{"as_of":"2026-08-19T16:45:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3ceaadfa756fa313eddb53bbaf79a6c5630ce923799405366f0ade8001950fbe","coverage":[{"denominator":40,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":40,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T09:46:26.853616Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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":"2026-08-14T11:52:01.497599Z","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":"2026-08-14T11:52:01.997318Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"cited_work":{"arxiv_id":"2601.13467","doi":null,"metadata_source":"pith","pith_arxiv_id":"2601.13467","snapshot_observed_at":"2026-08-14T11:52:01.997318Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","venue":"quant-ph","work_id":"10597642-99f4-4a94-8d57-e4b3678fccaa","year":2026},"citing_paper":{"arxiv_id":"2608.13400","last_updated":"2026-08-13T15:59:30Z","snapshot_observed_at":"2026-08-19T16:09:57.169023Z","submitted_at":"2026-08-13T15:59:30Z","title":"Langlands Duality and Invariant Differential Operators: the Case SL(2n+1)","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-14T11:52:01.497599Z"},"links":{"cited_paper":"/paper/2601.13467","citing_paper":"/paper/2608.13400"},"observation_digest":"sha256:bad8a8f4ddb58bced14760344c378d91ca82e335bc378bc28b2477f6109728a1","observation_id":"b78b068b-858c-4acb-a32d-9c7ff47d51fa","resolution":{"observed_at":"2026-08-14T11:52:02.001055Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2601.13467/citation-record","integrity":"/paper/2601.13467/integrity","json":"/paper/2601.13467/citation-record.json","paper":"/paper/2601.13467"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T09:46:23.827059Z","title":"Since∥P ⊥S′P ⊥∥op ≤ ∥S′∥op ≤1, the Cauchy-Schwarz relation in (30) gives Q(S) ij ≤ ∥S′∥op √gii gjj ≤ √gii gjj","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:23.827059Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:cf5cc967f13524b81ab1d3face090f651e2b6df9c9e20a77d2a3c61d7f2d569e","observation_id":"f57c0298-6504-4729-9c33-25dc96258191","resolution":{"observed_at":"2026-08-03T09:46:23.827059Z","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":"2026-08-03T09:46:23.914769Z","title":"Then |η(k)|= 2 Re eiθvAv∗ B ≤C(k)≤1, with equality|η|=Cwhen the witness phase is aligned with the A/B coherence","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:23.914769Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:9f1ca9c2bd8ca156a950f76d2250f7ab3836463db5e468f23c87acde528f689e","observation_id":"59c58a80-36b8-4afd-ae60-464afe7feb81","resolution":{"observed_at":"2026-08-03T09:46:23.914769Z","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":"2026-08-03T09:46:24.025495Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.025495Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:7b80b7539bfa3a25fc64848801c771ab103c7c1aff381757a270e4c3837a92f4","observation_id":"7f495f35-343f-4069-967f-f9549b2669cd","resolution":{"observed_at":"2026-08-03T09:46:24.025495Z","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":"2026-08-03T09:46:24.145984Z","title":"Quantum Entanglement as a Cohomological Obstruction,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.145984Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:16e4f514190b3bd8ea7331944bb3a81f67a944f4c1ea8ed12c9bcba6cd3bf310","observation_id":"eb998d84-4a92-4daa-87a8-04986efd41eb","resolution":{"observed_at":"2026-08-03T09:46:24.145984Z","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":"2026-08-03T09:46:24.225415Z","title":"Berry phase effects on electronic properties,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.225415Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:8197b324889d4f609168db501339487e3c82740f1866e9d0ecb131d1e9fb9441","observation_id":"278c7afd-c669-435a-838e-f71902788f7f","resolution":{"observed_at":"2026-08-03T09:46:24.225415Z","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":"2026-08-03T09:46:24.559282Z","title":"Hyperbolic band theory through Higgs bundles,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.559282Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:0068cbeeb7c6233acd3ac427f0e5dab55f45eebd099eba2a521c955efedcb05c","observation_id":"805e5347-913d-4fdc-8c2c-343628bbbf6a","resolution":{"observed_at":"2026-08-03T09:46:24.559282Z","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":"2026-08-03T09:46:24.370653Z","title":"Colloquium: