{"as_of":"2026-08-20T05:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e8e58272caf830fa83177eceeb38f861d1320eaf1496c71e1b40649c583adf7f","coverage":[{"denominator":72,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":72,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T03:22:14.826612Z","state":"measured"},{"denominator":72,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":72,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.25163/citation-record","integrity":"/paper/2607.25163/integrity","json":"/paper/2607.25163/citation-record.json","paper":"/paper/2607.25163"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T03:22:07.066852Z","title":"Absil, R","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.066852Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:af5bc3a5939d52183592c6c12536b2464bfea559d8d61cfe947cb1e9bee21ba4","observation_id":"2dd56ebf-dc0d-4cdc-ac43-98c4bb460197","resolution":{"observed_at":"2026-08-01T03:22:07.066852Z","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":"2026-08-01T03:22:07.183521Z","title":"Absil, R","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.183521Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:aa069b97b23adbb1e51ab37b0c28ebdca7b62908013fb0dd52d82698040244b5","observation_id":"3b36dbdb-0555-468e-9b93-5a872fd6242e","resolution":{"observed_at":"2026-08-01T03:22:07.183521Z","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":"2026-08-01T03:22:07.298137Z","title":"Cam- bridge University Press, Cambridge, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.298137Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:1207fc1c853d64e71447cc731637b1368ee5f5c98e84ef279ab5370cb7d01736","observation_id":"e0def22a-31a9-4cf8-b518-95a88dc4da43","resolution":{"observed_at":"2026-08-01T03:22:07.298137Z","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":"2026-08-01T03:22:07.434923Z","title":"What regularized auto- encoders learn from the data-generating distribution.The Journal of Machine Learning Research, 15(1):3563–3593, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.434923Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:408be24c0c90deaf54a8d790a02d242e00f38cbe0cb2f77e09542b04e34b2575","observation_id":"61d7aa22-9658-4438-8b2c-a7ff92da8762","resolution":{"observed_at":"2026-08-01T03:22:07.434923Z","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":"2026-08-01T03:22:07.584058Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.584058Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:02fd7983ff4fcef9baae513b0ebf9ef6c63ab510724c02647235e5bbaf432a03","observation_id":"6754ac33-d4ca-40a1-b925-f1300aa980ae","resolution":{"observed_at":"2026-08-01T03:22:07.584058Z","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":"2026-08-01T03:22:07.719495Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.719495Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:073209760b0d8679a37c261f2c7ba118eb23a91985f8d23ff4d71e4c4362addb","observation_id":"3ca3d1c6-c7e2-477e-92ca-c19bebc9afbb","resolution":{"observed_at":"2026-08-01T03:22:07.719495Z","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":"2026-08-01T03:22:07.856836Z","title":"Berger, R","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.856836Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:66f079c18ae9c7f087612d8ebf74d82169bf1d6f934209ab4483b9f48862b026","observation_id":"0ac0efb5-9afd-4cd1-b47a-a87e54f0887a","resolution":{"observed_at":"2026-08-01T03:22:07.856836Z","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":"2026-08-01T03:22:07.983630Z","title":"Bhattacharya and V","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:07.983630Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:479ae5958fda8d7a1c68d0d70c3f9a6bb407c9243cdca0d6561192a34e660bc2","observation_id":"b84e1b53-8088-40b2-ae58-ce0488a2a83c","resolution":{"observed_at":"2026-08-01T03:22:07.983630Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1904.13386","last_updated":"2019-05-14T13:49:37Z","snapshot_observed_at":"2026-08-14T16:39:10.926728Z","submitted_at":"2019-04-30T17:39:55Z","title":"Active Manifolds: A non-linear analogue to Active Subspaces","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.13386","snapshot_observed_at":"2026-08-01T03:22:08.142104Z","title":null,"venue":null,"work_id":null,"year":1904},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.142104Z"},"links":{"cited_paper":"/paper/1904.13386","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:e2a5086c72ff643d2ac4f9c9bc860cd570d8bc60e3d3b09791ba6a66f44b970c","observation_id":"5fec2085-5d1c-428d-baaf-e18f9e57eaab","resolution":{"observed_at":"2026-08-01T03:22:08.142104Z","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":"2026-08-01T03:22:08.223030Z","title":"Chatterjee","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.223030Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:434c3f8a1b6298d81c4b1dff4c225fbcf3e184e4118d143be140a7b758ac113f","observation_id":"b56b17a4-9078-4239-8ac5-1f05f1265ab0","resolution":{"observed_at":"2026-08-01T03:22:08.223030Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.13059","last_updated":"2023-02-25T11:06:06Z","snapshot_observed_at":"2026-08-16T15:52:46.399062Z","submitted_at":"2023-02-25T11:06:06Z","title":"Intrinsic