{"as_of":"2026-08-09T16:52:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:76e5b67a20f75b0fd997b98a29016a45e9c1ea1e41cb112a032f793ac8941abd","coverage":[{"denominator":56,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":56,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:41:01.398121Z","state":"measured"},{"denominator":57,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":57,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T15:46:28.579705Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-08T15:46:29.229680Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"cited_work":{"arxiv_id":"2507.05205","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.05205","snapshot_observed_at":"2026-08-08T15:46:29.229680Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","venue":"quant-ph","work_id":"fe4b3a67-a432-4ef7-8245-bbe6a47fa764","year":2025},"citing_paper":{"arxiv_id":"2502.06399","last_updated":"2025-07-16T08:03:27Z","snapshot_observed_at":"2026-08-08T19:21:29.015201Z","submitted_at":"2025-02-10T12:37:10Z","title":"A Linearly Convergent Algorithm for Computing the Petz-Augustin Mean","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-08T15:46:28.579705Z"},"links":{"cited_paper":"/paper/2507.05205","citing_paper":"/paper/2502.06399"},"observation_digest":"sha256:216018215ab8cb720fabf2f274fcdc3638ad1834ec7d6cd7cda146e5a2cd3f6c","observation_id":"c9f42eed-8126-45cc-a5a2-6cbac0690296","resolution":{"observed_at":"2026-08-08T15:46:29.232536Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.05205/citation-record","integrity":"/paper/2507.05205/integrity","json":"/paper/2507.05205/citation-record.json","paper":"/paper/2507.05205"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:02.361890Z","title":null,"venue":null,"work_id":"96accea0-58de-4c36-a35f-7842e5ffb26b","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:57.586670Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:87ea1070245e1568d2cb32a708e46e090abebbc3696520f4ab403f47286a508f","observation_id":"52b9cb9b-132f-45f7-81ac-c7e07244c666","resolution":{"observed_at":"2026-08-06T19:41:02.366203Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.347828Z","title":"Notation We take “log” to refer to the natural logarithm","venue":null,"work_id":"f8926229-2059-422a-847d-64ad697cd3cd","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:57.657181Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:fc6d56913174f68c27393a42824fb493d6f4e14233854c678edacd7c418fcdba","observation_id":"4fa73c5b-3270-4335-947d-357164673291","resolution":{"observed_at":"2026-08-06T19:41:02.352259Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.334087Z","title":"The following definition formalizes the alternating minimization problem under consideration","venue":null,"work_id":"d24da0eb-7bf7-46f1-a2f8-88692bad5c4d","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:57.731477Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:b4f58ed22d25021bcdc0bc2f21e6e7de0d3a68866f800881b3d9a79be62c6156","observation_id":"deeaa437-77c5-4f98-aaf9-cc546445b4cc","resolution":{"observed_at":"2026-08-06T19:41:02.338592Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.319751Z","title":"Our main results address the non-asymptotic convergence of the objective function values after n iterations of alternating minimization, denoted byxn","venue":null,"work_id":"b66eddc1-38a7-4810-a61c-b42a9a027eb1","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:57.812500Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:7bf5652fa07dbbd33310115891bc32bf11401d80506dab314c1e7682c9df27f7","observation_id":"d3d2c2f8-7695-4bc1-976b-14d5013a8f61","resolution":{"observed_at":"2026-08-06T19:41:02.324883Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.305288Z","title":"Probability mass functions Let X be a finite set","venue":null,"work_id":"c1ade4e6-3fbc-4a4e-8a3f-16187ef487ea","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:57.875675Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:e5d11bb76f716350565f054fa4a8b74855965b01d6c8da56b49e3f548f696055","observation_id":"a294b55e-a57c-489a-88fd-47d231ce0727","resolution":{"observed_at":"2026-08-06T19:41:02.310354Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.290179Z","title":"12 Definition 2(Alternating minimization: Iteration rule)","venue":null,"work_id":"c956f052-b8fd-4d14-ab72-9b950fc7914f","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:57.962550Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:26753152a8930e40c08bc0412eca30089810222080e48d89be9eb966eb168088","observation_id":"76ebebd9-3ef0-475f-aac9-eb71b00d3af1","resolution":{"observed_at":"2026-08-06T19:41:02.294930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.275060Z","title":"Let