Topological insulators,","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.370653Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:8d499cea75ad82c2d34bc9a323e7e45c309e58db8829f6e464c1e9a728a2f7df","observation_id":"5aaf336d-ddf1-4a36-a743-ff956bb333a2","resolution":{"observed_at":"2026-08-03T09:46:24.370653Z","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":"2026-08-03T09:46:24.455494Z","title":"Topological insulators and superconductors,","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.455494Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:572a683be34d048f590c49ce09d6dca4b1b27af740ef31bbc613d8458fa18a97","observation_id":"8e6b489e-6cd2-49fa-9d45-3736c0ec13e1","resolution":{"observed_at":"2026-08-03T09:46:24.455494Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.05489","last_updated":"2021-09-08T18:00:03Z","snapshot_observed_at":"2026-08-14T17:05:20.881657Z","submitted_at":"2020-08-12T18:00:11Z","title":"Hyperbolic band theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.05489","snapshot_observed_at":"2026-08-03T09:46:24.507326Z","title":"Hyperbolic band theory,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.507326Z"},"links":{"cited_paper":"/paper/2008.05489","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:4454cb3f8ee8e7a342fc58981755f76a0d3b72a514ab57306809fa0a8eb1d39a","observation_id":"720ba568-6460-4e0f-990b-1001320fca33","resolution":{"observed_at":"2026-08-03T09:46:24.507326Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.01087","last_updated":"2022-01-17T18:37:22Z","snapshot_observed_at":"2026-08-16T18:27:19.602061Z","submitted_at":"2021-05-03T18:00:07Z","title":"Crystallography of Hyperbolic Lattices","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.01087","snapshot_observed_at":"2026-08-03T09:46:24.999632Z","title":"Crystallography of hyperbolic lattices,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.999632Z"},"links":{"cited_paper":"/paper/2105.01087","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:ba96b11a5187a372257ccbee003d46e37a2ed3e6fc310f327223af5dc8948667","observation_id":"79fcf4d0-4eb1-42ab-b077-0a57f3add6e4","resolution":{"observed_at":"2026-08-03T09:46:24.999632Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.09314","last_updated":"2022-02-28T16:04:50Z","snapshot_observed_at":"2026-08-16T18:01:58.962442Z","submitted_at":"2021-08-20T18:00:03Z","title":"Automorphic Bloch theorems for hyperbolic lattices","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.09314","snapshot_observed_at":"2026-08-03T09:46:24.669344Z","title":"Automorphic Bloch theorems for hyperbolic lattices,","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.669344Z"},"links":{"cited_paper":"/paper/2108.09314","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:97b8cbcacdfbccc9410f206d875bc751183ad06370863ba109f00fed028ab5b1","observation_id":"fca3bbf8-1818-41a7-98c2-3dff39d14ce2","resolution":{"observed_at":"2026-08-03T09:46:24.669344Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.13314","last_updated":"2021-07-23T16:34:02Z","snapshot_observed_at":"2026-08-16T18:28:43.407353Z","submitted_at":"2021-04-27T16:39:55Z","title":"Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.13314","snapshot_observed_at":"2026-08-03T09:46:24.771295Z","title":"Hyperbolic band theory under magnetic field and Dirac cones on a higher genus surface,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.771295Z"},"links":{"cited_paper":"/paper/2104.13314","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:c1a2c3b6aac18b56c49c8d84e52e4b49ae3e5cfdcdca3cda4bdd69789e01dcb9","observation_id":"3cca2eb2-c3d0-443a-8092-e1d191a298c9","resolution":{"observed_at":"2026-08-03T09:46:24.771295Z","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":"10.1139/cjp-2022-0145","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Algebra of hyperbolic band theory under magnetic field,","venue":"Canadian Journal of