minimum average variance estimation for sufficient dimension reduction with symmetric positive definite matrices and beyond","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.13059","snapshot_observed_at":"2026-08-01T03:22:08.332607Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.332607Z"},"links":{"cited_paper":"/paper/2302.13059","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:3d78e24f4e8cafc216eace8c9a6c4dcc76aae991447e1accdb260b59afb75910","observation_id":"3b22a116-7ecb-4300-8b54-e9cc7ababebe","resolution":{"observed_at":"2026-08-01T03:22:08.332607Z","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":"2026-08-01T03:22:08.393151Z","title":"¨Uber systeme von linearen partiellen dif- ferentialgleichungen erster ordnung.Mathematische Annalen, 117:98–105, 1939","venue":null,"work_id":null,"year":1939},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.393151Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:b751c731e23b0e42cb8e911fd10ef2ac9baa3b892e66fdcfd93b49f712667495","observation_id":"dadc93e6-922b-4532-92b0-ab0cddc28559","resolution":{"observed_at":"2026-08-01T03:22:08.393151Z","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":"2026-08-01T03:22:08.458320Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.458320Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:810ea2b8fe7c7a564c93754b04af04d5069b5802645803415ef4d7af35fd3b64","observation_id":"7d27487d-8839-4740-a507-53f517de1c17","resolution":{"observed_at":"2026-08-01T03:22:08.458320Z","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":"2026-08-01T03:22:08.525193Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.525193Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:87469fc07f434f1a690a4679bfa662f322199b51556580c0dcb94b1094726972","observation_id":"979a00b1-349a-407e-96bb-50b2e7142307","resolution":{"observed_at":"2026-08-01T03:22:08.525193Z","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":"2026-08-01T03:22:08.595061Z","title":"G Constantine, A","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.595061Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:155becb87b57ee6925ef796624b39feead31e271fc0d1e4c768eaeb532b5bda7","observation_id":"2820f7cd-ccf0-46fc-828c-b9637c3e51f5","resolution":{"observed_at":"2026-08-01T03:22:08.595061Z","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":"2026-08-01T03:22:08.682839Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.682839Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:bd92c2b1df984479d0ab1d3c3a3bf6dec5189bd93585e436a6a92d0c589a1dc4","observation_id":"253d875f-987d-4748-bda0-492702f254a0","resolution":{"observed_at":"2026-08-01T03:22:08.682839Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1408.0545","last_updated":"2015-07-02T16:23:32Z","snapshot_observed_at":"2026-08-16T18:29:10.710955Z","submitted_at":"2014-08-03T21:13:13Z","title":"Computing active subspaces with Monte Carlo","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1408.0545","snapshot_observed_at":"2026-08-01T03:22:08.779296Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.779296Z"},"links":{"cited_paper":"/paper/1408.0545","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:73876859ee64dab1727a884735870116815adc0f54d8195c8bc052c5e1dfe422","observation_id":"f61ca9a7-e696-4599-9d04-93886cb14c05","resolution":{"observed_at":"2026-08-01T03:22:08.779296Z","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":"2026-08-01T03:22:08.898339Z","title":null,"venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:08.898339Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:bc3a9588381cccb285ccb199f38bf6111fedb0b0d3f5c6dba18f50e2a27e5c1c","observation_id":"691f31a2-8924-41de-9a0a-972ccfc8d344","resolution":{"observed_at":"2026-08-01T03:22:08.898339Z","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":"2026-08-01T03:22:09.021341Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.021341Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:b838a27bcc8e07701a1dfe2db590895e883da06b521a96b78f3f7a76d2287dbb","observation_id":"3bc768c0-7c35-4cff-9953-976a8b248244","resolution":{"observed_at":"2026-08-01T03:22:09.021341Z","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":"2026-08-01T03:22:09.147488Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.147488Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