{"as_of":"2026-08-08T07:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0eeec6a8e3dc0b7d06ab9e523ca18a20dbe87bf72e2998cc1c1b4efc138c14ed","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":1,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":1,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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":"2026-07-30T14:14:07.402194Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2408.15071","last_updated":"2024-08-27T13:59:12Z","snapshot_observed_at":"2026-08-03T13:13:12.790752Z","submitted_at":"2024-08-27T13:59:12Z","title":"Sobolev spaces via chains in metric measure spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.15071","snapshot_observed_at":"2026-07-30T14:14:07.402194Z","title":"Antonelli, E","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27008","last_updated":"2026-07-29T15:05:16Z","snapshot_observed_at":"2026-08-04T13:37:06.470057Z","submitted_at":"2026-07-29T15:05:16Z","title":"Stability of local Riemannian Ricci curvature lower bounds","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-07-30T14:14:07.402194Z"},"links":{"cited_paper":"/paper/2408.15071","citing_paper":"/paper/2607.27008"},"observation_digest":"sha256:3d5f0c925588f633ef81fbcf0556aa17001f59f26827d6873fa813be6271a875","observation_id":"a16852de-d536-4451-b729-2cafd6116665","resolution":{"observed_at":"2026-07-30T14:14:07.402194Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2408.15071/citation-record","integrity":"/paper/2408.15071/integrity","json":"/paper/2408.15071/citation-record.json","paper":"/paper/2408.15071"},"outbound":[],"paper":{"arxiv_id":"2408.15071","last_updated":"2024-08-27T13:59:12Z","latest_version":1,"primary_category":"math.MG","snapshot_observed_at":"2026-08-03T13:13:12.790752Z","submitted_at":"2024-08-27T13:59:12Z","title":"Sobolev spaces via chains in metric measure spaces"},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2408.15071."}