Physics","work_id":"1dc8e90e-497c-4396-aaed-fd1c067726ed","year":2023},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.885873Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:cb43e952ab1bd4e3f8d151a311f661499c4e30ee95ec43d02407539923caeafb","observation_id":"72b84942-bff7-41b3-874d-dd20fe5fcf13","resolution":{"observed_at":"2026-08-03T09:49:25.241831Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1102.0264","last_updated":"2011-11-29T11:29:39Z","snapshot_observed_at":"2026-08-15T04:56:02.539126Z","submitted_at":"2011-02-01T20:23:43Z","title":"The Sheaf-Theoretic Structure Of Non-Locality and Contextuality","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1102.0264","snapshot_observed_at":"2026-08-03T09:46:25.269364Z","title":"The sheaf-theoretic structure of non-locality and contextuality,","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.269364Z"},"links":{"cited_paper":"/paper/1102.0264","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:7214069297c5a0b8966ab6571028e8eff7d4565cfeaa2dba676cc9ef9f8e4009","observation_id":"dcb74b1f-7de3-42ce-866b-e833aa6435b0","resolution":{"observed_at":"2026-08-03T09:46:25.269364Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.02749","last_updated":"2022-08-09T05:40:27Z","snapshot_observed_at":"2026-08-16T16:41:08.716804Z","submitted_at":"2022-08-04T16:22:28Z","title":"On the hyperbolic Bloch transform","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.02749","snapshot_observed_at":"2026-08-03T09:46:25.050381Z","title":"On the hyperbolic Bloch transform,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.050381Z"},"links":{"cited_paper":"/paper/2208.02749","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:901d2d9196dfbd823fc0465d6678b483e03ef6bae9ea551f0407cfc2d4d4524b","observation_id":"76c1bec4-2ad2-441a-91dc-e288e12b1468","resolution":{"observed_at":"2026-08-03T09:46:25.050381Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1802.09549","last_updated":"2019-01-29T19:00:03Z","snapshot_observed_at":"2026-08-14T19:41:58.087236Z","submitted_at":"2018-02-26T19:00:20Z","title":"Hyperbolic Lattices in Circuit Quantum Electrodynamics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1802.09549","snapshot_observed_at":"2026-08-03T09:46:25.125677Z","title":"Hyperbolic lattices in circuit quantum electrodynamics,","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.125677Z"},"links":{"cited_paper":"/paper/1802.09549","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:16ae65476ab487318d66a091967b0c671175a0182e8df0f7effbc64f1affc98c","observation_id":"4487453e-6055-4f6b-b43a-7abcd45c6873","resolution":{"observed_at":"2026-08-03T09:46:25.125677Z","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":"2026-08-03T09:46:25.215590Z","title":"A scalable superconducting circuit framework for emulating physics in hyperbolic space,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.215590Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:6faabe5aa91b99975d127aa1cd513c96662b4a111f9d2aa748130ec3c687939f","observation_id":"8b6db8ec-7b92-4aba-804c-e177a041ec03","resolution":{"observed_at":"2026-08-03T09:46:25.215590Z","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":"2026-08-03T09:46:25.438346Z","title":"Separability criterion for density matrices,","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.438346Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:31ae8c30f74da793d3bf9951fd0d2dcdc93757e5bffffc08db9d31160fdb257d","observation_id":"3ff858d8-856a-44ff-89b3-832aeea852eb","resolution":{"observed_at":"2026-08-03T09:46:25.438346Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/0101032","last_updated":"2001-01-08T18:44:09Z","snapshot_observed_at":"2026-08-11T19:38:34.462761Z","submitted_at":"2001-01-08T18:44:09Z","title":"Detecting Quantum Entanglement","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/0101032","snapshot_observed_at":"2026-08-03T09:46:25.315114Z","title":"Detecting Quantum Entanglement,","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.315114Z"},"links":{"cited_paper":"/paper/quant-ph/0101032","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:532ad0bf92c6f26dfa82e9b9d57d8589c0ba13901252e628762da004eb3d41a2","observation_id":"e4f7ae20-f04f-422a-b826-7ca1d2adf901","resolution":{"observed_at":"2026-08-03T09:46:25.315114Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0811.2803","last_updated":"2009-02-27T21:43:38Z","snapshot_observed_at":"2026-08-19T10:34:58.666991Z","submitted_at":"2008-11-18T20:07:13Z","title":"Entanglement