α ∈ (0, 1) ∪ (1, ∞) and let Q, R ∈ P(X ) be such that Q ∼ R","venue":null,"work_id":"5316ad10-46c5-4fa4-8c33-8488939c970a","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:57.997786Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:96d7c76d29757e21f1bbae14952b0b3816cbe6e67fe7792ebe07f9fd9e2b5ffc","observation_id":"6ade059a-3c73-466b-aa5a-16b479635454","resolution":{"observed_at":"2026-08-06T19:41:02.280650Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.260608Z","title":"(A.36) follows from the additivity of Hilbert’s projective metric with respect to the product of PMFs","venue":null,"work_id":"d42f0e26-cc45-4e58-9bf6-e3b9a73c95a9","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.060925Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:2f9761f455d7fa6ee3ce1d23d9f487c8b356bbb73a52500831cd49afbd69b593","observation_id":"b783163a-9a95-4644-8bce-29f488f64972","resolution":{"observed_at":"2026-08-06T19:41:02.265140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.246860Z","title":"All of the following hold","venue":null,"work_id":"5fab890f-5aba-4f43-8f99-5c64c81839bf","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.120890Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:ff16da644cb876e1ae7de02f4a1f124bdd8b6f86266a7dc2dcdabb3953023501","observation_id":"77e8d43f-c534-45ea-84e8-7a7cac15c6f7","resolution":{"observed_at":"2026-08-06T19:41:02.251184Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.231863Z","title":"By the fixed-point property of minimizers for the doubly minimized PRMI [17], ˆσA = NB→A ◦ NA→B(ˆσA) ∈ S≪ρA(A), (C.14) ˆτB = NA→B(ˆσA) ∈ S≪ρB (B)","venue":null,"work_id":"72f0075b-f1aa-470e-a602-4e4b125cb638","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.196864Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:4302524c9fff3d750f9e8d0c72d89c1f96b5301f714498f5d73ce9490b3d437d","observation_id":"49c6761f-4739-416c-8842-46b7576e5ae0","resolution":{"observed_at":"2026-08-06T19:41:02.236768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.216967Z","title":"Let α ∈ (1, ∞) and let σ, τ∈ S(A) be such thatσ ∼ τ","venue":null,"work_id":"9982763c-366c-4903-8e4c-bade9524f045","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.288010Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:11ae92302efbdea9996a540e83014d43a3764fcc1e399e5817d69b889474e848","observation_id":"f8e44178-f7b4-4729-9025-7e856004e147","resolution":{"observed_at":"2026-08-06T19:41:02.221517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.202839Z","title":"Let σ, τ∈ S(A) be such that σ ∼ τ","venue":null,"work_id":"785fc013-44a6-4b60-999a-fd659157f8b8","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.376172Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:4f5e3427283a88c0c181a5fe5b55835c1a4a9d5e7215e6c40546d52021824d74","observation_id":"7eb5cc90-fd34-4ec2-90a3-e497ab7827ea","resolution":{"observed_at":"2026-08-06T19:41:02.207313Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.188368Z","title":"Let α ∈ ( 1 2 , 1), ρAB ∈ S(AB), σ(0) A ∈ S∼ρA(A)","venue":null,"work_id":"acf234b8-10d2-4000-984b-92525b9059ea","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.438896Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:bbf9fce1f70fffe556d3e693f024a2d626e6baa6814a83cbf5f3c1d4235d75d0","observation_id":"29ba6373-6193-4839-abac-c041ce275573","resolution":{"observed_at":"2026-08-06T19:41:02.192526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.174269Z","title":"Before presenting the proof, we first clarify our notation for Fréchet derivatives","venue":null,"work_id":"0f0aaf00-88d3-4867-acac-5679b52871b9","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.499257Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:af13159b80d15f6b2103a97a0a81831f2d1d3480b347e222dfae68e5168aa20f","observation_id":"504bb9f0-4f9f-4b14-9c2e-0ef1af924006","resolution":{"observed_at":"2026-08-06T19:41:02.179050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.159301Z","title":"Decomposition rules for quantum Rényi mutual infor- mation with an application to information exclusion relations.Journal of Mathematical Physics, 61(7),","venue":null,"work_id":"695492e0-f706-4f21-af39-7a7818079865","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.546394Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:fbdcf59b34966ce60485404d9cc0ecb921f23b7efca2a8d3c8c48666897355c3","observation_id":"2440d87e-d867-4630-9ac6-e1a6a6430f5f","resolution":{"observed_at":"2026-08-06T19:41:02.164040Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:40:59.504407Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.504407Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:ca8c6e9578f8391a083ce0d01ddb7b97d4849eab289c248f78ff47f434540ec2","observation_id":"94c677b3-8f0a-4084-bde9-73c15bb88a4d","resolution":{"observed_at":"2026-08-06T19:40:59.504407Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:58.654075Z","title":"Sandwiched