{"as_of":"2026-08-11T19:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5f6aa464eab59751b5ed3493883f63acedbc9de17a7c8bd271dc70cf565710de","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T03:53:30.602380Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.23039/citation-record","integrity":"/paper/2607.23039/integrity","json":"/paper/2607.23039/citation-record.json","paper":"/paper/2607.23039"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:53:27.240631Z","title":"Schlienz and G","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:27.240631Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:08acea88fff57e358140f898550a265d1650fe71460a66c05ad9c5cabc3a114c","observation_id":"2025872a-bb41-4491-b8e2-a5c41e92be91","resolution":{"observed_at":"2026-08-01T03:53:27.240631Z","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":"2026-08-01T03:53:27.323627Z","title":"Zhang and B","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:27.323627Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:f2d7981d344d33636d6f494871da11ef5cec42940f0bf1fb2e5e989aaa489e07","observation_id":"854d160a-b446-48ab-bcf9-cbdb2a209dc1","resolution":{"observed_at":"2026-08-01T03:53:27.323627Z","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":"2026-08-01T03:53:27.405050Z","title":"Turner and J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:27.405050Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:7ea29a565b91eb89239247ca73d118b3ed0f82b7ac880efbbf2bd9d141dc5b0a","observation_id":"469832fe-6b18-4344-9b29-fa93f8ea7a6f","resolution":{"observed_at":"2026-08-01T03:53:27.405050Z","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":"2026-08-01T03:53:27.513023Z","title":"Grassl, M","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:27.513023Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:04a1f3a6d88b0676d54002cf95a1a1b7290beddd5b268eea9ea7303b0a2a58d6","observation_id":"8e8a8c8b-1c10-492c-9b48-a108767d3ac5","resolution":{"observed_at":"2026-08-01T03:53:27.513023Z","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":"2026-08-01T03:53:27.653251Z","title":"Makhlin, Nonlocal properties of two-qubit gates and mixed states, and the optimization of quantum computations, Quant","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:27.653251Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:7a53aa05ca3f6c23421497f64f4a39f8d1504e6fbed12512b84568b7fff47eb1","observation_id":"a97e0ab7-c1c1-47f2-846f-d4f96d8f6643","resolution":{"observed_at":"2026-08-01T03:53:27.653251Z","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":"2026-08-01T03:53:27.780944Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:27.780944Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:b685a9dfa05a166e98adb04ce82d867d49ead230567a1095c75c1c6bd663297a","observation_id":"cdec093d-11e7-4afd-8d68-4f0aa7bcf134","resolution":{"observed_at":"2026-08-01T03:53:27.780944Z","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":"2026-08-01T03:53:27.908126Z","title":"Albeverio, L","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:27.908126Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:060b9ea9b4e806d1b648998a643858e128b20c0e4885ce150c1de38e816a1167","observation_id":"b0503620-13e4-4989-be82-2c36c87768f9","resolution":{"observed_at":"2026-08-01T03:53:27.908126Z","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":"2026-08-01T03:53:28.040473Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:28.040473Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:e6aa07ef36ebebf5aa4bea9bab1549d0df99300f8ce9e30e2a6bb5547f84fd02","observation_id":"9a13a45f-b63d-42ba-a3fb-92f479c7e307","resolution":{"observed_at":"2026-08-01T03:53:28.040473Z","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":"2026-08-01T03:53:28.163420Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:28.163420Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:d4bd68a2095f9bfdfa21e21a575ec7f99be1015d3ae3ac3e546c800265ff5348","observation_id":"595f56fc-0c3a-4718-8971-03c01cf1e8b0","resolution":{"observed_at":"2026-08-01T03:53:28.163420Z","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":"2026-08-01T03:53:28.271434Z","title":"Zhang, B","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:28.271434Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:8f6d39100f9b5224d75b7cafcde481c504116e239089cff911854e8bf56e8177","observation_id":"370de76a-505c-4806-a2ff-c019d4bd60da","resolution":{"observed_at":"2026-08-01T03:53:28.271434Z","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":"2026-08-01T03:53:28.408508Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:28.408508Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:4f0e700a709de83f26bdb7c1d97f114b3f60663dc01f4eeefb5b25ed195c6c76","observation_id":"caa65f0d-69ae-4acd-8b44-1ae080518128","resolution":{"observed_at":"2026-08-01T03:53:28.408508Z","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":"2026-08-01T03:53:28.572406Z","title":"Weyl,The Classical Groups, Princeton University Press, Princeton, 1946","venue":null,"work_id":null,"year":1946},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:28.572406Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:e83b44d888578005237d9f5029eb5570b5a46d9e4f8d5c3bcb2800f91dd5cdcd","observation_id":"8490a3d4-376e-4027-9171-93dbecbb04da","resolution":{"observed_at":"2026-08-01T03:53:28.572406Z","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":"2026-08-01T03:53:28.769688Z","title":"Goodman and N","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:28.769688Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:ef3c2027e5f2207947a14d4efbc0ac467fb0e0d0cf2537b61691d75405fb03cc","observation_id":"148bfcc9-6c7f-4582-b4cb-c7acd01d689f","resolution":{"observed_at":"2026-08-01T03:53:28.769688Z","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":"2026-08-01T03:53:28.926373Z","title":"Quesne,SU(2)×SU(2)scalars