detection","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0811.2803","snapshot_observed_at":"2026-08-03T09:46:25.368187Z","title":"Entanglement detection,","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.368187Z"},"links":{"cited_paper":"/paper/0811.2803","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:260222b91cf470ccd32ef1026e6bb5b1046dd6579d8d17f169f7c28e538e9df2","observation_id":"4f3abdee-a709-49dc-8362-d6683a1d2eaf","resolution":{"observed_at":"2026-08-03T09:46:25.368187Z","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":"2026-08-03T09:46:25.407793Z","title":"Computable measure of entanglement,","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.407793Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:75d5b28f13d3835f503949c69dc22945fd8994ad1298820331066a69e9733d15","observation_id":"0555b3b1-027e-4b9d-80c2-bf0cac3b8140","resolution":{"observed_at":"2026-08-03T09:46:25.407793Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1708.00419","last_updated":"2017-10-17T10:40:52Z","snapshot_observed_at":"2026-08-19T10:14:37.543302Z","submitted_at":"2017-07-27T15:45:27Z","title":"Quantum Hall Effect and Langlands Program","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1708.00419","snapshot_observed_at":"2026-08-03T09:46:25.627401Z","title":"Quantum Hall Effect and Langlands Program,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.627401Z"},"links":{"cited_paper":"/paper/1708.00419","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:82859c7bb5d7b4b6924e8b7cbe3c2c16807cf5556929541fa996229debc902e5","observation_id":"9b1b7dc2-fbcd-4ee8-86c3-7033bf659a16","resolution":{"observed_at":"2026-08-03T09:46:25.627401Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0503172","last_updated":"2005-04-06T09:28:47Z","snapshot_observed_at":"2026-08-12T01:07:14.084392Z","submitted_at":"2005-03-08T06:37:28Z","title":"Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0503172","snapshot_observed_at":"2026-08-03T09:46:25.505032Z","title":"Chern numbers in a discretized Brillouin zone: Efficient method to compute (spin) Hall conductances,","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.505032Z"},"links":{"cited_paper":"/paper/cond-mat/0503172","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:a5137d328f12636270350deefa98ad64a08ff371f9b169dbf5310f8105d38ec7","observation_id":"bebaec0b-1a20-4d64-bdc6-c9d82fa7f248","resolution":{"observed_at":"2026-08-03T09:46:25.505032Z","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":"2026-08-03T09:46:25.539662Z","title":"Parallel transport and “quantum holonomy","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.539662Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:2b8430705e47eb35f263bcccb0fe72e1edd44c2205d78dc863c6b69b4327455f","observation_id":"bb697c4d-a77d-4ad5-8a78-9e299c74ccf1","resolution":{"observed_at":"2026-08-03T09:46:25.539662Z","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":"2026-08-03T09:46:25.592005Z","title":"An extension of kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras,","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.592005Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:021aa71336e66cc1e80f9c443e7c4111d9e1fe9f041264f7e110063aa1c915df","observation_id":"18c2165b-4e3f-4592-8efb-9d644272fa64","resolution":{"observed_at":"2026-08-03T09:46:25.592005Z","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":"2026-08-03T09:46:25.889273Z","title":"Statistical distance and hilbert space,","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.889273Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:0403b7e5ffdeb592d022f8f64a62b933e1f32bb53648a497f8f56be750d12244","observation_id":"acdcb67d-b71a-4f51-bb9f-f202e9971832","resolution":{"observed_at":"2026-08-03T09:46:25.889273Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.11879","last_updated":"2022-07-17T04:51:41Z","snapshot_observed_at":"2026-08-18T08:25:46.574614Z","submitted_at":"2018-12-31T16:20:44Z","title":"Topological Aspects of Matters and Langlands Program","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.11879","snapshot_observed_at":"2026-08-03T09:46:25.663623Z","title":"Topological aspects of matters and Langlands