:543b04160f9818973da7fc2c5c0d1e1a61a99e9315321e3b7fd4560fe0d0232e","observation_id":"2d951ec6-02fb-41e0-945f-166441134e00","resolution":{"observed_at":"2026-08-01T03:22:09.147488Z","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":"2026-08-01T03:22:09.268084Z","title":"Edelman, T","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.268084Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:1573268813549da5c23b7deb0035a38b62be21dbf2db181d50745844e1f49eca","observation_id":"b54c9306-339b-4f6c-87e2-7c01c043faa5","resolution":{"observed_at":"2026-08-01T03:22:09.268084Z","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":"2026-08-01T03:22:09.402053Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.402053Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:c9ea9fa4fa3f655ef8286daf695501734303cd8bffbdf6e5c73bd677994c32f7","observation_id":"b55637e5-5eda-438b-80fb-5790dd45a250","resolution":{"observed_at":"2026-08-01T03:22:09.402053Z","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":"2026-08-01T03:22:09.535031Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.535031Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:243ef8459a2b5ab28656d64306dc5dd38f1c196c979057babf44137e300e1586","observation_id":"e8faddcf-f017-4d01-9278-2aec9f0a9144","resolution":{"observed_at":"2026-08-01T03:22:09.535031Z","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":"2026-08-01T03:22:09.649941Z","title":"Glaws, P","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.649941Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:efecd74fb82588b384858e5f9097dafe196ac351d28826d34e4afac80f5ce15d","observation_id":"484f1789-b957-4e37-9e3e-c0c591c77307","resolution":{"observed_at":"2026-08-01T03:22:09.649941Z","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":"2026-08-01T03:22:09.803942Z","title":"Glaws and P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.803942Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:350d8b84f80bfcef59503cd647345e92b9bdc3d5489b52e63a7e144ba34846dd","observation_id":"7855c1ea-e6c4-4acf-afd8-a800196cfac2","resolution":{"observed_at":"2026-08-01T03:22:09.803942Z","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":"2026-08-01T03:22:09.956912Z","title":"Glaws, P","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:09.956912Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:d905739c4a82a32f179a82267b8a20e5317eb17d92992373440c0cb2258d11e8","observation_id":"eb858ab4-6946-4738-a996-882e9239c968","resolution":{"observed_at":"2026-08-01T03:22:09.956912Z","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":"2026-08-01T03:22:10.127780Z","title":"Golub and C.F","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:10.127780Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:3cf9c159d7f8ef44393864d214ee76b1229ac484536805df3c4e627a05e749a1","observation_id":"c00917d6-c061-4cd7-a4f8-99afca818b3e","resolution":{"observed_at":"2026-08-01T03:22:10.127780Z","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":"2026-08-01T03:22:10.282186Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:10.282186Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:387786d88cf25b45a8f773741d0f6506d1d8301d96e7511990caf65f608e3113","observation_id":"fe26331d-4dd6-4bfa-854e-a918bf0618df","resolution":{"observed_at":"2026-08-01T03:22:10.282186Z","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":"2026-08-01T03:22:10.454734Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:10.454734Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:ca561f360cc92e904e868e6213524976367c823343ec38b06061ee9e1b5941b1","observation_id":"910a4dc1-d358-4f4a-9d49-0f6a0864b15b","resolution":{"observed_at":"2026-08-01T03:22:10.454734Z","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":"2026-08-01T03:22:10.619076Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:10.619076Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:7be84e844d132f1588a3258eb2c5873355b636da51620207c32ebfae5410077b","observation_id":"312ab239-6574-4674-944e-74020427d1b4","resolution":{"observed_at":"2026-08-01T03:22:10.619076Z","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":"2026-08-01T03:22:10.718978Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:10.718978Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:886c830f2ade668f93d74c105f4154569f1bbde9a45acee01d22c1bbd47105af","observation_id":"486283c0-305e-41f4-9405-c5041900df44","resolution":{"observed_at":"2026-08-01T03:22:10.718978Z","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":"2026-08-01T03:22:10.834241Z","title":"Hang and X Wang","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:10.834241Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:20dcfd2045ddc635124b27e75ea4381e4e1d027cf6c0859c1927e25b00453566","observation_id":"b2f8b772-4e14-4d21-972f-591b674b45b0","resolution":{"observed_at":"2026-08-01T03:22:10.834241Z","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":"2026-08-01T03:22:10.975996Z","title":"Hastie