{"as_of":"2026-08-12T14:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d5efa3771ec12fd891847e60f3138c2637e6ad024b64121a856f381159b5d03d","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":2,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":2,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T22:19:05.850802Z","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":"2026-05-09T05:55:29.222832Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.04794","last_updated":"2026-06-18T10:14:59Z","snapshot_observed_at":"2026-08-11T21:13:54.423604Z","submitted_at":"2024-12-06T06:00:35Z","title":"Multiplicity of solutions to a class of degenerate elliptic equations in both sub-critical and critical cases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.04794","snapshot_observed_at":"2026-08-06T22:19:05.850802Z","title":"Bal and S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.22177","last_updated":"2025-06-27T12:43:14Z","snapshot_observed_at":"2026-08-10T02:49:29.446095Z","submitted_at":"2025-06-27T12:43:14Z","title":"Existence and decay for a Grushin problem in $\\mathbb{R}^N$ with singular, convective, critical reaction","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T22:19:05.850802Z"},"links":{"cited_paper":"/paper/2412.04794","citing_paper":"/paper/2506.22177"},"observation_digest":"sha256:92599faf9935a54d4fb8c3f1f82e4208837a291a584f640d652c813c2d054564","observation_id":"42ef0912-587b-4754-86bb-d527ef6a96b7","resolution":{"observed_at":"2026-08-06T22:19:05.850802Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.04794","last_updated":"2026-06-18T10:14:59Z","snapshot_observed_at":"2026-08-11T21:13:54.423604Z","submitted_at":"2024-12-06T06:00:35Z","title":"Multiplicity of solutions to a class of degenerate elliptic equations in both sub-critical and critical cases","version":2},"cited_work":{"arxiv_id":"2412.04794","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.04794","snapshot_observed_at":"2026-06-19T17:11:51.177680Z","title":"Bal and S","venue":null,"work_id":"fc00ed22-98c5-44e4-9a8b-4ebb7acd1850","year":2024},"citing_paper":{"arxiv_id":"2605.02020","last_updated":"2026-05-03T18:58:56Z","snapshot_observed_at":"2026-07-06T23:15:07.159340Z","submitted_at":"2026-05-03T18:58:56Z","title":"Existence and multiplicity of solutions for a critical Grushin problem with a singular nonlinearity","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-08T19:27:14.903124Z"},"links":{"cited_paper":"/paper/2412.04794","citing_paper":"/paper/2605.02020"},"observation_digest":"sha256:2f6048860185588cc247c92d9048799a539f1f264bd030b3e8180dd314f4c3b5","observation_id":"e159388e-0dd6-463c-b9b4-86be8d4141ff","resolution":{"observed_at":"2026-06-19T17:11:51.177680Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2412.04794/citation-record","integrity":"/paper/2412.04794/integrity","json":"/paper/2412.04794/citation-record.json","paper":"/paper/2412.04794"},"outbound":[],"paper":{"arxiv_id":"2412.04794","last_updated":"2026-06-18T10:14:59Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-11T21:13:54.423604Z","submitted_at":"2024-12-06T06:00:35Z","title":"Multiplicity of solutions to a class of degenerate elliptic equations in both sub-critical and critical cases"},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2412.04794."}