Rényi divergence satisfies data processing inequality.Journal of Mathemat- ical Physics, 54(12), 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.654075Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:89ef9db23df10360b0064e636dff1e14f0cfe64e664c0d41351b008abeb84b94","observation_id":"d4eb97ed-4342-41ff-9835-7863ea110d45","resolution":{"observed_at":"2026-08-06T19:40:58.654075Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:58.716418Z","title":"Wilde, and Nilanjana Datta","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.716418Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:2a84149b5ef5ae28a07a79d19f4979e2a73c8b4631ca110d53c86275cf4b8efc","observation_id":"b771fc3a-55da-4150-b1c7-c1fc4778324b","resolution":{"observed_at":"2026-08-06T19:40:58.716418Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2304.12055","last_updated":"2023-05-04T10:41:04Z","snapshot_observed_at":"2026-07-06T15:19:17.083953Z","submitted_at":"2023-04-24T12:47:37Z","title":"Tight One-Shot Analysis for Convex Splitting with Applications in Quantum Information Theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.12055","snapshot_observed_at":"2026-08-06T19:40:58.777146Z","title":"Tight One-Shot Analysis for Convex Splitting with Applications in Quantum Information Theory, 2023.DOI: 10.48550/arXiv.2304.12055","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.777146Z"},"links":{"cited_paper":"/paper/2304.12055","citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:092c465306a07cab631d6955d6a27e04620d958d61806ca1075dc89c565e51da","observation_id":"f57a2d37-e895-4f83-9d93-7c071314d9a3","resolution":{"observed_at":"2026-08-06T19:40:58.777146Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:58.831078Z","title":"Wilde, Andreas Winter, and Dong Yang","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.831078Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:3cd8386c4532dcf69a146e6a67736a0203d5c5aad661ea1eacb6b0a8251c46a5","observation_id":"9fa71da2-4bb4-4047-921f-f79ea356dec0","resolution":{"observed_at":"2026-08-06T19:40:58.831078Z","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":"10.1007/s00220-024-05029-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Reliability Function of Quantum Information Decoupling via the Sandwiched Rényi Divergence","venue":"Communications in Mathematical Physics","work_id":"cc6d03d4-ec5c-4171-ad89-62dbf7bea35a","year":2024},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.909649Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:f968f89025e4c24f032438669ece91975fd82e1cab68627f21bbb4c11dfd7a7a","observation_id":"346d9b4f-a54b-4693-bd79-0f54de37fbd7","resolution":{"observed_at":"2026-08-06T19:41:01.794830Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00220-023-04890-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Operational Interpretation of the Sandwiched Rényi Divergence of Order 1/2 to 1 as Strong Converse Exponents","venue":"Communications in Mathematical Physics","work_id":"4f0457a0-7253-4364-b939-28407082ff98","year":2024},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.970560Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:f1a67a86130e3346192f3760936163b2e2f0daea99c1149d9e3228feee37347e","observation_id":"5137c2c8-2830-4589-8206-47140c959dcf","resolution":{"observed_at":"2026-08-06T19:41:01.781378Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.03213","last_updated":"2026-04-05T12:45:46Z","snapshot_observed_at":"2026-08-06T21:03:28.677879Z","submitted_at":"2024-06-05T12:51:22Z","title":"Doubly minimized Petz and sandwiched Renyi mutual information: Operational interpretation from binary quantum state discrimination","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.03213","snapshot_observed_at":"2026-08-06T19:40:59.033990Z","title":"Doubly minimized sandwiched Rényi mutual information: Properties and operational interpretation from strong converse exponent, 2024.DOI: 10.48550/arXiv.2406.03213","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.033990Z"},"links":{"cited_paper":"/paper/2406.03213","citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:2404fc095ece156dbb9dbe032ed615ca0be133cf8fcc387ecba70327e5b55b68","observation_id":"24429dee-b9dc-4735-b62c-722fbb285175","resolution":{"observed_at":"2026-08-06T19:40:59.033990Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:59.084980Z","title":"Gupta and Mark