590cedad9a89c84424bc89bfff75755cce2d16aa2015d74a2","observation_id":"43dd4031-b0aa-4699-884f-415b18f94800","resolution":{"observed_at":"2026-08-01T07:49:51.266776Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.03561","snapshot_observed_at":"2026-07-31T13:55:58.204204Z","title":"Liu and L","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.24479","last_updated":"2026-07-27T14:14:26Z","snapshot_observed_at":"2026-08-08T05:25:23.350647Z","submitted_at":"2026-07-27T14:14:26Z","title":"Two-copy nondistillability of Werner states: sharp partial-trace inequalities and finite-copy extensions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-31T13:55:58.204204Z"},"links":{"cited_paper":"/paper/2606.03561","citing_paper":"/paper/2607.24479"},"observation_digest":"sha256:4cd569c9bc667d7f0ebb259a28f0d94070165b89b7b93a24ea2824eea66231a3","observation_id":"44d6c3a7-358f-4092-a32a-c717712bb72c","resolution":{"observed_at":"2026-07-31T13:55:58.204204Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.03561/citation-record","integrity":"/paper/2606.03561/integrity","json":"/paper/2606.03561/citation-record.json","paper":"/paper/2606.03561"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:a3b57edd87e685dfdae35a76432b96b795ad19a57999fe945851ddbd2530c12e","observation_id":"6b23a34a-3a29-4574-ad36-21f967d1637e","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:54a2bdb17b73903041d32445b8a6a7bc0a97885d78f58f1a33232a0e979c1cc6","observation_id":"e317aee1-b447-4e4e-950e-13f0254b1a47","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"parse_uncertain"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:da1bd1188c96bbc33d235fe24e0dada7ca80108bb3b9f14769ed902e395b90bf","observation_id":"f5ed1a38-58da-4376-921d-e6f3528f96a2","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:bc5f17d6a6ad4b3c70299788f36e4b7e85c8012ecc8e5a6999022e8c62e523c1","observation_id":"56012bb9-59f4-45ad-a84e-d5ebe22ddf02","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"[ 17] Definition 3","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:1b4ed913f85e5c027aaafc240b329d97f37fb19c9e15ec19ffd789f67fa30dd9","observation_id":"6464a680-5020-4963-ab6d-8f1610989948","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:d534c090f4095ff2534723b34c88bfe35ecabc1dbdd48955dd8489f41084b264","observation_id":"e4efee0c-83d9-4fc0-badf-78498c4b0718","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"(10) Lemma 6","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:bfc40f8f193e7d65883dc2a2f00f6e4b94e47bfb33272e7d5d9f393e35245177","observation_id":"753e535a-4e39-49c8-998f-d72a04a10b68","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Inequality (4) is saturated if and only if rank A = 1","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:2940711bc0887fe6f51acc3e1e804ebd42907e86fe4bb113f20cd44161f756e3","observation_id":"896c1a18-9531-470a-a3c2-89fdbb7ccbd5","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Inequality (4) is saturated if and only if rank B = 1","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:c3ecad468131e49756a1ab3a72a2147d79b39b6c37434019865460db1c44704d","observation_id":"94d2220b-b176-43c8-8c03-35d3176b8855","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:1690675dec92b62090be79cea66d98c5a7c9915b50d8eb904b6b42ee443ca4e7","observation_id":"27c92051-f133-4117-835a-c7aa265e0473","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:e7d455fb2d6927ff9713fe3ac894ab221e2c01c72ec2277caff354a124b91e15","observation_id":"8b3c6a3e-98d5-4a80-9894-4e49a5900be6","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:3f3532a90e8d327489e87f0b5be9c1cf97a84b068cc02ef0fc299f5abcbd2c78","observation_id":"52fc1f31-d6c7-4b5c-8ec8-8076544d3e8c","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:ebb798149e489e93696de895c077f06cbb51af22f978a824f4be763ad3420d6d","observation_id":"1baa6551-3550-444a-ad7f-c56318bd9cac","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"4 Part 1, 2, 3, 4, 5, and 7 of the theorem are respectively supported by Lemma 8, 9, 10, 11, 12, and 15","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:609f4000614ce3e915feaccd1052a6b6e97d1595266d65ff486f380c0f4ae225","observation_id":"b73306f4-a4cd-4116-b0a8-86600b36201d","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:d7bb68601120e5756330728cd1eca0a96a052eee02ba0f8a64479aa2b2cbf20d","observation_id":"1f47bb04-b0be-40fd-a6ef-cfc22e7bf3c2","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"According to equation (53c) of [ 15], σ2 1(X) + σ2 2(X) = 1 2 only if A and B are both normal","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:b0cfa6f0ffe9cec56869729f34a2b7189ab89b7aeffeeb96bb15d0b242ea8949","observation_id":"c7593223-d749-450d-9ffb-787ec437e344","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"According