{"as_of":"2026-08-10T20:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:41b97b7ee94493eec12dae92e57c1be45cd2331f28a08a7b7103c44ea37f4fd3","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-30T05:17:38.609387Z","state":"measured"},{"denominator":38,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":38,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2606.30173/citation-record","integrity":"/paper/2606.30173/integrity","json":"/paper/2606.30173/citation-record.json","paper":"/paper/2606.30173"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Tensor completion using low-rank tensor train decomposition by","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:3ca14a1e07e56c17da0fc277277bfe3d111933d6eacc23635ec1e65fedb7815c","observation_id":"f8edf1e1-df43-46bc-88c2-2bda40d48fbd","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Provable tensor-train format tensor completion by","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:5289a4736ede09f49a4c1394ea92b2740b0ebd0f4255b87927a37d647cfca3fb","observation_id":"ef28113e-2391-4aae-bbaf-225ef5ec5465","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"SIAM Journal on Scientific Computing , volume=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:7a60b34ec2948328c5c07c04a4525059fa7d6e7e49add71cdc56d0a5e923028e","observation_id":"584a460b-b436-4870-a384-000a05c1eb7b","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"ICPR (2) , pages=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:75d29e2fee05f6b0262eb858b96701559abad1bc97c6e2bf68a0633108852fa0","observation_id":"6ca08c26-4261-43ae-9ffa-af48b3b164aa","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"International Conference on Intelligence and Security Informatics , pages=","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:f20b6dfd3f370dd3c07cb8a358b4f45b02e722bbaf323fb0ff886622ac0b0b34","observation_id":"189591f0-fb02-4302-82d9-7cf7627fba8c","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"SIAM Journal on Scientific Computing , volume=","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:25d54104ac0d039e5633c87db9ebce9b311c6d3f5ec54727bae2ca10c5a1d394","observation_id":"67982cac-ba87-4f09-9bd7-0a43e6c2ada1","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Communications of the ACM , volume=","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:001c01d28c38fac942d45d80f03bf57f091cc0bdce858f5d56dde284f523c61a","observation_id":"fe3b7ce4-0a96-45ad-bfcb-0049837231ee","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:e3ab6191459bdf1a5062926ce12b8589895d028ef3318d371a5075fff6b3987f","observation_id":"f3e86bb6-458b-418d-a9ce-6865f01634fb","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Optimization","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:470555591b31d3ed44fd1a6ee6bcafa11ff83e421647b97bebdc877637cfc97a","observation_id":"1fd07cfd-3974-4b2e-821c-be64a550be08","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"IEEE Transactions on Pattern Analysis and Machine Intelligence , volume=","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:ff9bb7a38ec2ce95e94db1bf28bb10ee3e3196fe048c39706f82b89923bfa5d3","observation_id":"68753f88-c126-47ae-b5a2-2e2cd9bc4682","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"IEEE Transactions on Signal Processing , volume=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:79eaa9ae84255cd8b2fc6cebc9498e45e241636a1905ce1c98b0d43b1198d43a","observation_id":"5ad8e850-2f2c-41b3-b930-0846d4140794","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"SIAM Journal on Optimization , volume=","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:1fc4c292c1a97d503670d7d2ba3526c9bbc03a4634c3b7ca5bd32cf24aca0e64","observation_id":"eb9cf1d9-527a-47b7-8bb8-c889ce73bb5d","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"BIT Numerical Mathematics , volume=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:2902ba009b112be30effb6d183be9f6397bd98c9bff0c494dc1a147439efa303","observation_id":"5989e8a7-5aaf-46b7-ba77-f074364c6541","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Numerische Mathematik , volume=","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:85fb442d8db6c530a0cf88f74e96df56215d66d2a8b11a703742249e43356624","observation_id":"e9b30fe2-1c9c-4cfe-9ce2-e6e32b5f63b7","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Guarantees