M","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.084980Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:10bc6be9920462a34c005cbb8602e02984294c9ba3c29bbe8fb7fa791083d3f4","observation_id":"5446efe2-d5c6-4a0b-98fb-8f59d0c3ad35","resolution":{"observed_at":"2026-08-06T19:40:59.084980Z","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":"10.1063/1.4908102","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:01.738133Z","title":"Seshadreesan, and Mark M","venue":null,"work_id":"f04f02ea-147a-4170-8e72-4781563f9325","year":2015},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.143031Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:5acfcd13c3867cc62ba4e2c31108494ef4fd7ec8e6f4abf86c7369f918f06ee0","observation_id":"00a611a9-1d15-4bf2-97c2-99ca1c62c8f0","resolution":{"observed_at":"2026-08-06T19:41:01.742297Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2015.24178","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:02.083950Z","title":"Coding Theorems for Compound Problems via Quantum Rényi Divergences.IEEE Transactions on Information Theory, 61(6):2997–3012, 2015","venue":null,"work_id":"5c117583-6ec1-495d-835d-b7666e91a087","year":2015},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.202614Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:e811be6ba6bd7b055cc85a9cb2764e9cecb84aef90a0ae5e862af6e508e38bc4","observation_id":"c94fb572-0dea-4fbc-9e66-46e743adb0f3","resolution":{"observed_at":"2026-08-06T19:41:02.092641Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:40:59.262949Z","title":"Strong Converse Exponent for Classical-Quantum Channel Coding","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.262949Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:8caab609a2b2ed333976c6c6a5568a32987ad64dc1cfbe7734ab5f5b8c8a16d3","observation_id":"c71320ed-dfcc-4b7e-8c11-367eb3406139","resolution":{"observed_at":"2026-08-06T19:40:59.262949Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:59.333205Z","title":"Correlation detection and an operational interpre- tation of the Rényi mutual information","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.333205Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:e14c123b324a93ca76f82c0c8e2949ac5a07bf731d61fa6d21e1f03167328397","observation_id":"3668e94e-4091-4431-98e8-337b0d62cb42","resolution":{"observed_at":"2026-08-06T19:40:59.333205Z","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":"10.1007/jhep06(2024)195","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Rényi mutual information in quantum field theory, tensor networks, and gravity","venue":"Journal of High Energy Physics","work_id":"da9955ef-59e5-4c3b-b753-83ad03e08775","year":2024},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.397623Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:bc540b61b9dce087b22e7025c76419afa8342d3b538cbf651a06bcf37149a2aa","observation_id":"1a17cb3a-c46c-4d01-8be4-8d071092bcd0","resolution":{"observed_at":"2026-08-06T19:41:01.709344Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:40:59.453810Z","title":"Rényi Mutual Information in Quantum Field Theory.Physical Review Letters, 130(021603), 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.453810Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:319be457b602afd9ccb8404674ab1d533fca24944a78259527dc9a13d5d0df8e","observation_id":"6d6145a5-4a12-4966-a30c-2e3a2916c83e","resolution":{"observed_at":"2026-08-06T19:40:59.453810Z","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":"2026-08-06T19:41:02.102720Z","title":"Zaslavski","venue":null,"work_id":"7f6761df-751a-469b-98be-f74587e1a1fc","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.316544Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:f27609d45a0231578cd97cf6834ac3d5a8241bd4b92cb914d531875fbe640be5","observation_id":"3514be62-a5ba-4f09-904c-6eb510c603df","resolution":{"observed_at":"2026-08-06T19:41:02.107049Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2406.01699","last_updated":"2026-04-05T12:43:29Z","snapshot_observed_at":"2026-08-06T01:04:19.933627Z","submitted_at":"2024-06-03T18:01:00Z","title":"Doubly minimized Petz and sandwiched Renyi mutual information: Properties","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.01699","snapshot_observed_at":"2026-08-06T19:40:59.540960Z","title":"Doubly minimized Petz Rényi mutual information: Properties and operational interpre- tation from direct exponent, 2024.DOI: 