to Lemmas 18 and 19 of [ 15], σ2 1(X) + σ2 2(X) = 1 2 only if A is normal and B is 2 2 block-diagonal","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:eb323c8a01da06ff6cc4d53148470168c31865168923e9e25e7fa3475779c187","observation_id":"cc4a70af-828f-4a70-827f-f1ecb99309c0","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:30c109555d5a567c99551ca7711edb4101b74998504a61a904d20c3e58c8991c","observation_id":"da0d80a7-330a-419e-abd1-021157349cf5","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:36214847f8f2551474d5feb810669176af862931fad624894b8e3757e644919f","observation_id":"1f230c98-9fc6-4312-8054-d7847e74ee3b","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"From these conditions the conclusion follows","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:2522d1d3353efaf7e980f732db8126f6104e4fe078c083b9583870cec736ce3d","observation_id":"0941faa2-c427-4858-a2fe-63ec69d1f244","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:06c0f1d47bd439adf1caeaa9de441c560b2eabc4a2608b51bb79ea0b0219e642","observation_id":"35e78543-c241-4ce2-9c00-f431b9ac731e","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"We can see that in the first case, A is necessarily 2 2 block-diagonal, and so is B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:66131897b88eb4466cd1720a5ea28302bbb209f4d6f10ba246ef247f8299b2e8","observation_id":"373b7f11-5cab-4cf1-b4ec-9823a6bd0629","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:ab92782f211ce041d492fed476f314fe34ed179b54eea4322290ef8fc6a83654","observation_id":"162040c8-d79f-4d57-b58e-f2d0deacf5fb","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Lemma 21","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:023060786548dbd5224431897361fff99b79bdf9d7146fdad97e07719bdac8ed","observation_id":"cffc0fec-656d-494d-8490-4d4a053c3f0f","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:28ccfda691680070331cb59696bfa6ffda210632cfd63b65643039d97ee72be6","observation_id":"06fbf283-f6c2-4c8d-8059-0d4f68e1b361","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"(29) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3355, 0.3355, 0.2821, 0.2821, 0.1841, 0.1841, 0.1548, 0.1548, 0, , 0]","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:637732121d0beae94a5b25ef110a35bd039931f974370c7c20ea96a2b83d5cb0","observation_id":"85603f12-7424-4444-9683-af6eb53169eb","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"(31) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.4251, 0.4251, 0.2632, 0.2632, 0.0044, 0.0044, 0.0027, 0.0027, 0, , 0]","venue":null,"work_id":null,"year":1937},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:b3880cc011f9fa0acbec06ce737e0a8aa789d198015b5d39dc2b725cd22e2b55","observation_id":"3eb17751-1287-45a4-8a68-f08a4c964353","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"(33) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3996, 0.3996, 0.2003, 0.2003, 0.2003, 0.2003, 0.1004, 0.1004, 0, , 0]","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:5e0a1a2c1ceaac8847f3fbd28393804929eca4629f022caac9fd5403e6a2de4d","observation_id":"41fe3b05-9d7d-404d-af63-b9fe515393ce","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"(35) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3586, 0.3586, 0.3001, 0.3001, 0.1358, 0.1358, 0.1137, 0.1137, 0, , 0]","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:eec949e8701efc4ef9a9d313d09dd86b96443f3200fdf6bce780f35e4c6adc0d","observation_id":"80b3f0d6-be9c-44eb-8cc4-f26cb4c2c792","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"(37) • The 16-dimensional vector formed by the singular values of matrix X: [0.5, 0.5, 0.3172, 0.3172, 0.2408, 0.2408, 0.2408, 0.2408, 0.1828, 0.1828, 0, , 0]","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:53b89da860b444d34d57dc81b69f1f2b95c51d543be170228dbc8bc843323078","observation_id":"6506067c-153f-45ad-9bed-f72b18f2552b","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:9fc264e21ebd4b3628fa4227b7237dc8b420af266902f83dc1678c15afed4334","observation_id":"3bcfe5e7-7450-49c4-a240-cac05ce58418","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"In case 1, we claim that a1 = b1 = a2 = b2, ja1j = jb1j = ja2j = jb2j = 1 4 and b3 = b4 = a3 = a4 = 0","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:da53295f6c62c7a4ec93b2bac9bbdcc1643da37a0f1289fdfd585f55862a641b","observation_id":"75bfd2dc-33c4-429d-b014-64fcfbd580f8","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:e5425f9ac87073aef4e5700b200cf77cfdc877760689a67cd8eb0470aa871f4c","observation_id":"f3c2d813-d329-4c05-bb1c-953a18d17a16","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:7ef326e600f72ba17dd0890e750b97a359bc4c7c30c838550ccc9e0484ed1472","observation_id":"ec9105fe-260a-4f09-8ab2-e62adbb432f1","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:b3bcbbb77ddf9f85c3fcb900da48060c2137d0800308833eef2b23a0e1f33d47","observation_id":"721339d2-e01f-4529-b390-ce666d2e3e48","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"parse_uncertain"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:7fcff29b1a356d9e8f4ecdaa6f433e7d06a13cdbbd893305d2b37715b8f263a1","observation_id":"8157d706-f207-4251-9752-64bf8e3bbfa7","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"We