and W","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:10.975996Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:19455d4eca52c526bf5567288f3f4930d98e250bd881f07c725ce213bea5712e","observation_id":"792addd6-ce76-494a-8c07-03145ca170a8","resolution":{"observed_at":"2026-08-01T03:22:10.975996Z","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":"2026-08-01T03:22:11.110065Z","title":"Partially isometric matrices.J","venue":null,"work_id":null,"year":1967},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.110065Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:9dab5858f1990dc34c32e758e662a6d7326f613e5b147d549e5124b7d008d794","observation_id":"b0f46488-6fe0-474b-8146-aeedc0ffe468","resolution":{"observed_at":"2026-08-01T03:22:11.110065Z","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":"2026-08-01T03:22:11.226368Z","title":"M Hokanson and P","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.226368Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:01eacbc6c4506b7944ef5ae81254bf7fbccb19dcdb7863f617a48f5d48cb842a","observation_id":"4d520578-67ae-44b8-9072-9fd07e4241f4","resolution":{"observed_at":"2026-08-01T03:22:11.226368Z","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":"2026-08-01T03:22:11.311387Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.311387Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:238cec6000d3a0e1ad53cc5f1917f85e85da2be52d3ac7f2ddc9e84d8ed8189d","observation_id":"fa2a3380-8e4a-4acf-bd11-8f8a8bfcbeb5","resolution":{"observed_at":"2026-08-01T03:22:11.311387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1906.00105","last_updated":"2020-10-12T21:49:30Z","snapshot_observed_at":"2026-08-14T16:22:45.134756Z","submitted_at":"2019-05-31T22:18:13Z","title":"A Lipschitz Matrix for Parameter Reduction in Computational Science","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1906.00105","snapshot_observed_at":"2026-08-01T03:22:11.426487Z","title":null,"venue":null,"work_id":null,"year":1906},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.426487Z"},"links":{"cited_paper":"/paper/1906.00105","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:c088c42c082bf8c9490ecbd804d4e71a0cf1fd2c2172f020461d9a145e0deef9","observation_id":"970f1383-e269-42ba-80de-dd66744ba5cb","resolution":{"observed_at":"2026-08-01T03:22:11.426487Z","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":"2026-08-01T03:22:11.540157Z","title":"Huckemann, T","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.540157Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:91c1b943c430a64446bd140c6d4fcf0c9149bc86743a1e4b3621391ce96f88eb","observation_id":"17c53b6a-3679-4d17-8e5d-5e7278d76a8c","resolution":{"observed_at":"2026-08-01T03:22:11.540157Z","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":"2026-08-01T03:22:11.656433Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.656433Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:9438bf184c23e9e9b1adcb1553c43527b3566467d4ace24e658e88c20d199e60","observation_id":"7855f4cc-74e6-4bd8-9d24-ce9c094f5852","resolution":{"observed_at":"2026-08-01T03:22:11.656433Z","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":"2026-08-01T03:22:11.787460Z","title":"Joshi, E","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.787460Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:9f679a2fcc92480b84df0fa443115d3a55a7c796b1723d6289b926ff96074456","observation_id":"932bf37a-0ae2-45f5-811b-743c704fea39","resolution":{"observed_at":"2026-08-01T03:22:11.787460Z","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":"2026-08-01T03:22:11.921816Z","title":null,"venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:11.921816Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:89b030696029cdbf86286313db153b5e4056872b812cbf46b9ea292d2743a9f3","observation_id":"0da0ffca-b0d2-4598-b9d1-f14fec62fdad","resolution":{"observed_at":"2026-08-01T03:22:11.921816Z","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":"2026-08-01T03:22:12.038625Z","title":"Klassen, A","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.038625Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:bc720699fe3f866579dc5fb960143a03b3b5fb977f7ad32953e584eee3585839","observation_id":"c4b5dbeb-361c-4742-963c-64417e03ac6f","resolution":{"observed_at":"2026-08-01T03:22:12.038625Z","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":"2026-08-01T03:22:12.178434Z","title":"Lee.Riemannian Manifolds: An Introduction to