10.48550/arXiv.2406.01699","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.540960Z"},"links":{"cited_paper":"/paper/2406.01699","citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:37cd096c95c672c8da2a42ffb4d12efbf209f3e9433932db9f4bec5de285b89b","observation_id":"ad5c7a5e-591d-4d2f-afd0-4e751289bfa7","resolution":{"observed_at":"2026-08-06T19:40:59.540960Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:59.639838Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.639838Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:08a482cecfc134beb41c33bef0b740c897c0de46ae1198cd96e925bf4d070677","observation_id":"226a18ef-b534-4d9d-8a2c-fd270a9975e1","resolution":{"observed_at":"2026-08-06T19:40:59.639838Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:59.763727Z","title":"Two Measures of Dependence","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.763727Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:2638d86a9625de54de0d01e3de02cd273398f4d596afe86bdcbf865126a7349b","observation_id":"58cc5bb1-f863-488d-be61-a4291b989618","resolution":{"observed_at":"2026-08-06T19:40:59.763727Z","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":"2026-08-06T19:41:02.143865Z","title":"Min-reflected entropy = doubly minimized Petz Rényi mutual information of order 1/2,","venue":null,"work_id":"bbf9920f-b8b9-4c73-9737-afc8d4910acc","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:59.880158Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:e771074de343207286894e61d4693be8f22a7d58f0fbe495d9783bece477d480","observation_id":"f529028f-ac11-4e63-a095-d881eaf38b1f","resolution":{"observed_at":"2026-08-06T19:41:02.148361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:01.394155Z","title":"Positive Definite Matrices","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.394155Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:03e2986c559efae2736a7f63ab50a3de658634b2b8354f09b99a9e0b5a2d3b17","observation_id":"07e96cf4-5454-457e-94fb-cbd96c593485","resolution":{"observed_at":"2026-08-06T19:41:01.394155Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.10950","last_updated":"2025-04-30T05:00:36Z","snapshot_observed_at":"2026-08-08T11:52:00.918865Z","submitted_at":"2024-04-16T23:18:07Z","title":"Alternating Optimization Approach for Computing $\\alpha$-Mutual Information and $\\alpha$-Capacity","version":5},"cited_work":{"arxiv_id":"2404.10950","doi":"10.48550/arxiv.2404.10950","metadata_source":"pith","pith_arxiv_id":"2404.10950","snapshot_observed_at":"2026-08-07T06:16:28.064256Z","title":"Alternating Optimization Approach for Computing $\\alpha$-Mutual Information and $\\alpha$-Capacity","venue":"cs.IT","work_id":"56a7c667-c9b1-4b93-9528-837276575092","year":2024},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.128465Z"},"links":{"cited_paper":"/paper/2404.10950","citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:da5c2e991b64dff6578a3424fc05b619c8fbbb9396d34c97387bfcce61c52aa0","observation_id":"6269307c-a0dc-41c8-94d3-91b59ee04c67","resolution":{"observed_at":"2026-08-06T19:41:01.625750Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.130351Z","title":"Linear Convergence in Hilbert’s Projective Metric for Computing Augustin Information and a Rényi Information Measure,","venue":null,"work_id":"cebb3479-4138-4fe2-9e55-dcdca443b0dc","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.267312Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:7deee5396a3aa7090a694447803c19c48ea3c755c351a34929598fb11c8afb2c","observation_id":"e19bd9da-67f1-4388-a293-0bc9305bf3ae","resolution":{"observed_at":"2026-08-06T19:41:02.134663Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11590-021-01753-w","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:01.581277Z","title":"On the rate of convergence of alternating minimization for non-smooth non-strongly convex optimization in Banach spaces","venue":null,"work_id":"7f17fee0-5c3b-40fc-aded-ac28d79a7b22","year":2021},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.461071Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:b74754859927beb6944315f93724d3cc52e707baebc6350b007eb53c17ea9a19","observation_id":"3e135871-e602-4774-8608-6e21016050e4","resolution":{"observed_at":"2026-08-06T19:41:01.585693Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:02.116510Z","title":"Quasi-entropies for finite quantum systems.Reports on Mathematical Physics, 23(1):57–65,","venue":null,"work_id":"17a0b032-9ef2-413f-a11c-20b38c17e611","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.555763Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:4c670dd38e9bb31b2a68ff1e79811cb95615f80ccc53c853fd45a3d9de8b7db9","observation_id":"bd0cf9b7-d019-46e2-9014-d2d8ed77dac0","resolution":{"observed_at":"2026-08-06T19:41:02.120566Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00013-017-1066-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":null,"venue":"Archiv der