{"as_of":"2026-08-18T06:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:95d98108673cb5458639cb2755c5ba3b800e39c8a6cff60dd3014142d5a993be","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":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-17T06:30:58.91139+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T06:04:09.706749Z","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":"2026-07-02T23:57:27.990609Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.11782","snapshot_observed_at":"2026-08-12T18:23:49.145676Z","title":"Convergence of adam for non-convex objectives: Relaxed hyperparameters and non-ergodic case","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.11747","last_updated":"2024-11-18T17:19:40Z","snapshot_observed_at":"2026-08-17T13:39:22.891252Z","submitted_at":"2024-11-18T17:19:40Z","title":"Anisotropic Gaussian Smoothing for Gradient-based Optimization","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T18:23:49.145676Z"},"links":{"cited_paper":"/paper/2307.11782","citing_paper":"/paper/2411.11747"},"observation_digest":"sha256:6f56994718052461b56aa587a1522728372e34019a9e3b777b1a5bd3f6f2d27b","observation_id":"91f76ef9-c471-4125-a0ad-d1d96311a53c","resolution":{"observed_at":"2026-08-12T18:23:49.145676Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.11782","snapshot_observed_at":"2026-08-16T06:04:09.706749Z","title":"Convergence of Adam for Non-convex Ob- jectives: Relaxed Hyperparameters and Non-ergodic Case","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.19426","last_updated":"2025-04-28T02:17:50Z","snapshot_observed_at":"2026-08-17T09:02:43.677169Z","submitted_at":"2025-04-28T02:17:50Z","title":"Sharp higher order convergence rates for the Adam optimizer","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T06:04:09.706749Z"},"links":{"cited_paper":"/paper/2307.11782","citing_paper":"/paper/2504.19426"},"observation_digest":"sha256:f3c7776914bed1f066d75af8c10e6a184c53d13ac68b360fbfc37954d2dce809","observation_id":"449966e4-f16d-4285-a2b5-8a5db4a37bcd","resolution":{"observed_at":"2026-08-16T06:04:09.706749Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.11782","snapshot_observed_at":"2026-08-07T15:09:12.575287Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2505.16363","last_updated":"2025-05-22T08:16:48Z","snapshot_observed_at":"2026-08-17T00:03:56.902894Z","submitted_at":"2025-05-22T08:16:48Z","title":"AdamS: Momentum Itself Can Be A Normalizer for LLM Pretraining and Post-training","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T15:09:12.575287Z"},"links":{"cited_paper":"/paper/2307.11782","citing_paper":"/paper/2505.16363"},"observation_digest":"sha256:a68b24948dc34c0dcf367630136a026f84dc1a9022c260fb94af3bab065c16cc","observation_id":"9c6d270c-be68-45b0-b164-53450e6e1a82","resolution":{"observed_at":"2026-08-07T15:09:12.575287Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","version":1},"cited_work":{"arxiv_id":"2307.11782","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2307.11782","snapshot_observed_at":"2026-07-02T23:57:27.990609Z","title":"Convergence of adam for non-convex objectives: Relaxed hyperparameters and non-ergodic case","venue":null,"work_id":"e736f894-86b3-4d64-81bf-14b2545ada2d","year":2023},"citing_paper":{"arxiv_id":"2509.15816","last_updated":"2026-05-10T06:58:46Z","snapshot_observed_at":"2026-08-12T12:31:17.777645Z","submitted_at":"2025-09-19T09:43:37Z","title":"On the Convergence of Muon and Beyond","version":5},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-05-18T15:56:30.602824Z"},"links":{"cited_paper":"/paper/2307.11782","citing_paper":"/paper/2509.15816"},"observation_digest":"sha256:8c0dd29826d26faafc783643af729b8ba82c3598b8f348801c2c88408f2a7265","observation_id":"496e0674-4c33-4819-873e-f38e87aeb69b","resolution":{"observed_at":"2026-05-18T15:56:34.188997Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","version":1},"cited_work":{"arxiv_id":"2307.11782","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2307.11782","snapshot_observed_at":"2026-07-02T23:57:27.990609Z","title":"Convergence of adam for non-convex objectives: Relaxed hyperparameters and non-ergodic case","venue":null,"work_id":"e736f894-86b3-4d64-81bf-14b2545ada2d","year":2023},"citing_paper":{"arxiv_id":"2606.08783","last_updated":"2026-06-26T09:55:08Z","snapshot_observed_at":"2026-07-06T23:48:11.819398Z","submitted_at":"2026-06-07T18:59:24Z","title":"OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-06-27T17:47:21.377462Z"},"links":{"cited_paper":"/paper/2307.11782","citing_paper":"/paper/2606.08783"},"observation_digest":"sha256:9f65fb60221e69995c3d4cea04d3c2344abeed96286f951c88b3f009ec31c457","observation_id":"e4ddd552-3d89-4f1d-b629-137e6c37118d","resolution":{"observed_at":"2026-07-02T23:57:27.992159Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","version":1},"cited_work":{"arxiv_id":"2307.11782","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2307.11782","snapshot_observed_at":"2026-07-02T23:57:27.990609Z","title":"Convergence of adam for non-convex objectives: Relaxed hyperparameters and non-ergodic case","venue":null,"work_id":"e736f894-86b3-4d64-81bf-14b2545ada2d","year":2023},"citing_paper":{"arxiv_id":"2606.08783","last_updated":"2026-06-26T09:55:08Z","snapshot_observed_at":"2026-07-06T23:48:11.819398Z","submitted_at":"2026-06-07T18:59:24Z","title":"OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality","version":2},"reference_index":84,"source":"arxiv_source","source_observed_at":"2026-06-29T05:33:27.870787Z"},"links":{"cited_paper":"/paper/2307.11782","citing_paper":"/paper/2606.08783"},"observation_digest":"sha256:bbe8dfd61fc014d3a59f08d414ef7a2466b9e14b1209484ae9b89e6b9d387200","observation_id":"83c24c68-9d31-47ef-ab02-ff1d359d4421","resolution":{"observed_at":"2026-06-29T05:43:08.848247Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"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"}},{"citation":{"cited_paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.11782","snapshot_observed_at":"2026-07-11T20:46:05.467029Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.04233","last_updated":"2026-07-05T11:11:40Z","snapshot_observed_at":"2026-08-16T20:56:16.792561Z","submitted_at":"2026-07-05T11:11:40Z","title":"Unified convergence analysis for gradient descent optimization methods in the training of deep neural networks","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-07-11T20:46:05.467029Z"},"links":{"cited_paper":"/paper/2307.11782","citing_paper":"/paper/2607.04233"},"observation_digest":"sha256:197ccae306f19de01eb3af904bc15d5b3d31ba3883deb17a2de2bb9d6dcb1540","observation_id":"edc81e3d-4ecf-4032-bf68-180408aa39d8","resolution":{"observed_at":"2026-07-11T20:46:05.467029Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2307.11782/citation-record","integrity":"/paper/2307.11782/integrity","json":"/paper/2307.11782/citation-record.json","paper":"/paper/2307.11782"},"outbound":[],"paper":{"arxiv_id":"2307.11782","last_updated":"2023-07-20T12:02:17Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-16T15:14:42.430863Z","submitted_at":"2023-07-20T12:02:17Z","title":"Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case"},"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 7 inbound Pith citation observations for arXiv:2307.11782."}