{"as_of":"2026-08-19T11:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:48d42bf0599fb50e2acde31b15b2f635c147b055ce6c4fceab1102e80adf6fab","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":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":6,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":6,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T23:43:00.997235Z","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":"2026-05-11T21:21:11.381264Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2407.08904","last_updated":"2024-07-12T00:42:35Z","snapshot_observed_at":"2026-08-16T13:34:55.501608Z","submitted_at":"2024-07-12T00:42:35Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08904","snapshot_observed_at":"2026-08-11T23:43:00.997235Z","title":"Hu and K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.02382","last_updated":"2025-04-16T05:24:55Z","snapshot_observed_at":"2026-08-13T14:09:45.110753Z","submitted_at":"2024-12-03T11:07:58Z","title":"Decentralized projected Riemannian stochastic recursive momentum method for nonconvex optimization","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T23:43:00.997235Z"},"links":{"cited_paper":"/paper/2407.08904","citing_paper":"/paper/2412.02382"},"observation_digest":"sha256:7284ef427370a50d4767a7cd3166025cb946b66470d6f40797644363337711fd","observation_id":"c18ad8f7-1b3b-4f27-9cab-2cb3feda81df","resolution":{"observed_at":"2026-08-11T23:43:00.997235Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08904","last_updated":"2024-07-12T00:42:35Z","snapshot_observed_at":"2026-08-16T13:34:55.501608Z","submitted_at":"2024-07-12T00:42:35Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08904","snapshot_observed_at":"2026-08-07T15:20:14.629791Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression.arXiv preprint arXiv:2407.08904, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.15537","last_updated":"2025-05-21T13:58:13Z","snapshot_observed_at":"2026-08-11T20:25:10.073326Z","submitted_at":"2025-05-21T13:58:13Z","title":"Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T15:20:14.629791Z"},"links":{"cited_paper":"/paper/2407.08904","citing_paper":"/paper/2505.15537"},"observation_digest":"sha256:c60d731dced0ff9db91805fca49d4affe98f30de4ff8823be86906236df36dc3","observation_id":"c4996b15-8e5a-4953-80f3-2595a58f1877","resolution":{"observed_at":"2026-08-07T15:20:14.629791Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08904","last_updated":"2024-07-12T00:42:35Z","snapshot_observed_at":"2026-08-16T13:34:55.501608Z","submitted_at":"2024-07-12T00:42:35Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08904","snapshot_observed_at":"2026-08-07T11:22:59.945778Z","title":"and Deng, K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.02879","last_updated":"2025-08-09T03:52:46Z","snapshot_observed_at":"2026-08-13T17:20:07.317936Z","submitted_at":"2025-06-03T13:46:15Z","title":"Distributed Retraction-Free and Communication-Efficient Optimization on the Stiefel Manifold","version":2},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T11:22:59.945778Z"},"links":{"cited_paper":"/paper/2407.08904","citing_paper":"/paper/2506.02879"},"observation_digest":"sha256:1fb0e60ec0bf8bb2674149d355065e3a10b70c3e1801fa12febf1bf02909fa4c","observation_id":"31507356-274d-476e-bd4e-0e793b7fab7c","resolution":{"observed_at":"2026-08-07T11:22:59.945778Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08904","last_updated":"2024-07-12T00:42:35Z","snapshot_observed_at":"2026-08-16T13:34:55.501608Z","submitted_at":"2024-07-12T00:42:35Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08904","snapshot_observed_at":"2026-08-07T05:44:05.121164Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression,","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.07351","last_updated":"2025-06-09T01:57:25Z","snapshot_observed_at":"2026-08-10T12:10:19.722096Z","submitted_at":"2025-06-09T01:57:25Z","title":"Decentralized Optimization on Compact Submanifolds by Quantized Riemannian Gradient Tracking","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:44:05.121164Z"},"links":{"cited_paper":"/paper/2407.08904","citing_paper":"/paper/2506.07351"},"observation_digest":"sha256:c64d7373dceb1e6cbc9150dbbe025d2aeea81e377070cce150763684f666a2dc","observation_id":"b869794f-0af7-49d0-b382-e324983fa217","resolution":{"observed_at":"2026-08-07T05:44:05.121164Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08904","last_updated":"2024-07-12T00:42:35Z","snapshot_observed_at":"2026-08-16T13:34:55.501608Z","submitted_at":"2024-07-12T00:42:35Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression","version":1},"cited_work":{"arxiv_id":"2407.08904","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2407.08904","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression","venue":null,"work_id":"62113722-ce05-4741-93fe-fb123111fd2b","year":2024},"citing_paper":{"arxiv_id":"2604.23754","last_updated":"2026-04-28T11:45:47Z","snapshot_observed_at":"2026-08-13T16:29:16.866667Z","submitted_at":"2026-04-26T15:08:12Z","title":"A Retraction-Free EXTRA Method for Decentralized Optimization on the Stiefel Manifold","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-08T05:52:40.242207Z"},"links":{"cited_paper":"/paper/2407.08904","citing_paper":"/paper/2604.23754"},"observation_digest":"sha256:f67d40c80e993fb61b05ff9e7572b455aa668501355ecab2aa5258727c96d0f2","observation_id":"7cd9ac85-356c-483c-93f9-a90767dd7ba2","resolution":{"observed_at":"2026-05-11T21:21:11.387823Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08904","last_updated":"2024-07-12T00:42:35Z","snapshot_observed_at":"2026-08-16T13:34:55.501608Z","submitted_at":"2024-07-12T00:42:35Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08904","snapshot_observed_at":"2026-08-02T03:41:15.557447Z","title":"Improving the communication in decentralized manifold op- timization through single-step consensus and compression.arXiv preprint arXiv:2407.08904, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.14178","last_updated":"2026-07-27T06:26:29Z","snapshot_observed_at":"2026-08-17T04:26:06.049786Z","submitted_at":"2026-07-15T13:27:20Z","title":"ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-02T03:41:15.557447Z"},"links":{"cited_paper":"/paper/2407.08904","citing_paper":"/paper/2607.14178"},"observation_digest":"sha256:adf192284a3025532acedcd5f90251ecad305e035719ab0e4831194fe5ad727a","observation_id":"8bd987cd-26a9-4e17-8a15-b53dfeeacfb4","resolution":{"observed_at":"2026-08-02T03:41:15.557447Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2407.08904/citation-record","integrity":"/paper/2407.08904/integrity","json":"/paper/2407.08904/citation-record.json","paper":"/paper/2407.08904"},"outbound":[],"paper":{"arxiv_id":"2407.08904","last_updated":"2024-07-12T00:42:35Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-16T13:34:55.501608Z","submitted_at":"2024-07-12T00:42:35Z","title":"Improving the communication in decentralized manifold optimization through single-step consensus and compression"},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 6 inbound Pith citation observations for arXiv:2407.08904."}