Mathematik","work_id":"611aa6c3-93e3-4ef3-bdda-2ea4676cdf02","year":2017},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.756829Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:195ab3a3ee8355d2b81c91f3f1bff1cd6cc9b7b56eebc84821a54da41151a4b8","observation_id":"85767fba-2d7e-4d15-8706-9907eb7034e1","resolution":{"observed_at":"2026-08-06T19:41:01.561919Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:00.855264Z","title":"Cambridge Tracts in Math- ematics","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.855264Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:b557bee74ae1acbf92028e58f9a7b46026d711880cbeabd68abf0a436184ed61","observation_id":"9c1005e7-4abb-46d8-a023-87f2e9e017ad","resolution":{"observed_at":"2026-08-06T19:41:00.855264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1304.7921","last_updated":"2013-04-30T09:00:09Z","snapshot_observed_at":"2026-07-06T03:12:18.947596Z","submitted_at":"2013-04-30T09:00:09Z","title":"Birkhoff's version of Hilbert's metric and its applications in analysis","version":1},"cited_work":{"arxiv_id":"1304.7921","doi":"10.48550/arxiv.1304.7921","metadata_source":"pith","pith_arxiv_id":"1304.7921","snapshot_observed_at":"2026-08-07T06:16:28.064256Z","title":"Birkhoff's version of Hilbert's metric and its applications in analysis","venue":"math.MG","work_id":"f46631fa-1780-43da-b66d-4dc854ed3bbb","year":2013},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.967165Z"},"links":{"cited_paper":"/paper/1304.7921","citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:fb3fbf6911d1ea49a9760387dab69af64a24c3d339e017fd681fc24baaa2369e","observation_id":"3b4e85c0-fd24-4a95-8040-a98fc2650994","resolution":{"observed_at":"2026-08-06T19:41:01.538382Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:01.044551Z","title":"Kastoryano, and Michael M","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.044551Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:598e49fda63481d0040e576b975590663cfda264ecc0dbca450acc22e49a74af","observation_id":"1680fff0-7bc3-4055-a5ab-119a29e52a61","resolution":{"observed_at":"2026-08-06T19:41:01.044551Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:01.145245Z","title":"Bauschke and Patrick L","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.145245Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:72871112b9f4703201aca05a11c757438e66097ef1928d8a235a3d07942012a7","observation_id":"340d5bc5-8ae9-43fa-824f-a091088471d3","resolution":{"observed_at":"2026-08-06T19:41:01.145245Z","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":"10.1007/978-3-030-60300-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T00:03:56.115653Z","title":"Zaslavski","venue":"SpringerBriefs in optimization","work_id":"d1bf5b67-3dd9-4ff8-a91f-437b2df79f0a","year":2020},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.224152Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:b1c91b0a9512923e162612c9b95bc4f4a2e5807348bbbdbb092ecaa7fa671f2e","observation_id":"4027bec7-a8fc-4fd4-af84-771e0c083585","resolution":{"observed_at":"2026-08-06T19:41:01.498321Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:01.377055Z","title":"Quantum Information Processing with Finite Resources","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.377055Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:3125be62ee69a6ff8bf278169bd85410eaa5560db797efdba66e3b0b0e0c444e","observation_id":"ed427a0a-f58a-47e3-8ea2-1a40ab8183d9","resolution":{"observed_at":"2026-08-06T19:41:01.377055Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:01.380975Z","title":"Extensions of Jentzsch’s Theorem","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.380975Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:948760a5c8f933bf38f9ea1488d41cf244649bd79b59f8c2bf1001e72dacab5c","observation_id":"368b2ff1-fb3f-499f-9735-1f577242d856","resolution":{"observed_at":"2026-08-06T19:41:01.380975Z","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":"stable/2490087","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:01.924896Z","title":"An Inequality for Positive Linear Integral Operators","venue":null,"work_id":"56481d5e-c418-42e7-b61e-65f840980e5e","year":1963},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.385560Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:3cbb3bdb3e6847803f2ff4ea58ba6428d3f8306567c03ba03d1666216c6a9d23","observation_id":"09f12033-31df-46f6-b332-7517ecf3fbdc","resolution":{"observed_at":"2026-08-06T19:41:01.932623Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+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":"2026-08-06T19:41:01.389902Z","title":"On the Convergence of Block Coordinate Descent Type