program,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.663623Z"},"links":{"cited_paper":"/paper/1812.11879","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:af08af7a5941abd86569c26a7077a5717b0617f4506087c139eb7c5265f544b7","observation_id":"c94dc388-86ec-4819-b494-8bf2ccdc4771","resolution":{"observed_at":"2026-08-03T09:46:25.663623Z","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":"2026-08-03T09:46:25.724568Z","title":"Model for a quantum hall effect without landau levels: Condensed-matter realization of the","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.724568Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:a5d4c49ab006ee0ae7235d79da3cfefebfb9f06932b49f188c630adb2ea30160","observation_id":"cb5ebef1-e328-45d9-9692-aa79e22a4bc0","resolution":{"observed_at":"2026-08-03T09:46:25.724568Z","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":"2026-08-03T09:46:25.789543Z","title":"Riemannian structure on manifolds of quantum states,","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.789543Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:c0fb0443b56c2e5ebb5193b73044ba52fd0f8baa7973f53f2df57e4ffcde34c4","observation_id":"f784bfa7-5d08-4e56-92cf-0910eb0f530a","resolution":{"observed_at":"2026-08-03T09:46:25.789543Z","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":"2026-08-03T09:46:26.272708Z","title":"Computation of Uhlmann’s parallel transport for density matrices and the Bures metric on three-dimensional Hilbert space,","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.272708Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:b5500a5bd7e31db34c1064301ee5c3092535363392e5830403103a0bfe4bc458","observation_id":"0cadf2df-0cee-4fc7-b2d4-c31881f7faec","resolution":{"observed_at":"2026-08-03T09:46:26.272708Z","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":"2026-08-03T09:46:25.987330Z","title":"Statistical distance and the geometry of quantum states,","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:25.987330Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:7b7e9cca0415457a30cf67cf4e2ab08b1b1b86f9c46c1bc7d37d39e9906fe418","observation_id":"e1a9064a-7bea-4e1c-ba33-8aca3c5f92be","resolution":{"observed_at":"2026-08-03T09:46:25.987330Z","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":"2026-08-03T09:46:26.080612Z","title":"Topological indices for open and thermal systems via uhlmann’s phase,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.080612Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:446d94046d3d17f865459e4ae28bfeeb0238ff82927b645f404f675fdf9d27d8","observation_id":"7a18d364-86de-412b-89a3-b3f529f00d2e","resolution":{"observed_at":"2026-08-03T09:46:26.080612Z","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":"2026-08-03T09:46:26.178583Z","title":"Uhlmann phase as a topological measure for one-dimensional fermion systems,","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.178583Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:f6e33f2426b48560233ff6085dc687d9d720432942f3ad1d60868b7a0724a947","observation_id":"3d44cd96-5057-4a58-a911-63cfef11e071","resolution":{"observed_at":"2026-08-03T09:46:26.178583Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.08670","last_updated":"2024-09-13T09:35:05Z","snapshot_observed_at":"2026-08-16T13:18:52.541249Z","submitted_at":"2024-09-13T09:35:05Z","title":"Proof of the geometric Langlands conjecture IV: ambidexterity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.08670","snapshot_observed_at":"2026-08-03T09:46:26.651084Z","title":"Proof of the geometric Langlands conjecture IV: ambidexterity,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.651084Z"},"links":{"cited_paper":"/paper/2409.08670","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:2451d205bfc499dec7f0ed4c41bc0127869f731865bea20cf5c47444c2b87024","observation_id":"fef28ac1-bb33-4e13-8eed-b08bd418e597","resolution":{"observed_at":"2026-08-03T09:46:26.651084Z","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":"2026-08-03T09:46:26.371531Z","title":"Proof of the geometric langlands conjecture i: construction of the