Curvature","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.178434Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:dc2dfe367f7fe0c8efcaa45c060a5087f45f561300c1dfc9fe40eb0090eb3192","observation_id":"33d33204-abe2-486e-85b4-ecb8ff067570","resolution":{"observed_at":"2026-08-01T03:22:12.178434Z","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":"2026-08-01T03:22:12.323430Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.323430Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:07408b4c224082822fce6f00f9b7c3f283cff7b28680e9bbf636c04cadc38121","observation_id":"ef6b0fd9-ebc2-4dfb-b5d3-7740eff535b8","resolution":{"observed_at":"2026-08-01T03:22:12.323430Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.08373","last_updated":"2019-06-05T19:21:35Z","snapshot_observed_at":"2026-08-14T17:40:47.023299Z","submitted_at":"2018-12-20T06:23:55Z","title":"Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.08373","snapshot_observed_at":"2026-08-01T03:22:12.406719Z","title":"Lee and K","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.406719Z"},"links":{"cited_paper":"/paper/1812.08373","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:e34b480907cb3026dc9ed249271f6fa64aa87bae50f0a2b4ca28f8c2cdfb476f","observation_id":"8adf313f-69fc-44d0-a490-09b4a9faeb35","resolution":{"observed_at":"2026-08-01T03:22:12.406719Z","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":"2026-08-01T03:22:12.517362Z","title":"Lewis, R","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.517362Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:3226958634dc45967735dadd4145aff30218afcb8d20a434b99bc62992b8e3b2","observation_id":"7ad20c18-e68c-4e45-a74c-4dd174b36ef0","resolution":{"observed_at":"2026-08-01T03:22:12.517362Z","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":"2026-08-01T03:22:12.671494Z","title":"Li.Sufficient dimension reduction: Methods and applica- tions with R","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.671494Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:bac1d7d98fee2dd0c8ccad7ce9b082e7af56eeb699ccb9955b8368e7658e04b3","observation_id":"e63c4395-11de-4841-9997-067865f6640a","resolution":{"observed_at":"2026-08-01T03:22:12.671494Z","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":"2026-08-01T03:22:12.801253Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.801253Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:4232641f3232b48474dc66ce9bdacc52633d35b2d60f6a66f689f59c8e86921c","observation_id":"a88fa8ff-ab79-4bbd-b0aa-edf0fae78cc9","resolution":{"observed_at":"2026-08-01T03:22:12.801253Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1604.04588","last_updated":"2016-04-18T20:35:33Z","snapshot_observed_at":"2026-08-14T22:01:29.930761Z","submitted_at":"2016-04-15T18:13:48Z","title":"Mathematical Analysis and Dynamic Active Subspaces for a Long term model of HIV","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1604.04588","snapshot_observed_at":"2026-08-01T03:22:12.920799Z","title":"Loudon and S","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:12.920799Z"},"links":{"cited_paper":"/paper/1604.04588","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:b80fbc45d46ddf222bb3410ae3d245eba92cdea8fbeca4b3368c10c4e392b6ff","observation_id":"86c6cee1-c791-41b2-8404-df8e1e57db67","resolution":{"observed_at":"2026-08-01T03:22:12.920799Z","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":"2026-08-01T03:22:13.032386Z","title":"Lukaczyk, F","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.032386Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:e3d3ae587efd8d3664ef9328241619b93d90f57b9d0c4c2f348e46fba7ee96c2","observation_id":"abc1c7ee-438a-4862-9cad-ad5e49a56ddb","resolution":{"observed_at":"2026-08-01T03:22:13.032386Z","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":"2026-08-01T03:22:13.136915Z","title":"Mallasto and A","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.136915Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:8ad5cf43a9da799a84410a335b940cf186cae35cbdadb642348439ca04981bea","observation_id":"1b8da4e9-c29b-443f-8b83-088c006c5264","resolution":{"observed_at":"2026-08-01T03:22:13.136915Z","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":"2026-08-01T03:22:13.249806Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.249806Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:6497e39dc768443f57fa891bba94d2397de75aa92791ffe747dc762f4d13169c","observation_id":"4183f3f7-7628-4486-b72c-e0423da0730f","resolution":{"observed_at":"2026-08-01T03:22:13.249806Z","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":"2026-08-01T03:22:13.332610Z","title":"Mukherjee, Q","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.332610Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:44d7d016688a1564e31b91fce349f0b0ed584ed750ec3e5c936ed908128acd95","observation_id":"9478d85b-aa7b-47df-af96-8d217724e4a7","resolution":{"observed_at":"2026-08-01T03:22:13.332610Z","