can verify that all of the three cases above saturate the original conjecture","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:6380c443b5cd2fd80cf44f6323f8027a54cb869ffccee934e056ad44fd3894d1","observation_id":"e0cd520b-a1bb-4460-87ec-677ee58b3bcf","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:a72dde2bf6849d1a0877b1eb0ffa242eb27e9dffd7d9dc993fa0650168b7cacc","observation_id":"199760a8-642a-43e5-aa02-e37f18f4464b","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Z11 (11) Z11 (12) Z11 (12)∗ Z11 (22) # , Z 22 = Y22Y22 ∗ =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:a7605616f3c1e80f6e7510aa4810ff85815a8094eb6feaa2d96ab95616cc8200","observation_id":"f9125981-e010-4862-a9c5-2d130718533b","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:cfce2a8d5a7f4eeacf0117b56dc2d2bc0dfde1886dc10e94f96654ed5679e803","observation_id":"0a96e221-96e0-4148-bb2d-b6052dcad904","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:ebf122b5da7b57adcea640571f3d0eb44ee436bcb4f8ba3991660332a62ce1c8","observation_id":"75e0efd6-253f-4878-b772-e6a0bd906401","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"W e first deal with case 1","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:839badd9b912678d30ed12802239a9aa91eaef4d06f729a67dc46e972c91661f","observation_id":"2b62e0c6-e547-4398-a4fe-a95412524922","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"(C33) The corresponding maximum eigenvector is a1 b2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:239601ac554530df7d3151cdd5862c2ee00627f34b3fa14f4e474045c7096242","observation_id":"f170f253-3a96-4842-9eb3-48e81c31f9ce","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Five open problems in quantum information theory","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:1b3546a74994205b94a53b128d3333a3badf12110a9c38258ae5e0182e3e1b4f","observation_id":"507300a5-2ed5-4f2b-9adc-0a136aaea4c6","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Inseparable two spin- 1 2 density matrices can be distilled to a singlet form","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:2f4b2d68cfbc8b7d93488277a3f658393f491188892372e312766e4693a331de","observation_id":"f02325bd-bcf0-4976-9f44-7ece991ac7d0","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Horodecki and P","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:a638990516ca7c9fbb4a22622dab5eb10bc44644e2c8f369c5365fe4b4b7ee4d","observation_id":"38943985-e5a2-426e-890e-a3ebf4af835e","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Kraus, M","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:36b3769f9a511861756bbaebf79f072b102979d9c798a4c259397ae27123cba1","observation_id":"ad9f74a3-65b7-4c63-9b2e-263b05b2c8a4","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:f98b31591c58f75bd91974829ce448bc60c9757849e23edd92487a4e9cc4ad78","observation_id":"c01e13bf-4d54-422f-a28f-660fbec73e4f","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:728148a08be6a193c6c2366e3db284860d7a6e94116a84720d315c3e77f5691a","observation_id":"b7659e7b-1b71-4340-9dad-f7d787514dc6","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:f939beb048c069e5ba277528484a3356c195a1a2e5880fbc2729dbf733c270c2","observation_id":"0ffa75f8-4f15-48b8-98d7-c9a1474fe20e","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Classes of n-copy undistillable quantum states with negative partial transposition","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:c8bb6945f7b874c04fcc19626c217c314ede33e96ecaf1fc724fe28abf6a6e52","observation_id":"d83515c4-1154-4756-8244-e30ed1aaba8b","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Devetak and A","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:a4d94fc3f37b67c662748ca3a335e06f0158bec2e515eb71d1b0307a836b62dd","observation_id":"4db2b033-e39e-469c-89fd-60d7345d3539","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Vianna and Andrew C","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:5c519fbcee421da73d29dda56e2c0105dc4535609836647d88abdc3b9e7b6e07","observation_id":"8e7c8dcc-5b2f-4453-a972-a270da7b237f","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Distillability and ppt entanglement of low-rank quantum states","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:657989d0c176fd400d97f68184e8c901df87bdc4dbc5c50d8177e7a6132d846b","observation_id":"d48c3595-75c2-4b22-9f75-e674646c753d","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Rank-three