of","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:12720a72111b94aae27eaceffbcc5280146c08b056bb40760db5a5019620300e","observation_id":"d2a2a6cd-df76-4148-a4b0-9d04c5545b93","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:9a3f4aaaeab2a37268292a883fdb44f4a60d0aee5fdd5593b7aab7269c018b6f","observation_id":"9af9e4f0-0b0a-4558-8d20-3e3d338bc0d9","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Low-rank tensor completion: a","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:8aaca7e2c5e6f371af279e2730ef5de2561fe7744a271bf4a273ef312b5fe3b3","observation_id":"1824611e-52cb-43a9-a21c-e91111fecc84","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2209.04786","last_updated":"2023-04-18T10:53:59Z","snapshot_observed_at":"2026-08-03T20:36:46.953351Z","submitted_at":"2022-09-11T04:56:04Z","title":"Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric","version":3},"cited_work":{"arxiv_id":"2209.04786","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2209.04786","snapshot_observed_at":"2026-06-30T14:54:45.708702Z","title":"arXiv preprint arXiv:2209.04786 , year=","venue":null,"work_id":"b66e1b47-a419-486a-9aa8-3e794d3c7edf","year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"cited_paper":"/paper/2209.04786","citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:2fb7384dbb804bf0976fd2636f74983a99e124ee1981822d566d1a7203362eb4","observation_id":"d34c8fba-c7a8-4da1-a574-90e1b553d420","resolution":{"observed_at":"2026-06-30T14:54:45.710385Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"2023 , publisher=","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:3edcd387bb0e2fda7e8a8ebe712543c3f425ffc45f2af23fa04e0e6c33fd0f73","observation_id":"959fda7a-ba6e-4774-94b7-a1e6606c0f99","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:88434cf60c8e198f11c35cc669fdf29809997490f3660742c17e44129ee368b3","observation_id":"f366ba0d-983b-4196-af2b-f4e20d05114c","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:aea4b3844641bb448f16fd2640feb746905af173e6453676db7dde95f24fca0b","observation_id":"fda80819-5e2b-4816-970a-67aa0ab81e80","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:0382db6d602a59402969641350c94a42b18389ce4ae5809f1204c3f707a7dce7","observation_id":"682f9f00-2a1a-4d9f-b1b5-a720c82df118","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Manopt, a","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:f374fca13f0ef0691c796e3fdcda85608b9c0d06d7a788887a71ecb57c176344","observation_id":"80a57572-f738-425f-8d4b-20edf340c5a7","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:a73ec72ebd59b353ca9cf965ececd98f256d48136bdc6244a8ea2a988a25465a","observation_id":"00c9a0cd-a9b5-45c7-8842-d04e7ba5847a","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Numerical","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:dd9d6037c40a9307f00f5c4f1abd4b56ffc61b95cd3fcc5908e430cb7269ecb8","observation_id":"bcbfc11c-23b8-4c3a-8ab2-35822a0c0f16","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Optimization , volume=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:35488ae96c110ce22670bef39ff5dfe7a9f92ce55052bade57d5e9dae48afc6c","observation_id":"179c99f2-b9da-4442-973f-e6da52da4a7f","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Handbook of variational methods for nonlinear geometric data , pages=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:25a7d68ec9bececda95f31a87e4652c9fa60ac3d969bac8cabff9d09ae4b6f49","observation_id":"186731f4-875d-4daf-a031-dff6ac419682","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Optimization methods on","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:58889a231cbb8f84d62b30502950e8c9c7094c7a5d469c87289f239b5ea439a9","observation_id":"329af15f-5b45-4724-abfa-9e4e2492f007","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Computational Optimization and Applications , volume=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:22ac9606ab614bb73e9ddb16445727a2df0baf373393ab2d4f0cc6a1e9232e46","observation_id":"7647cdfd-b497-402a-8194-2439893ed7e2","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"SIAM Journal on Matrix Analysis and Applications , volume=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:cd16a78b0996191838ceaceca6630ee1f333c93696ed3747cb3d8ad59f410837","observation_id":"172adb29-fe84-4243-aaab-ac42bb669289","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Computational Optimization and Applications , volume=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:ec50ddb10e0adb3fc04c4d334e83c67c00bb3b0267730bbf56c9e4a8e075c6ac","observation_id":"e086319b-8320-4a63-bc47-853706ae593d","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2011.13395","last_updated":"2020-11-26T17:16:52Z","snapshot_observed_at":"2026-07-31T01:23:34.973862Z","submitted_at":"2020-11-26T17:16:52Z","title":"Second-order optimization for tensors with fixed tensor-train rank","version":1},"cited_work":{"arxiv_id":"2011.13395","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2011.13395","snapshot_observed_at":"2026-06-30T14:54:45.710845Z","title":"arXiv preprint arXiv:2011.13395 , year=","venue":null,"work_id":"23902342-04fd-4a59-a8e8-9654aa5c4578","year":2011},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"cited_paper":"/paper/2011.13395","citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:ab1359288b152cf7c3775f541c61ce74d9377bea16492d5e183bec8c3f305d2e","observation_id":"0742db59-fbf5-4d4f-b33e-dc0db12aa0f9","resolution":{"observed_at":"2026-06-30T14:54:45.712375Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Two Newton methods on the manifold of fixed-rank matrices endowed with","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:40dfb978ba88f0301d9e3da5198033b6a0852355f2d8033ae31bb5a8de18602f","observation_id":"b7b71eaa-0344-48d7-9052-8be51df203dc","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.06765","last_updated":"2024-08-13T23:20:05Z","snapshot_observed_at":"2026-07-06T12:47:20.833330Z","submitted_at":"2022-03-13T21:36:19Z","title":"On the analysis of optimization with fixed-rank matrices: a quotient geometric view","version":2},"cited_work":{"arxiv_id":"2203.06765","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2203.06765","snapshot_observed_at":"2026-06-30T14:44:45.973686Z","title":"arXiv preprint arXiv:2203.06765 , year=","venue":null,"work_id":"5613f101-4489-4bcf-9b81-517f83b71233","year":null},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"cited_paper":"/paper/2203.06765","citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:1863e108e8d17d8e2254e03e9d28b84f42b4f1cc8c52c944b92cd4786f387c34","observation_id":"b43af30b-6cdd-4941-88ab-c456c1c7f3db","resolution":{"observed_at":"2026-06-30T14:44:45.974950Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"Riemannian optimization using three different metrics for","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:07d3ecd02c6d6d2636fcad6a931e1c16c81528589fe101af28dd539117d3ff8a","observation_id":"29c52d7b-fee2-43fb-8a9c-231c955074fe","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"SIAM Journal on Optimization , volume=","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:464dbd44d664de57f2ac28bbb9d63c2eb52e00a57d21ae23a30b38bd3a0ae2ee","observation_id":"b31399aa-ded9-46bd-8a58-6a5b4e9f3052","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"On geometric connections of embedded and quotient geometries in","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:339645ca9e49c64e6e6f439a79a45dd779e821b044557db03916187b11fe482e","observation_id":"a754609b-689c-47fd-ab49-7f8d49966f53","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-30T05:17:38.609387Z","title":"SIAM Journal on Numerical Analysis , volume=","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-06-30T05:17:38.609387Z"},"links":{"citing_paper":"/paper/2606.30173"},"observation_digest":"sha256:0efa8173ce3f6086b10f7b5022f0769c548b05e140f172507a0160d91b27019f","observation_id":"85ecdfb0-d95c-4ffb-ab8c-1c8374751688","resolution":{"observed_at":"2026-06-30T05:17:38.609387Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.30173","last_updated":"2026-06-29T11:49:44Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-01T08:58:00.153670Z","submitted_at":"2026-06-29T11:49:44Z","title":"Low-Rank Tensor Completion using Tensor Train Decomposition via Riemannian Optimization on the Quotient Geometry"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":35,"verified_exact":3,"verified_fuzzy":0},"total_outbound_references":38},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2606.30173."}