functor,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.371531Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:5231fea22f488b450a137a700bd88cba2dbb20b3a9765327fd9517f3f258e563","observation_id":"d038742e-a2ed-4cca-a2a9-fd94462222dc","resolution":{"observed_at":"2026-08-03T09:46:26.371531Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.03648","last_updated":"2024-09-11T06:41:16Z","snapshot_observed_at":"2026-08-16T13:54:57.821182Z","submitted_at":"2024-05-06T17:12:15Z","title":"Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.03648","snapshot_observed_at":"2026-08-03T09:46:26.468130Z","title":"Proof of the geometric langlands conjecture ii: Kac-moody localization and the fle,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.468130Z"},"links":{"cited_paper":"/paper/2405.03648","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:b78b04601da0c48e950a7087965e38aa6af746593f7257080becf6da86b7fcdb","observation_id":"44c515f7-3ea9-4237-9797-910d97aa8d36","resolution":{"observed_at":"2026-08-03T09:46:26.468130Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.07051","last_updated":"2024-09-11T06:54:14Z","snapshot_observed_at":"2026-08-16T13:19:32.618508Z","submitted_at":"2024-09-11T06:54:14Z","title":"Proof of the geometric Langlands conjecture III: compatibility with parabolic induction","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.07051","snapshot_observed_at":"2026-08-03T09:46:26.554725Z","title":"Proof of the geometric langlands conjecture iii: compatibility with parabolic induction,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.554725Z"},"links":{"cited_paper":"/paper/2409.07051","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:2c8c227a2f0057e4486b76be9d2ad413f81c68c2479bf3547ff1ec4078106b05","observation_id":"ee1e8fea-e2ad-4f83-a94b-e583b0963a90","resolution":{"observed_at":"2026-08-03T09:46:26.554725Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0604151","last_updated":"2007-01-16T13:47:57Z","snapshot_observed_at":"2026-07-07T04:57:17.922142Z","submitted_at":"2006-04-21T19:17:43Z","title":"Electric-Magnetic Duality And The Geometric Langlands Program","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0604151","snapshot_observed_at":"2026-08-03T09:46:26.755593Z","title":"Electric-Magnetic Duality And The Geometric Langlands Program,","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.755593Z"},"links":{"cited_paper":"/paper/hep-th/0604151","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:b511aa61c573eb2a24d3a23f061af5e6acc60c4652c9377dc867f73288782dde","observation_id":"601fc044-368b-43f0-8e35-b7b7cd7e9e51","resolution":{"observed_at":"2026-08-03T09:46:26.755593Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0512172","last_updated":"2005-12-15T18:28:21Z","snapshot_observed_at":"2026-08-13T03:15:13.183399Z","submitted_at":"2005-12-15T18:28:21Z","title":"Lectures on the Langlands Program and Conformal Field Theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0512172","snapshot_observed_at":"2026-08-03T09:46:26.853616Z","title":"Lectures on the Langlands program and conformal field theory,","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:26.853616Z"},"links":{"cited_paper":"/paper/hep-th/0512172","citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:0fbd3a9fa5fc93c9b7bdb85d55581c558475fb016c9e7f1630afa7dc1c20ed07","observation_id":"68276942-a237-4465-b287-a8d06fce83f4","resolution":{"observed_at":"2026-08-03T09:46:26.853616Z","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":"2026-08-03T09:46:24.289449Z","title":null,"venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data","version":2},"reference_index":2010,"source":"pdf_text","source_observed_at":"2026-08-03T09:46:24.289449Z"},"links":{"citing_paper":"/paper/2601.13467"},"observation_digest":"sha256:42cbeaa1ffb6c7fad59c4abdc7ed345e9397dbe047774acff7ddf7c87909e435","observation_id":"6159ebea-4ac8-4ebb-9679-24c5eb99c625","resolution":{"observed_at":"2026-08-03T09:46:24.289449Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2601.13467","last_updated":"2026-06-10T06:33:18Z","latest_version":2,"primary_category":"quant-ph","snapshot_observed_at":"2026-08-16T02:46:13.198404Z","submitted_at":"2026-01-19T23:41:35Z","title":"Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data"},"reference_resolution":{"displayed":40,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":39,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":40},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 1 inbound Pith citation observation for arXiv:2601.13467."}