{"as_of":"2026-08-08T06:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:194e7312fbff600042163fb6ba7f7f740947d173dabcfecefb04f59b2849b925","coverage":[{"denominator":4,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T15:13:41.637825Z","state":"measured"},{"denominator":6,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":6,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+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":"2026-08-07T11:45:38.604395Z","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":"2026-05-18T01:20:34.580327Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.16105","last_updated":"2025-05-22T01:19:35Z","snapshot_observed_at":"2026-08-07T15:04:37.653671Z","submitted_at":"2025-05-22T01:19:35Z","title":"Sums and differences of sets (improvement over AlphaEvolve)","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.16105","snapshot_observed_at":"2026-08-07T11:45:38.604395Z","title":"https://arxiv.org/abs/2505.16105","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.01896","last_updated":"2025-06-02T17:20:25Z","snapshot_observed_at":"2026-08-07T11:29:36.329455Z","submitted_at":"2025-06-02T17:20:25Z","title":"Sums and differences of sets: a further improvement over AlphaEvolve","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T11:45:38.604395Z"},"links":{"cited_paper":"/paper/2505.16105","citing_paper":"/paper/2506.01896"},"observation_digest":"sha256:20370a6573d301030edde67c1382e488c09dae1d9bf1ec59de928d4d81208949","observation_id":"13db3997-9582-4336-9132-cc54374a7f71","resolution":{"observed_at":"2026-08-07T11:45:38.604395Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.16105","last_updated":"2025-05-22T01:19:35Z","snapshot_observed_at":"2026-08-07T15:04:37.653671Z","submitted_at":"2025-05-22T01:19:35Z","title":"Sums and differences of sets (improvement over AlphaEvolve)","version":1},"cited_work":{"arxiv_id":"2505.16105","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.16105","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Sums and differences of sets (improvement over AlphaEvolve)","venue":null,"work_id":"e4774957-2634-4c97-91a0-50fa848cbdcd","year":2025},"citing_paper":{"arxiv_id":"2511.02864","last_updated":"2025-12-22T12:49:01Z","snapshot_observed_at":"2026-08-07T08:27:55.662438Z","submitted_at":"2025-11-03T16:04:07Z","title":"Mathematical exploration and discovery at scale","version":3},"reference_index":140,"source":"pdf_text","source_observed_at":"2026-05-18T01:18:42.333269Z"},"links":{"cited_paper":"/paper/2505.16105","citing_paper":"/paper/2511.02864"},"observation_digest":"sha256:f406c199adc112e02563b424cffb7ec8300aac801b12b0d78cd61182f1f46d3e","observation_id":"1ea79638-1b2c-45ad-b186-d8a5f9484624","resolution":{"observed_at":"2026-05-18T01:20:34.582725Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.16105/citation-record","integrity":"/paper/2505.16105/integrity","json":"/paper/2505.16105/citation-record.json","paper":"/paper/2505.16105"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T15:13:42.579723Z","title":"https://bit.ly/43mWCVC","venue":null,"work_id":"79f9ba70-197a-4a33-a385-0a933de234a8","year":null},"citing_paper":{"arxiv_id":"2505.16105","last_updated":"2025-05-22T01:19:35Z","snapshot_observed_at":"2026-08-07T15:04:37.653671Z","submitted_at":"2025-05-22T01:19:35Z","title":"Sums and differences of sets (improvement over AlphaEvolve)","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T15:13:41.295824Z"},"links":{"citing_paper":"/paper/2505.16105"},"observation_digest":"sha256:060c1c25a0deb9419f9e75223491e12af0a3719513c5f857a24cebf9f3af61f2","observation_id":"fc3966b0-e40d-4022-a7ee-57aff16cc995","resolution":{"observed_at":"2026-08-07T15:13:42.632495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:13:42.353404Z","title":"https://gmplib.org/","venue":null,"work_id":"178292e6-8d42-473a-8f95-f836693a6b3e","year":null},"citing_paper":{"arxiv_id":"2505.16105","last_updated":"2025-05-22T01:19:35Z","snapshot_observed_at":"2026-08-07T15:04:37.653671Z","submitted_at":"2025-05-22T01:19:35Z","title":"Sums and differences of sets (improvement over AlphaEvolve)","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T15:13:41.456776Z"},"links":{"citing_paper":"/paper/2505.16105"},"observation_digest":"sha256:d5a5273c7a4621213cf7c7b0193007c2bec40e96809d7a0f7a73b97040f47a6d","observation_id":"5f518543-eb7c-4ff8-8507-2ce21e62f315","resolution":{"observed_at":"2026-08-07T15:13:42.479110Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:13:42.152533Z","title":"Gyarmati, F","venue":null,"work_id":"6f0eee72-ad06-4117-ac48-dc763965175d","year":2007},"citing_paper":{"arxiv_id":"2505.16105","last_updated":"2025-05-22T01:19:35Z","snapshot_observed_at":"2026-08-07T15:04:37.653671Z","submitted_at":"2025-05-22T01:19:35Z","title":"Sums and differences of sets (improvement over AlphaEvolve)","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T15:13:41.517329Z"},"links":{"citing_paper":"/paper/2505.16105"},"observation_digest":"sha256:57abfd5fe815c1e38adbac7e08c75afcd17452674ade02afa4889f93993cc088","observation_id":"17bca28e-0ff1-4272-ac58-635fa4c6c66e","resolution":{"observed_at":"2026-08-07T15:13:42.245514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-07T15:13:41.851089Z","title":null,"venue":null,"work_id":"263ee200-fdca-4b98-9026-30cf5e9cb3ea","year":2025},"citing_paper":{"arxiv_id":"2505.16105","last_updated":"2025-05-22T01:19:35Z","snapshot_observed_at":"2026-08-07T15:04:37.653671Z","submitted_at":"2025-05-22T01:19:35Z","title":"Sums and differences of sets (improvement over AlphaEvolve)","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T15:13:41.637825Z"},"links":{"citing_paper":"/paper/2505.16105"},"observation_digest":"sha256:6b8c791c3d86f3df0eb6c1acce6f743c3cca96eedaeaa70e96d6cebe11fef922","observation_id":"32a53695-9707-49f1-8948-985f51b49d87","resolution":{"observed_at":"2026-08-07T15:13:41.987622Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.16105","last_updated":"2025-05-22T01:19:35Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-07T15:04:37.653671Z","submitted_at":"2025-05-22T01:19:35Z","title":"Sums and differences of sets (improvement over AlphaEvolve)"},"reference_resolution":{"displayed":4,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":1,"verified_exact":0,"verified_fuzzy":3},"total_outbound_references":4},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 4 of 4 outbound references and 2 inbound Pith citation observations for arXiv:2505.16105."}