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":"2026-08-01T03:22:13.414407Z","title":null,"venue":null,"work_id":null,"year":1956},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.414407Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:c766f74dbc99011d7ebfa040188b912b73bebed870064bd84d77149b2bedb3f3","observation_id":"3c7d701d-1c0c-4bb3-9ba5-0088d982bd75","resolution":{"observed_at":"2026-08-01T03:22:13.414407Z","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":"2026-08-01T03:22:13.498192Z","title":"Nilsson, F","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.498192Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:aaeb2851c7bb0db0700c2ff4cb0bd8b3ad6b48ce7acbf521adadbde9e5674cc7","observation_id":"b595a186-2518-4f16-a74d-4e408fc8b28a","resolution":{"observed_at":"2026-08-01T03:22:13.498192Z","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":"2026-08-01T03:22:13.579422Z","title":"Ozertem and D","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.579422Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:956961d85c7010014a1866b41ee7b80caff1fff47579b9239a4518357ee0bb74","observation_id":"01b105a3-fec3-40f8-aa45-40840408f4e6","resolution":{"observed_at":"2026-08-01T03:22:13.579422Z","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":"2026-08-01T03:22:13.661694Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.661694Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:6adae861b0764a2c6af32d85221d3db7c5da33152b2ae60b3f34dae5c068b409","observation_id":"0e937d4e-540d-4cf1-8c7b-9b95eb1e2772","resolution":{"observed_at":"2026-08-01T03:22:13.661694Z","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":"2026-08-01T03:22:13.762467Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.762467Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:1686f71c67b89b62e3bc6de953a6ba6150a85400ae7ecfd61f1c6dd02c8f6547","observation_id":"7df7a3c6-fc1c-4d08-a51f-e24ca3af3071","resolution":{"observed_at":"2026-08-01T03:22:13.762467Z","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":"2026-08-01T03:22:13.845178Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.845178Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:20d70fb3b8e9c9d5a15ac7b11c46573db9052e49695f02563f3124f160916fc7","observation_id":"1429d0ae-5f50-484f-834e-a2665d606000","resolution":{"observed_at":"2026-08-01T03:22:13.845178Z","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":"2026-08-01T03:22:13.927096Z","title":"Romor, M","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:13.927096Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:76a80c34a758fdcea4624b17ecce2563d733929285bfe274fcbba22dcce9ce4e","observation_id":"fb5c569c-69a7-40e8-88f3-629d1432b435","resolution":{"observed_at":"2026-08-01T03:22:13.927096Z","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":"2026-08-01T03:22:14.009996Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.009996Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:53cd605e59ccad7b007946e2e9dab7daf3d4c63de61b83c04e8ff9593e8db6e7","observation_id":"4454b440-cd8f-42e2-8702-f6e70641edd0","resolution":{"observed_at":"2026-08-01T03:22:14.009996Z","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":"2026-08-01T03:22:14.091554Z","title":"Serani and M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.091554Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:524405666e2fb6256b9385a65876d00455e3cbe91a9d24f89e44015f50b87029","observation_id":"12a9a053-76f4-4542-91c0-65b05a74eba9","resolution":{"observed_at":"2026-08-01T03:22:14.091554Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.10212","last_updated":"2026-06-10T17:56:45Z","snapshot_observed_at":"2026-08-07T17:21:33.999002Z","submitted_at":"2026-06-08T22:05:16Z","title":"Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.10212","snapshot_observed_at":"2026-08-01T03:22:14.173149Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.173149Z"},"links":{"cited_paper":"/paper/2606.10212","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:535cf33caf5cb4320620f85b3aff0669ae88706d59ad6e0ee41918eddea19ea0","observation_id":"bfa13f27-e028-4c2f-9161-a275debc21c1","resolution":{"observed_at":"2026-08-01T03:22:14.173149Z","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":"2026-08-01T03:22:14.255448Z","title":"Srivastava and E","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.255448Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:df6ce5a42ac237552bcfd29b34f02e1e70db30c1ccc77ea2ac2182c5d9426b5f","observation_id":"adf140cb-781f-4015-89e0-ce8e8e6214a1","resolution":{"observed_at":"2026-08-01T03:22:14.255448Z","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":"2026-08-01T03:22:14.337762Z","title":"Klassen.Functional and Shape Data