in the enveloping algebra ofSU(4), J","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:28.926373Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:4c034e9d29afde109898aa95d6345096266e529af294b4fa8fa3f2ea62648a5b","observation_id":"3a1e9ccf-71fc-4b5c-86bf-3123d25e9c13","resolution":{"observed_at":"2026-08-01T03:53:28.926373Z","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":"2026-08-01T03:53:29.107808Z","title":"Hochster and J","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:29.107808Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:5b7d7b7170af79effa72b0eb4716108f568c6d6d6f28a834a4553521163fc7d9","observation_id":"54961059-a5cc-4a60-9252-49a3f7a147a1","resolution":{"observed_at":"2026-08-01T03:53:29.107808Z","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":"2026-08-01T03:53:29.240167Z","title":"Sturmfels,Algorithms in Invariant Theory, Springer, Vienna, 1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:29.240167Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:fb256c064bfa91c0782b1813f5478a51edd71d32664667fbc72e4033db1923d1","observation_id":"0d2fa599-d635-4658-9111-fd4c9cd647b5","resolution":{"observed_at":"2026-08-01T03:53:29.240167Z","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":"2026-08-01T03:53:29.443965Z","title":"Derksen and G","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:29.443965Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:32b79a96346d9a97c8614689ecfa5ecaae114a7de7853b39f5fb9d7a5c57ef6f","observation_id":"74cb529a-44c3-4604-9be4-5bee91cf7c8f","resolution":{"observed_at":"2026-08-01T03:53:29.443965Z","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":"2026-08-01T03:53:29.627693Z","title":null,"venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:29.627693Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:a4943b51dfd000338fd6b807e69e3791de73545b7038e19a9298efccdaddcbf6","observation_id":"8d87e8e3-c064-4570-b44c-64b9b8924986","resolution":{"observed_at":"2026-08-01T03:53:29.627693Z","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":"2026-08-01T03:53:29.747510Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:29.747510Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:f9e070dd1b3bf85bba5ef29c9096f99defbcb9b49e3610b111de6814d5814112","observation_id":"6fe92741-f475-48c4-b510-87d9db6a2237","resolution":{"observed_at":"2026-08-01T03:53:29.747510Z","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":"2026-08-01T03:53:29.889384Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:29.889384Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:f3cb48fbd9cf29844e5ee3ffb060bd321285afd83487d6137e25bd0d5426badd","observation_id":"2607ef7b-049e-4149-804f-3f3f3c86fc29","resolution":{"observed_at":"2026-08-01T03:53:29.889384Z","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":"2026-08-01T03:53:30.044047Z","title":"Almumin, J","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:30.044047Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:1f778f249b803e055a572d9c729c96ba16118496970bd967456e645e39156523","observation_id":"108ff518-3d5c-4849-b3e3-5c39ccdc3d65","resolution":{"observed_at":"2026-08-01T03:53:30.044047Z","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":"2026-08-01T03:53:30.183596Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:30.183596Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:3f4f642b778f1e2b05d7e84a2d0bed1e05f1a75f0382c7309df27637b95c61d6","observation_id":"13c0f2e4-a35c-4aa5-ad6c-3b197a937402","resolution":{"observed_at":"2026-08-01T03:53:30.183596Z","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":"2026-08-01T03:53:30.331176Z","title":"Penrose, Applications of negative dimensional tensors, inCombinatorial Mathematics and Its Applications, edited by D","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:30.331176Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:c2942f838294c5e91191f6e45c94bcb74a493f0f82e45ee9911e5516ac819d46","observation_id":"98e1027a-bb95-4207-a8a3-26289703f2d2","resolution":{"observed_at":"2026-08-01T03:53:30.331176Z","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":"2026-08-01T03:53:30.484768Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:30.484768Z"},"links":{"citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:bb43b986f04328a91fde5ffa323f772064a5570e9820740f484c4624b92392d2","observation_id":"8af56f2f-dd27-4ecc-bc95-9d88bcc8622d","resolution":{"observed_at":"2026-08-01T03:53:30.484768Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.16878","last_updated":"2026-07-18T16:34:31Z","snapshot_observed_at":"2026-08-08T04:02:02.836949Z","submitted_at":"2026-07-18T16:34:31Z","title":"Bargmann invariants and local unitary equivalence","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.16878","snapshot_observed_at":"2026-08-01T03:53:30.602380Z","title":"Ma and R","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T03:53:30.602380Z"},"links":{"cited_paper":"/paper/2607.16878","citing_paper":"/paper/2607.23039"},"observation_digest":"sha256:874dae6ba2ee7c64fa1854ff0f0c1ac552c342a265f58af74ec0f6dfefd5bf1b","observation_id":"9c06056b-de4a-4c0f-bf9e-b3c1bcdebfe7","resolution":{"observed_at":"2026-08-01T03:53:30.602380Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.23039","last_updated":"2026-07-25T04:51:12Z","latest_version":1,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-08T05:08:28.831828Z","submitted_at":"2026-07-25T04:51:12Z","title":"Revisiting the invariant ring of two-qubit mixed states"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":25,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":25},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+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 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2607.23039."}