bipartite entangled states are distillable","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:0efd0af30c05cc85a41dd56bb7d973798124dc984f4aeb3401f88893219549bd","observation_id":"f530b472-e71b-4c99-8788-2bb900178778","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Distillability of non-positive-partial-transpose bipartite quantum states of rank four","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:a601fe6020fbeb36719e145cde745ac3bc02869c1773824f906ea60fc331f74d","observation_id":"3f48021c-e033-4525-a25f-ea2b2144ef4c","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"A few steps more towards npt bound entangle- ment","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:a2b7ce1d84eddb9607422054973ad00ff0f55728f3754568325d6593f209d19d","observation_id":"ff0efc84-120e-4c53-bac2-0e3ffffca5c1","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"A matrix inequality for entanglement distillation problem","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:36eb7a60fc096d4c1cf3883a8505fb432ffb0372e5bb8e16ebaf0b8918159854","observation_id":"2a42bcfc-48f0-46e2-ad80-3fb0bf653847","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"On the distillability conjecture in matrix theory","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:c884c448b65c209bd43ef8a050c79d08cac798529d609281d72d0d8381747380","observation_id":"39be44d0-986b-41c5-ab06-7273b076119c","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"A note on a conjecture from distillability of quantum entanglement","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:d2baf84aa27d4ea3cdc61b93852596fe5d793299dcc74db730180e77e90561cc","observation_id":"b41cb2b1-691f-49a6-a815-0dbb28ec36c2","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Proving the distillability problem of two-copy 4 × 4 werner states for monomial matrices","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:27bf59896799c4886c61ba7520587abec775ac91207eadc2c7f6b9feea35cbb7","observation_id":"c359b957-f8fa-4292-812d-a1543a761352","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"On some norm inequalities involving the commutator and xy-yxt","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:1c4d6c5708d8d9fa6ab720364d7b69d55a2f7f89428272ed139248305edf6b54","observation_id":"718948cc-596f-4ca5-a815-65915c35661c","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Commutators with maximal frobenius norm","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:e2d0beffb6130c4543adb99ef1242802c717dd3a6b14d8ff28ad9f158a332e89","observation_id":"9613cb57-2459-4401-a339-356efc965c2c","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Michel and B.I","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:ff41e9b5514dd9b980b65b2269bc359cf189590caf706c17b8270edf29468df0","observation_id":"71e40a0d-bce9-4c57-aecf-d0b6f1e600c6","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":null,"venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:2af8ea0690181c49ef4b03d7c413d2eacc3e82d2c99eff8a71fb7964b5c12817","observation_id":"eb1cd73d-b466-41fb-96c1-f3879e8c0bd4","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"On the periodicity of singular vectors and the holomorphic block-circulant svd on the unit circum- ference","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:3140b1fab64ab8ded82bf9e474fc00156f38cfe9a44ad57807b7ff4d59ceae12","observation_id":"ed6081e8-d201-4400-a935-3891d0e3dee8","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Differentiability of a function and of its compositions with functions of one variable","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:c9ad0c912bb2f6aa9ff1a82f516a97ab1feff358363dc8996efdf8d5bdf1b568","observation_id":"c679950c-d215-46e5-8738-02af142c609f","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-28T09:27:14.693975Z","title":"Horn and Charles R","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-06-28T09:27:14.693975Z"},"links":{"citing_paper":"/paper/2606.03561"},"observation_digest":"sha256:aa5e99c8c20513344c0ff33fae9ec47d24549342fd95ae3a62ef4018799bd57f","observation_id":"a179cda7-47d8-4078-88c8-eb91055e10c7","resolution":{"observed_at":"2026-06-28T09:27:14.693975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.03561","last_updated":"2026-06-02T12:29:10Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-11T07:19:44.604578Z","submitted_at":"2026-06-02T12:29:10Z","title":"On the saturated cases of the distillability conjecture"},"reference_resolution":{"displayed":68,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":2,"unresolved":66,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":68},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 68 of 68 outbound references and 2 inbound Pith citation observations for arXiv:2606.03561."}