{"as_of":"2026-08-16T19:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0611159fc4b68a8d060783cf586ebd7e4fab55e290495762f942ec8e33ee3e47","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:00:14.426587Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.04025/citation-record","integrity":"/paper/1908.04025/integrity","json":"/paper/1908.04025/citation-record.json","paper":"/paper/1908.04025"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:00:15.175073Z","title":"Bertrand","venue":null,"work_id":"66ccc2c1-0e76-41cb-9a27-09957d8387a1","year":null},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.272649Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:509609a52943b01e7f8bbefbf3c0c3e58efc297c15dfa9e2e37c396729c17c04","observation_id":"3421995c-efa2-4f7e-aab6-7d7eb1cd72ea","resolution":{"observed_at":"2026-08-14T14:00:15.182430Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:15.153461Z","title":"Bóna, Combinatorics of permutations","venue":null,"work_id":"5c52367c-c421-42ed-88fb-14b9b0286740","year":2012},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.279404Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:6d8f6e6ffa7fd264e13755f49b7186dacfa0520df43f439a3be0ca1b3fbbc216","observation_id":"47ec30c2-577a-4d24-a989-b81888f3693e","resolution":{"observed_at":"2026-08-14T14:00:15.160193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1903.04113","last_updated":"2020-01-21T20:53:09Z","snapshot_observed_at":"2026-08-16T17:50:19.578315Z","submitted_at":"2019-03-11T03:32:01Z","title":"Stack words and a bound for 3-stack sortable permutations","version":4},"cited_work":{"arxiv_id":"1903.04113","doi":null,"metadata_source":"pith","pith_arxiv_id":"1903.04113","snapshot_observed_at":"2026-08-14T14:00:14.527897Z","title":"Stack words and a bound for 3-stack sortable permutations","venue":"math.CO","work_id":"de6f4e25-23b2-4eff-9ffd-1d2feea161fd","year":2019},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.287369Z"},"links":{"cited_paper":"/paper/1903.04113","citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:d3fa0b419559fedcf46432a707f7124a4459d0750622ace9660457b5b1b1e651","observation_id":"ff84f70f-93f2-494f-af3e-e45555c2212e","resolution":{"observed_at":"2026-08-14T14:00:14.534916Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:15.132674Z","title":"Bóna, A survey of stack-sorting disciplines","venue":null,"work_id":"2c2df556-67f3-4ae1-aaab-a88ced7a0c9b","year":2003},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.293255Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:a63109ab91e64c04256c02bc52e278baedac3d11e811fee919a0ef4ad5a66bc1","observation_id":"64af8086-5a51-4060-8f84-2d2fb8604102","resolution":{"observed_at":"2026-08-14T14:00:15.138358Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:15.106608Z","title":"Bóna, Symmetry and unimodality in t-stack sortable permutations","venue":null,"work_id":"7795a2e4-482a-4d5f-88a1-b9030b756103","year":2002},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.299888Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:75f99b091feee7071c6f3f3a0cae4d6574ee38d625938f217dc2faaf36ae7e38","observation_id":"e24411c7-852d-4c14-b2d3-db852df09ae2","resolution":{"observed_at":"2026-08-14T14:00:15.112701Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:15.080429Z","title":"Bousquet-Mélou, Multi-statistic enumeration of two -stack sortable permutations","venue":null,"work_id":"7e285f40-5eec-4ea6-95a2-6715598a4e3f","year":1998},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.306644Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:c180690c67440b79a96aa555499c279755f470e5c4900cda5e79a3e4262f4347","observation_id":"5bb9b1a0-c0e9-4c7b-9f57-c0e5e0f14d20","resolution":{"observed_at":"2026-08-14T14:00:15.089880Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:15.058356Z","title":"Bousquet-Mélou, Sorted and/or sortable permutation s","venue":null,"work_id":"f1db6592-1835-4969-a070-01951e8e5bcc","year":2000},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.312161Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:081e964a7f8d537a7ae3a3feb0ea74644a675b99b96e9d4faf6bd613019e3eda","observation_id":"350c6cd4-78e3-4b67-ad13-73598dc17ce0","resolution":{"observed_at":"2026-08-14T14:00:15.067254Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:15.034485Z","title":"Defant, Catalan intervals and uniquely sorted permut ations","venue":null,"work_id":"60ea0c7a-7760-4b22-a773-385757009f5b","year":2020},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.317846Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:446496a78c5cf2c059c0a20568752c1a9916fdf06363bd3f8f44241780d85c9c","observation_id":"1c703528-60a1-41da-9363-47fa70c6b7da","resolution":{"observed_at":"2026-08-14T14:00:15.040979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:15.012952Z","title":"Defant, Counting 