Methods","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.389902Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:6d43bc3d43dba61e6ab90d535d670b0f47a5422609b243dd643c37d674c182c2","observation_id":"1913e580-e1d2-4cf5-95ed-239dbbf406ee","resolution":{"observed_at":"2026-08-06T19:41:01.389902Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:01.398121Z","title":"Matrix Analysis","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.398121Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:fb9a58f6498b36e6386c4477dde86a8d21984939eeb9a5e4ae7319d2c6ac7d9f","observation_id":"c82db811-5b66-4ba9-9dcf-4200386b65ab","resolution":{"observed_at":"2026-08-06T19:41:01.398121Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:41:00.665180Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":1986,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.665180Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:f60180fef8c8bd99520aef75f082281919f6456e2e27de50302c1ef5e6603f73","observation_id":"51a50f43-fa18-4c44-820b-83d0b77b3969","resolution":{"observed_at":"2026-08-06T19:41:00.665180Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:40:58.596696Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-06T19:40:58.596696Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:dd2cb6677cda64f83426c80be62667c25042289e28b4ccd6bc5938b62afb2207","observation_id":"4dec37dc-8d1e-4584-a4d6-99de51f558e7","resolution":{"observed_at":"2026-08-06T19:40:58.596696Z","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":"10.1007/978-3-031-12644-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-08T00:03:56.115653Z","title":null,"venue":"SpringerBriefs in optimization","work_id":"e1fc4f62-26b8-445d-8e01-63c13ebec944","year":null},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:01.371168Z"},"links":{"citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:9dbe3e95d6d66e5896cd4fc2ef18e4567a3da811d5ca51e367ff4ecb3ce468bf","observation_id":"4d4169c5-7ac1-4f4d-8767-7cb238d64a8b","resolution":{"observed_at":"2026-08-06T19:41:01.484220Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.02640","last_updated":"2024-09-27T07:39:08Z","snapshot_observed_at":"2026-08-09T13:14:19.742831Z","submitted_at":"2024-09-04T12:15:22Z","title":"Linear Convergence in Hilbert's Projective Metric for Computing Augustin Information and a R\\'{e}nyi Information Measure","version":2},"cited_work":{"arxiv_id":"2409.02640","doi":"10.48550/arxiv.2409.02640","metadata_source":"pith","pith_arxiv_id":"2409.02640","snapshot_observed_at":"2026-08-07T06:16:28.064256Z","title":"Linear Convergence in Hilbert's Projective Metric for Computing Augustin Information and a R\\'{e}nyi Information Measure","venue":"math.OC","work_id":"0085e167-85f2-487b-9428-25a6e0b174b2","year":2024},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.375773Z"},"links":{"cited_paper":"/paper/2409.02640","citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:2b1318b95d1d1f78d7147aeae485f1894fe3c5ca1389b7fd9d01bf29914a8e60","observation_id":"f2b499a0-d4c9-43d5-bf68-d65b514ab3f1","resolution":{"observed_at":"2026-08-06T19:41:01.605615Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.18433","last_updated":"2025-02-25T18:27:38Z","snapshot_observed_at":"2026-08-07T17:49:22.188991Z","submitted_at":"2025-02-25T18:27:38Z","title":"Min-reflected entropy = doubly minimized Petz Renyi mutual information of order 1/2","version":1},"cited_work":{"arxiv_id":"2502.18433","doi":"10.48550/arxiv.2502.18433","metadata_source":"pith","pith_arxiv_id":"2502.18433","snapshot_observed_at":"2026-08-07T06:16:28.064256Z","title":"Min-reflected entropy = doubly minimized Petz Renyi mutual information of order 1/2","venue":"quant-ph","work_id":"1db73ca9-5f56-4c08-ab24-256185b6f694","year":2025},"citing_paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-06T19:41:00.010038Z"},"links":{"cited_paper":"/paper/2502.18433","citing_paper":"/paper/2507.05205"},"observation_digest":"sha256:0ce0309fd3cacc974093789925d48d260675c8710fba616f4f0482075da3d710","observation_id":"7d96e6ad-aa67-41d6-aa4b-71c0a1bba9d4","resolution":{"observed_at":"2026-08-06T19:41:01.650906Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.05205","last_updated":"2025-07-07T17:11:58Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-09T15:30:53.552190Z","submitted_at":"2025-07-07T17:11:58Z","title":"Alternating minimization for computing doubly minimized Petz Renyi mutual information"},"reference_resolution":{"displayed":56,"state_counts":{"malformed_identifier":0,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":24,"verified_exact":13,"verified_fuzzy":18},"total_outbound_references":56},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 1 inbound Pith citation observation for arXiv:2507.05205."}