{"as_of":"2026-08-15T11:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:24d0a51257c672fc0064fdc045fd13bbc438233f09b2434e1c952db85a55225c","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":"2026-08-15T06:32:42.880941+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":"2026-08-09T22:04:26.443645Z","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":"2026-05-11T21:16:26.216557Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2410.04907","last_updated":"2026-06-04T13:30:16Z","snapshot_observed_at":"2026-08-12T22:29:18.855632Z","submitted_at":"2024-10-07T10:48:36Z","title":"Decomposition Polyhedra of Piecewise Linear Functions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.04907","snapshot_observed_at":"2026-08-09T22:04:26.443645Z","title":"Decomposition polyhedra of piecewise linear functions","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2501.18915","last_updated":"2025-05-31T03:36:26Z","snapshot_observed_at":"2026-08-15T09:40:59.456670Z","submitted_at":"2025-01-31T06:33:58Z","title":"Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-09T22:04:26.443645Z"},"links":{"cited_paper":"/paper/2410.04907","citing_paper":"/paper/2501.18915"},"observation_digest":"sha256:33c9c837c12588f4bf35c55ebc3e5f7ec320e1ca20eb89d9a38f15a548ad5480","observation_id":"4fdd1e19-4f52-4469-961f-e2df32a9ffd1","resolution":{"observed_at":"2026-08-09T22:04:26.443645Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.04907","last_updated":"2026-06-04T13:30:16Z","snapshot_observed_at":"2026-08-12T22:29:18.855632Z","submitted_at":"2024-10-07T10:48:36Z","title":"Decomposition Polyhedra of Piecewise Linear Functions","version":2},"cited_work":{"arxiv_id":"2410.04907","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2410.04907","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"and Hertrich, C","venue":null,"work_id":"7bf773d3-6c81-4da1-b6dc-36856bbd1562","year":null},"citing_paper":{"arxiv_id":"2604.23634","last_updated":"2026-04-26T09:48:06Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-04-26T09:48:06Z","title":"On the Supremum of Singleton Ratios in Submodular Functions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-08T06:05:55.260140Z"},"links":{"cited_paper":"/paper/2410.04907","citing_paper":"/paper/2604.23634"},"observation_digest":"sha256:803625c1a0c557d833e0b0668f6079598691f7625afb8ac0939c094523ee6e20","observation_id":"ec878cf5-cadb-4b5b-8172-822ae06518e1","resolution":{"observed_at":"2026-06-05T02:16:16.697629Z","resolver_source":"arxiv_id","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2410.04907/citation-record","integrity":"/paper/2410.04907/integrity","json":"/paper/2410.04907/citation-record.json","paper":"/paper/2410.04907"},"outbound":[],"paper":{"arxiv_id":"2410.04907","last_updated":"2026-06-04T13:30:16Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-12T22:29:18.855632Z","submitted_at":"2024-10-07T10:48:36Z","title":"Decomposition Polyhedra of Piecewise Linear Functions"},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2410.04907."}