{"as_of":"2026-08-12T19:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8f8f2da2c84ff6cf8b2a7b31845d27301844d2d5510e3a30816e37832340e9ec","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T13:03:35.467354Z","state":"measured"},{"denominator":11,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":11,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+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/2507.21366/citation-record","integrity":"/paper/2507.21366/integrity","json":"/paper/2507.21366/citation-record.json","paper":"/paper/2507.21366"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:03:38.009962Z","title":"SOP 1, SOP2, and antichain tree property","venue":null,"work_id":"8538901f-05ba-4a57-af8a-15e80101e2bb","year":2024},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:33.501422Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:92afc72e74a6ff5ab33b09b956801a6b267684726273c8a09855ab333f8cdc88","observation_id":"18747f83-58ee-436c-97f9-f9a91d7892dd","resolution":{"observed_at":"2026-08-06T13:03:38.089092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T13:03:37.726796Z","title":"On the antichain tree property","venue":null,"work_id":"3169fdab-22c4-49c3-9061-3e41f2d5a323","year":2022},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:33.706933Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:192d5fcb731807f821e7f6cfd2a70fe53639a36778fc48c0298c111654b7c804","observation_id":"4552928a-1720-4947-8777-a1c5783e029e","resolution":{"observed_at":"2026-08-06T13:03:37.858408Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.19236","last_updated":"2025-07-06T13:13:37Z","snapshot_observed_at":"2026-08-12T05:38:40.634782Z","submitted_at":"2024-09-28T04:50:01Z","title":"A Walk on the Wild Side: Notions of maximality in first-order theories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.19236","snapshot_observed_at":"2026-08-06T13:03:33.900720Z","title":"A Walk on the Wild Side: Notions of maximality in first-order theories","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:33.900720Z"},"links":{"cited_paper":"/paper/2409.19236","citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:9f17461fe46d9ecc23a4e5eb4faac0fff6961dd7722651e7900dbbc344261ddd","observation_id":"fdbbecfb-54e0-46aa-a5f3-f4b34c9c5aee","resolution":{"observed_at":"2026-08-06T13:03:33.900720Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:03:37.323242Z","title":"Remarks on generic stability in independent theories","venue":null,"work_id":"0045b3d5-ff45-457b-b443-bf871c98959d","year":2020},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:34.148142Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:634d8c15159231cea8c9ce08a631532dd2cd2d977619834e3a1aa6b0a82be3fe","observation_id":"b02b7aad-7f11-4aa4-a703-977b2605d518","resolution":{"observed_at":"2026-08-06T13:03:37.540545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T13:03:36.946809Z","title":"Keisler measures in the wild","venue":null,"work_id":"481ed4ff-4b12-450d-9f05-0b0f6de3801e","year":2023},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:34.366937Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:ac52e64e042a150030fff5ca32487f812fa61e21cf2cc9f6388b04adf5acaa61","observation_id":"4e8c9607-06d4-405f-9e56-ca2e8080d2b6","resolution":{"observed_at":"2026-08-06T13:03:37.144635Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T13:03:36.721662Z","title":null,"venue":null,"work_id":"203af874-1361-4cf6-87a4-4390f7054867","year":1981},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:34.530262Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:efcbc1bb65777f59b2bfd7b481e80fb590ab2140c7f7e19a8f8971ca35ae1b90","observation_id":"813dcaa9-197e-4540-bffb-4c9b4abef9ed","resolution":{"observed_at":"2026-08-06T13:03:36.803898Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2306.08239","last_updated":"2025-07-28T21:48:35Z","snapshot_observed_at":"2026-08-12T05:39:23.020306Z","submitted_at":"2023-06-14T04:39:08Z","title":"Bi-invariant types, reliably invariant types, and the comb tree property","version":3},"cited_work":{"arxiv_id":"2306.08239","doi":null,"metadata_source":"pith","pith_arxiv_id":"2306.08239","snapshot_observed_at":"2026-08-06T13:03:35.974901Z","title":"Bi-invariant types, reliably invariant types, and the comb tree property","venue":"math.LO","work_id":"8301007d-fa52-431b-acc7-3118bd7845af","year":2023},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:34.742335Z"},"links":{"cited_paper":"/paper/2306.08239","citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:011f7f0da75b7b038b12aa8fadfce31c31438f6e4022f53f6d2b352243dd1f64","observation_id":"2c425946-9de0-4848-8e88-d709223fe679","resolution":{"observed_at":"2026-08-06T13:03:36.094386Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T13:03:36.474465Z","title":"Generic stability independence and treeless theories.Forum of Mathematics, Sigma, 12, 2024","venue":null,"work_id":"913f1550-2596-4c11-9e7d-a95f443f44fe","year":2024},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:34.933572Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:2d4aafe232857465ad6d0a3b0f7c44a49f71ed5d6b578c2664c0c3d3ec45e652","observation_id":"470d2985-1c0f-47e9-a738-c5d0d92ab257","resolution":{"observed_at":"2026-08-06T13:03:36.604827Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2211.04213","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:03:35.746193Z","title":"Some Remarks on Kim-dividing in NATP Theories","venue":null,"work_id":"bb692426-3eb7-4b6e-a648-14cad37f0a65","year":2022},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:35.161296Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:11c4b179d1a643577e7ba010e90c628a285d3aa1f8677a3f962df7f993463eab","observation_id":"cafa587d-3539-4b84-8260-4968af0d0303","resolution":{"observed_at":"2026-08-06T13:03:35.840748Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-06T13:03:36.203564Z","title":"A New Kim’s Lemma","venue":null,"work_id":"e2c3f33d-efaa-4f56-9f1c-71652d2c8de6","year":2024},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:35.346567Z"},"links":{"citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:158d0f557afabed1497310e45d020618c5a7df33fa32ee8b987a3820be42e053","observation_id":"8f39a828-5257-4f39-ace1-9fc1b949a171","resolution":{"observed_at":"2026-08-06T13:03:36.287834Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.08512","last_updated":"2023-06-14T15:50:15Z","snapshot_observed_at":"2026-07-06T13:21:49.288193Z","submitted_at":"2022-06-17T02:20:17Z","title":"On NSOP$_2$ Theories","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.08512","snapshot_observed_at":"2026-08-06T13:03:35.467354Z","title":"On NSOP 2 Theories","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T13:03:35.467354Z"},"links":{"cited_paper":"/paper/2206.08512","citing_paper":"/paper/2507.21366"},"observation_digest":"sha256:1da6c3f69503706ab9596a9356ab0c3ffc435dd072e294a6cd5d5e80ea56bc6e","observation_id":"80789042-8358-4bfd-a3b4-2b8083586879","resolution":{"observed_at":"2026-08-06T13:03:35.467354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.21366","last_updated":"2025-07-28T22:24:56Z","latest_version":1,"primary_category":"math.LO","snapshot_observed_at":"2026-08-12T05:39:14.751518Z","submitted_at":"2025-07-28T22:24:56Z","title":"A combinatorial characterization of Kim's lemma for pairs of bi-invariant types"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":2,"verified_fuzzy":6},"total_outbound_references":11},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2507.21366."}