Analysis","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.337762Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:06c0756cb24ac789043c478bc29b9ae3a7f3938760a8e88f0cb45248c47471d3","observation_id":"0a9ec581-df67-4cd6-ba4b-59f1b4ceadec","resolution":{"observed_at":"2026-08-01T03:22:14.337762Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1602.06620","last_updated":"2016-02-22T01:35:37Z","snapshot_observed_at":"2026-08-14T22:09:24.936890Z","submitted_at":"2016-02-22T01:35:37Z","title":"A randomized algorithm for enumerating zonotope vertices","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1602.06620","snapshot_observed_at":"2026-08-01T03:22:14.421778Z","title":"Stinson, D","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.421778Z"},"links":{"cited_paper":"/paper/1602.06620","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:2da871b6af2234dffb529ca5d10e06789b735ff6a2f17e2732ee0f8a3d068abc","observation_id":"c31e6011-0d8a-4036-a9ce-034fd29a187b","resolution":{"observed_at":"2026-08-01T03:22:14.421778Z","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":"2026-08-01T03:22:14.480737Z","title":"Walker.The Shapes of Things: A Practical Guide to Dif- ferential Geometry and the Shape Derivative","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.480737Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:a358dd22b652c5a12cc16dbaf5b7a4f7cd85e927d09e50287ee9ec8ff7b11f0d","observation_id":"b9aff6a7-79c5-4d2a-a6a3-1f3f0443061e","resolution":{"observed_at":"2026-08-01T03:22:14.480737Z","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":"2026-08-01T03:22:14.560153Z","title":"Efficient calibration of a tur- bine disc heat transfer model under uncertainty.Journal of Thermophysics and Heat Transfer, pages 1–11, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.560153Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:265a2f06c3fcba09ca7c8984a2599aca85ff7e9b548343e007fa8a8d9e42d88c","observation_id":"c0a7a05a-4e58-4673-9247-e7b90cdc915e","resolution":{"observed_at":"2026-08-01T03:22:14.560153Z","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":"2026-08-01T03:22:14.642754Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.642754Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:9639e818c430660a439d203d0492bfdb96aa8f44b0dd1035b9e379b016de5ed1","observation_id":"ca710914-2e31-4ba3-942c-eb952097fa95","resolution":{"observed_at":"2026-08-01T03:22:14.642754Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.00292","last_updated":"2020-07-01T07:32:16Z","snapshot_observed_at":"2026-07-06T09:34:21.565917Z","submitted_at":"2020-07-01T07:32:16Z","title":"Fr\\'echet Sufficient Dimension Reduction for Random Objects","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.00292","snapshot_observed_at":"2026-08-01T03:22:14.704213Z","title":"Ying and Z","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.704213Z"},"links":{"cited_paper":"/paper/2007.00292","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:e5e726f9fc607c74dcf05c39339d006dacec6086d9e20c9e90b9a6d53e8c9c36","observation_id":"96182883-0199-48e0-a494-d0b7d57b02a5","resolution":{"observed_at":"2026-08-01T03:22:14.704213Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1801.07922","last_updated":"2019-11-08T09:37:37Z","snapshot_observed_at":"2026-08-17T04:50:22.462328Z","submitted_at":"2018-01-24T11:06:33Z","title":"Gradient-based dimension reduction of multivariate vector-valued functions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1801.07922","snapshot_observed_at":"2026-08-01T03:22:14.772887Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.772887Z"},"links":{"cited_paper":"/paper/1801.07922","citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:c6012239848b232d16b0ccf9e7cbf57e026d630d7d876d1474fb71896b3980f0","observation_id":"6fe2520b-bd23-4ccb-b9dd-fd098ab24e76","resolution":{"observed_at":"2026-08-01T03:22:14.772887Z","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":"2026-08-01T03:22:14.826612Z","title":"Zanoni, G","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-01T03:22:14.826612Z"},"links":{"citing_paper":"/paper/2607.25163"},"observation_digest":"sha256:f12bd6ee36bc3b0b6ca23b611017e9155ce7ea9389bab603f02f35e9b5f6a0bf","observation_id":"b7d404c5-2927-458e-8f33-5018dc1a1b06","resolution":{"observed_at":"2026-08-01T03:22:14.826612Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.25163","last_updated":"2026-07-28T00:22:24Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-08T01:26:32.839101Z","submitted_at":"2026-07-28T00:22:24Z","title":"A Riemannian View on Active Subspaces"},"reference_resolution":{"displayed":72,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":72,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":72},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 72 of 72 outbound references and 0 inbound Pith citation observations for arXiv:2607.25163."}