{"as_of":"2026-08-21T09:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:66b4ed7f0fab38a10c8ba9903b1e8bf3ddc3d96b3f2b7f1a3a97cd0733ca027b","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":"2026-08-12T17:08:49.061359Z","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":"2026-08-21T06:32:19.484+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/2411.13015/citation-record","integrity":"/paper/2411.13015/integrity","json":"/paper/2411.13015/citation-record.json","paper":"/paper/2411.13015"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T17:08:49.125933Z","title":"Summing this over 0 ≤ k ≤ m − 1 = log2 n − 1 yields: m−1X k=0 X |S|=k H(pS) = O(nτ log n) as wished","venue":null,"work_id":"5649245f-9a98-4b66-876a-04256593bc49","year":null},"citing_paper":{"arxiv_id":"2411.13015","last_updated":"2025-06-16T11:37:24Z","snapshot_observed_at":"2026-08-16T11:52:45.650907Z","submitted_at":"2024-11-20T03:36:48Z","title":"Strong XOR Lemma for Information Complexity","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-12T17:08:49.061359Z"},"links":{"citing_paper":"/paper/2411.13015"},"observation_digest":"sha256:8a2f70edc1de9df0b331f2b39b14b2e76a40746a452feb7a583477315880dab9","observation_id":"b32254a7-66e5-452d-ad86-6752b8a500fb","resolution":{"observed_at":"2026-08-12T17:08:49.134441Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+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":"2026-08-12T17:08:49.149834Z","title":"Strong XOR Lemma for Communication with Bounded Rounds : (extended abstract)","venue":null,"work_id":"16cbaffe-af2b-4364-ae1e-7f43aa626416","year":1982},"citing_paper":{"arxiv_id":"2411.13015","last_updated":"2025-06-16T11:37:24Z","snapshot_observed_at":"2026-08-16T11:52:45.650907Z","submitted_at":"2024-11-20T03:36:48Z","title":"Strong XOR Lemma for Information Complexity","version":2},"reference_index":1982,"source":"pdf_text","source_observed_at":"2026-08-12T17:08:49.052372Z"},"links":{"citing_paper":"/paper/2411.13015"},"observation_digest":"sha256:3311d6194da8e3bcb0c4d0cacab967aced91d200a6b3bd426b1abbb3bb60c898","observation_id":"6918994f-0bc9-4b82-ad66-b24b7e779eef","resolution":{"observed_at":"2026-08-12T17:08:49.157447Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.01802","last_updated":"2024-07-01T20:58:34Z","snapshot_observed_at":"2026-08-21T01:18:26.018582Z","submitted_at":"2024-07-01T20:58:34Z","title":"An XOR Lemma for Deterministic Communication Complexity","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.01802","snapshot_observed_at":"2026-08-12T17:08:49.012741Z","title":"A Technique for Hardness Amplification Against AC0","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.13015","last_updated":"2025-06-16T11:37:24Z","snapshot_observed_at":"2026-08-16T11:52:45.650907Z","submitted_at":"2024-11-20T03:36:48Z","title":"Strong XOR Lemma for Information Complexity","version":2},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-12T17:08:49.012741Z"},"links":{"cited_paper":"/paper/2407.01802","citing_paper":"/paper/2411.13015"},"observation_digest":"sha256:ae2f4a3a9fb8fb77f90364243d228a0a94bc89943ae438b6d8ae899f13ae31fc","observation_id":"ae0adab2-ea12-43ab-8acf-e9dcf6cd292c","resolution":{"observed_at":"2026-08-12T17:08:49.012741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2411.13015","last_updated":"2025-06-16T11:37:24Z","latest_version":2,"primary_category":"cs.CC","snapshot_observed_at":"2026-08-16T11:52:45.650907Z","submitted_at":"2024-11-20T03:36:48Z","title":"Strong XOR Lemma for Information Complexity"},"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":"2026-08-21T06:32:19.484+00:00","source":"crossref"},{"observed_at":"2026-08-21T06:32:16.066871+00:00","source":"retraction_watch"}],"thesis":"As of 21 August 2026, this Paper Citation Record lists 3 of 3 outbound references and 0 inbound Pith citation observations for arXiv:2411.13015."}