{"as_of":"2026-08-14T07:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:dc62b803a020621371d3783888e8f1cfc6307e485706bcc6ff0b21294f426256","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T10:19:04.104385Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T04:41:45.360150Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-12T04:41:45.392036Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"cited_work":{"arxiv_id":"2411.19374","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.19374","snapshot_observed_at":"2026-08-12T04:41:45.392036Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","venue":"math.NA","work_id":"5d0d6f73-4ca0-4452-8102-5ba0be05089f","year":2024},"citing_paper":{"arxiv_id":"2412.01181","last_updated":"2024-12-02T06:40:08Z","snapshot_observed_at":"2026-08-13T19:05:19.405413Z","submitted_at":"2024-12-02T06:40:08Z","title":"Training Stiff Neural Ordinary Differential Equations with Explicit Exponential Integration Methods","version":1},"reference_index":1960,"source":"pdf_text","source_observed_at":"2026-08-12T04:41:45.360150Z"},"links":{"cited_paper":"/paper/2411.19374","citing_paper":"/paper/2412.01181"},"observation_digest":"sha256:3037fcb5c39a2b9327f3e807f168646f4288e53ce022b93b4a0ef64d686053b4","observation_id":"96b77f1f-920a-4323-997c-c673782e71d3","resolution":{"observed_at":"2026-08-12T04:41:45.397248Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2411.19374/citation-record","integrity":"/paper/2411.19374/integrity","json":"/paper/2411.19374/citation-record.json","paper":"/paper/2411.19374"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.316825Z","title":"(11) Evaluating Single-step Exponential Methods for Stiff ODEs 4","venue":null,"work_id":"e18114a5-5335-4bfd-a882-fd58360b6a09","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.049509Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:5f0e6bc0b23304ca4a31118aa01c7c20d8fbd72585fbd28c1fa0d22351d0e965","observation_id":"cb741da0-3ed1-4734-9247-d9e22a385fa2","resolution":{"observed_at":"2026-08-12T10:19:04.321003Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.300207Z","title":"(12) The local truncation error of this method shows why the lit- erature discourages the use of integrating factor exponential integration methods","venue":null,"work_id":"606accf8-26de-45bc-b57e-f7433b857a1a","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.054146Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:91e13092d91e3bcb6eade2117b32c00d8c62178ecbbc00af4f8d0a3d960be0af","observation_id":"abf6e83f-822a-412e-8687-2c29cb78e8de","resolution":{"observed_at":"2026-08-12T10:19:04.305956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.284344Z","title":null,"venue":null,"work_id":"dfc90092-8718-4dd6-b1a3-e2e09c92ebc8","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.058443Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:d146b20554b81389ea59dff912e97a2b56d132a5a2ccbfa6122cdc077b394a93","observation_id":"62380c28-6675-479b-baa2-9e28a268b9ce","resolution":{"observed_at":"2026-08-12T10:19:04.289510Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.268874Z","title":null,"venue":null,"work_id":"848991ec-4c74-44cc-b98e-6043cc3816df","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.062946Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:a6f210a552d70c8cc9d5c0adae043cce0ab55efffcecf80676df89797c380964","observation_id":"0859f059-dc4d-4923-bc21-fbd3311ecf38","resolution":{"observed_at":"2026-08-12T10:19:04.273959Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.253751Z","title":"(16) Although this ETD4RK method is formally fourth-order, Ref","venue":null,"work_id":"acbe7018-8a26-4fac-9fad-18f3f8373bd4","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.067401Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:49028541fb0d74c5d3d10c3c59aa1aa28c417d2ef53e9639ac5093c508f82d7f","observation_id":"a3a041cd-c4d1-47f6-93db-fc7df817d580","resolution":{"observed_at":"2026-08-12T10:19:04.258847Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.235425Z","title":"This scheme belongs to the class of exponential Runge-Kutta schemes","venue":null,"work_id":"d03915e5-4948-4611-b286-20e74bdc193e","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.072297Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:60ba9740a327d5d0a1f6f1802480e8b6f53546324c3b52d0e5334b51c781b8ff","observation_id":"8ab13591-2e85-4a83-a84f-fd9fe53577df","resolution":{"observed_at":"2026-08-12T10:19:04.241172Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.219722Z","title":null,"venue":null,"work_id":"e7c25517-aa9f-4637-b612-b9d4aa4ef372","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.077298Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:7863162fb7e3d4b3694becd9b5ef26b26ede93f1b48a79eb6369aa34ef50a1e5","observation_id":"20d3d044-c41a-4402-baf7-a5d7951a7d31","resolution":{"observed_at":"2026-08-12T10:19:04.223827Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.206197Z","title":null,"venue":null,"work_id":"5e9a6933-47e8-4004-b95c-5ac6ef83f307","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.083119Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:ed8de962346eac4a94f9739464bf8d2ada0b8a667698c09bd1a094315c90fdde","observation_id":"21ffbf84-e515-4868-85c5-0376611b755c","resolution":{"observed_at":"2026-08-12T10:19:04.210308Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.190974Z","title":"Generalized integrating factor exponential methods Generalized integrating factor methods44–46 extend the tra- ditional integrating factor approach previously discussed","venue":null,"work_id":"50b82ed8-5ac3-4fea-a7d2-7166e574c4ad","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.088044Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:8c2b045b70ba1cc2b9020d9f4083698e2cbd0884856246235027411d66236a91","observation_id":"bdf9a86f-4c57-4712-9391-ab7a9d3345e3","resolution":{"observed_at":"2026-08-12T10:19:04.196263Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.174695Z","title":"However, there is a considerable decrease in stability as the order of the method increases","venue":null,"work_id":"07d233d1-e0cb-4a13-bbe9-592e21594102","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.093989Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:e788fe03e769305154bf6ef789f7e469376f76c5d41cc24e59c7248f61af2f0c","observation_id":"de7fb7f7-51e2-4475-8b04-a140b76d5948","resolution":{"observed_at":"2026-08-12T10:19:04.179887Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T10:19:04.157349Z","title":"(27) (28)","venue":null,"work_id":"205555df-eab3-4024-ba27-1ab90fb45a96","year":null},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.099562Z"},"links":{"citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:c0f8734f4d725678914f502755c932437eefdb577f84f4a71fdaee419258db3d","observation_id":"7cb8f9fb-0bfc-4c5a-93fa-0bf8562bce64","resolution":{"observed_at":"2026-08-12T10:19:04.163632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2012.07244","last_updated":"2022-02-06T15:35:49Z","snapshot_observed_at":"2026-08-13T20:46:55.304841Z","submitted_at":"2020-12-14T04:05:26Z","title":"Bayesian Neural Ordinary Differential Equations","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.07244","snapshot_observed_at":"2026-08-12T10:19:04.104385Z","title":"High Irradiance RESponse","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T10:19:04.104385Z"},"links":{"cited_paper":"/paper/2012.07244","citing_paper":"/paper/2411.19374"},"observation_digest":"sha256:8a1e55a439e2183d7c1161453aff419838a3b1cc64ef350f6972d3af602cc084","observation_id":"fc0a4d18-b861-41d4-a4e2-2781dd508681","resolution":{"observed_at":"2026-08-12T10:19:04.104385Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2411.19374","last_updated":"2024-11-28T20:53:05Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-14T01:11:00.725912Z","submitted_at":"2024-11-28T20:53:05Z","title":"Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":7},"total_outbound_references":12},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2411.19374."}