{"as_of":"2026-08-11T01:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6fe6a19e7e7d505b98ddaa2d5f106384603b4ecda97921e48eadfc174ccb7ee0","coverage":[{"denominator":3,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T14:07:48.083293Z","state":"measured"},{"denominator":3,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":3,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"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":[],"links":{"evidence":"/evidence","html":"/paper/2501.15782/citation-record","integrity":"/paper/2501.15782/integrity","json":"/paper/2501.15782/citation-record.json","paper":"/paper/2501.15782"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T14:07:48.132146Z","title":"We know that we can rewrite the definition of (𝛾,𝛽 )-fairness as follows: 𝐾∑︁ 𝑖=1 𝑈 1−𝛾 𝑖 (w) 𝐾 ! 1 1−𝛾 ≤𝛽· 𝐾∑︁ 𝑖=1 𝑈 1−𝛾 𝑖 (x) 𝐾 ! 1 1−𝛾","venue":null,"work_id":"212551f2-315d-4c90-9082-c40065ebd78a","year":null},"citing_paper":{"arxiv_id":"2501.15782","last_updated":"2025-01-27T05:02:05Z","snapshot_observed_at":"2026-08-10T13:54:44.293139Z","submitted_at":"2025-01-27T05:02:05Z","title":"Online Allocation with Multi-Class Arrivals: Group Fairness vs Individual Welfare","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T14:07:48.083293Z"},"links":{"citing_paper":"/paper/2501.15782"},"observation_digest":"sha256:36e71bd2fe84425ba02602d850f97eca90e70bf1d1dc39d417327128dec8bab7","observation_id":"713faef5-0d27-4101-a914-09f5cc9e6ec2","resolution":{"observed_at":"2026-08-10T14:07:48.139358Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-08-10T14:07:48.150343Z","title":"Υ𝑗(1)+ ∫ Υ𝑗(𝑣𝑗) Υ𝑗(1) 𝜙(𝜂)𝑑𝜂 # = ∑︁ 𝑗∈𝐴","venue":null,"work_id":"0513417d-79b0-4cd8-b82d-991219be8bc1","year":null},"citing_paper":{"arxiv_id":"2501.15782","last_updated":"2025-01-27T05:02:05Z","snapshot_observed_at":"2026-08-10T13:54:44.293139Z","submitted_at":"2025-01-27T05:02:05Z","title":"Online Allocation with Multi-Class Arrivals: Group Fairness vs Individual Welfare","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T14:07:48.077076Z"},"links":{"citing_paper":"/paper/2501.15782"},"observation_digest":"sha256:22bc065190b0e86181b6e30787ecc0044d00db2932518d3203b2a239eb796bb4","observation_id":"92129980-d987-457b-9f5a-d6830038ac77","resolution":{"observed_at":"2026-08-10T14:07:48.155048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.02403","last_updated":"2024-08-05T11:55:41Z","snapshot_observed_at":"2026-08-10T08:06:43.261356Z","submitted_at":"2024-08-05T11:55:41Z","title":"Online Fair Allocation with Best-of-Many-Worlds Guarantees","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.02403","snapshot_observed_at":"2026-08-10T14:07:48.070833Z","title":"Max-min Fair Resource Allocation in SD-RAN","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2501.15782","last_updated":"2025-01-27T05:02:05Z","snapshot_observed_at":"2026-08-10T13:54:44.293139Z","submitted_at":"2025-01-27T05:02:05Z","title":"Online Allocation with Multi-Class Arrivals: Group Fairness vs Individual Welfare","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-10T14:07:48.070833Z"},"links":{"cited_paper":"/paper/2408.02403","citing_paper":"/paper/2501.15782"},"observation_digest":"sha256:fc394f6d96fb76ac471caec003c7681548848c3de1db2fb9bfb26ad2a13df4eb","observation_id":"026bf627-09d0-4e08-abea-aeb0bd17c04f","resolution":{"observed_at":"2026-08-10T14:07:48.070833Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2501.15782","last_updated":"2025-01-27T05:02:05Z","latest_version":1,"primary_category":"cs.GT","snapshot_observed_at":"2026-08-10T13:54:44.293139Z","submitted_at":"2025-01-27T05:02:05Z","title":"Online Allocation with Multi-Class Arrivals: Group Fairness vs Individual Welfare"},"reference_resolution":{"displayed":3,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":2},"total_outbound_references":3},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 3 of 3 outbound references and 0 inbound Pith citation observations for arXiv:2501.15782."}