{"as_of":"2026-08-18T01:29:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:7d09cf33eb3a3ba6688ae1b802e58ad59aff5b2c73f2cd8dbbe6c15977a725e2","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T21:09:07.670834Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-06-30T14:54:45.708702Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2209.04786","last_updated":"2023-04-18T10:53:59Z","snapshot_observed_at":"2026-08-16T16:33:25.446039Z","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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.04786","snapshot_observed_at":"2026-08-10T16:17:16.873755Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2501.13385","last_updated":"2025-01-23T05:03:50Z","snapshot_observed_at":"2026-08-10T15:58:09.933117Z","submitted_at":"2025-01-23T05:03:50Z","title":"Fast and Provable Tensor-Train Format Tensor Completion via Precondtioned Riemannian Gradient Descent","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T16:17:16.873755Z"},"links":{"cited_paper":"/paper/2209.04786","citing_paper":"/paper/2501.13385"},"observation_digest":"sha256:ea788a995fdf3184e42c7893a20e712f1e2d455795cadd7d1c8885d3756e6d06","observation_id":"f8c11c06-fbd8-4539-b89e-c5f23528fe42","resolution":{"observed_at":"2026-08-10T16:17:16.873755Z","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":"2026-08-16T16:33:25.446039Z","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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.04786","snapshot_observed_at":"2026-08-15T21:09:07.670834Z","title":"Tensor completion via tensor train based low-rank quotient geometry under a preconditioned metric.arXiv preprint arXiv:2209.04786, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2505.11261","last_updated":"2025-05-16T13:54:07Z","snapshot_observed_at":"2026-08-15T20:52:28.053995Z","submitted_at":"2025-05-16T13:54:07Z","title":"Fourier Low-rank and Sparse Tensor for Efficient Tensor Completion","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T21:09:07.670834Z"},"links":{"cited_paper":"/paper/2209.04786","citing_paper":"/paper/2505.11261"},"observation_digest":"sha256:201a3ceba92c9915900d9e604d2dfe3d0706037d6d81061e48e17c76a0aad19b","observation_id":"493f6d92-4bbe-4050-a3a3-99cb8e6b8d2d","resolution":{"observed_at":"2026-08-15T21:09:07.670834Z","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":"2026-08-16T16:33:25.446039Z","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":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.04786","snapshot_observed_at":"2026-07-13T21:02:01.705689Z","title":"Tensor com- pletion via tensor train based low-rank quotient geometry under a pre- conditioned metric.arXiv preprint arXiv:2209.04786, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2603.21141","last_updated":"2026-07-09T23:34:30Z","snapshot_observed_at":"2026-08-16T08:17:57.550340Z","submitted_at":"2026-03-22T09:33:15Z","title":"Tucker Tensor Train Taylor Series","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-13T21:02:01.705689Z"},"links":{"cited_paper":"/paper/2209.04786","citing_paper":"/paper/2603.21141"},"observation_digest":"sha256:b2be64da5a37c7548b3924ddf5233409c66e8d0dc91e7f47e79b9a3a82733f21","observation_id":"4008e3f3-ced3-4681-90c2-9df584a8e3a8","resolution":{"observed_at":"2026-07-13T21:02:01.705689Z","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":"2026-08-16T16:33:25.446039Z","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":"2026-08-12T07:03:00.062425Z","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":"sha256:3912becc57e383b84cfef99993254afb7f4f0c95d0e557b0f65965c21c09cb1c","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 2026-08-17T06:30:58.91139+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2209.04786/citation-record","integrity":"/paper/2209.04786/integrity","json":"/paper/2209.04786/citation-record.json","paper":"/paper/2209.04786"},"outbound":[],"paper":{"arxiv_id":"2209.04786","last_updated":"2023-04-18T10:53:59Z","latest_version":3,"primary_category":"math.OC","snapshot_observed_at":"2026-08-16T16:33:25.446039Z","submitted_at":"2022-09-11T04:56:04Z","title":"Tensor Completion via Tensor Train Based Low-Rank Quotient Geometry under a Preconditioned Metric"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-17T06:30:58.91139+00:00","source":"crossref"},{"observed_at":"2026-08-17T06:30:54.323127+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 4 inbound Pith citation observations for arXiv:2209.04786."}