3-stack-sortable permutations","venue":null,"work_id":"f87661fa-e233-4564-a7f3-81389f03d382","year":2020},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.323677Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:dea3342ff116927bc466da1940b7829a622396cdadb12a4a69f793f65de95d4d","observation_id":"3c9a3c81-6b94-4c2f-92cb-5fae7b97538d","resolution":{"observed_at":"2026-08-14T14:00:15.019072Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.991941Z","title":"Defant, Descents in t-sorted permutations","venue":null,"work_id":"edea73d8-9d0e-4775-80ca-223b5621d9e9","year":null},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.329044Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:8078a3b3289d788f68ef49279f445c35dd728ff9c278ab34998baefc33160380","observation_id":"8cb6901f-c5d1-46f8-a2c4-e561824b66f3","resolution":{"observed_at":"2026-08-14T14:00:14.997675Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.973489Z","title":"Defant, Fertility numbers","venue":null,"work_id":"90dfdcaa-62f7-4c62-b7a5-e5cf5515a9b6","year":null},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.334377Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:7f20607c66190494046098d8f6aa6dd0153ca840b98bf5aa38a25909364c3b88","observation_id":"439a6e69-f508-4e63-87a6-0482a1212dfb","resolution":{"observed_at":"2026-08-14T14:00:14.979702Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.809051Z","title":"Defant, Fertility, strong fertility, and postorder Wilf equivalence","venue":null,"work_id":"08da7747-09d0-4aa3-beae-fb44b4882832","year":2020},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.340245Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:3832dbad6fa0895d30a92d22274828061d709caea5be92a84438d8b8a3abe313","observation_id":"4e6a129a-c37b-4faa-ad46-ece8c28f82be","resolution":{"observed_at":"2026-08-14T14:00:14.813976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.792280Z","title":"Defant, Preimages under the stack-sorting algorith m","venue":null,"work_id":"ba6b95ae-ed33-420a-844b-49b210c8bb63","year":2017},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.346885Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:55d0f4d513ae9e0369b88dbee4033051d687eeff50b1b54adefe91773c225f7d","observation_id":"aa9d3402-6638-481c-b484-fbd923740104","resolution":{"observed_at":"2026-08-14T14:00:14.797632Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.774908Z","title":"Defant, M","venue":null,"work_id":"a40a907f-c3ef-44df-a2d0-04326627a10f","year":null},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.353092Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:95d8d73953fa3d7c5f01c7e734a57e086d54a6d68d24e1cdb27af47194d1c104","observation_id":"397a9a35-14d9-4b7d-ba1b-8a9fa97b8eda","resolution":{"observed_at":"2026-08-14T14:00:14.781119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.757597Z","title":"Goulden and J","venue":null,"work_id":"45eddd6b-5578-43e6-b635-6e12eccdcc9a","year":1996},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.358922Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:186a39fd99a61d2cf2b9443f57e1458222dd614166c39d3e1b590f12cfa643f3","observation_id":"be3f1f70-f83c-447a-aff0-79782b9a411f","resolution":{"observed_at":"2026-08-14T14:00:14.762905Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.740689Z","title":null,"venue":null,"work_id":"8a792e72-c41c-4f6d-a0bb-f9fe3ad06a58","year":1999},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.364277Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:6c1442ad982b6d0db32dd612ae47cbea79b3fcaf3e8d93bb0fea458f7f334f02","observation_id":"7110a91e-5ee2-4f55-8369-8817a681066a","resolution":{"observed_at":"2026-08-14T14:00:14.745469Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.724245Z","title":"Kitaev, Patters in Permutations and Words, Springer -Verlag, Berlin, Heidelberg, 2011","venue":null,"work_id":"d63d6911-f983-4a6c-a31f-29d952b5a438","year":2011},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.371097Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:c5d50cf6e7f04bf3fb6ae448468e159e58a217e09a0c06b3248ee935146a8ee6","observation_id":"4afcd8ce-3543-45c9-8ef1-970f8303eff5","resolution":{"observed_at":"2026-08-14T14:00:14.729516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.707891Z","title":null,"venue":null,"work_id":"0441d5bb-05eb-438f-9793-fa5721a26c20","year":1973},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.376540Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:728e7aa5d77dcd1efc1c212bd36f6b629147e396d77ef1a0eeec2d642b9a611e","observation_id":"f75776fa-70a4-4198-862a-ca6bac6a3fa4","resolution":{"observed_at":"2026-08-14T14:00:14.713414Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.684628Z","title":"Krattenthaler","venue":null,"work_id":"f0476dfa-f5ab-4171-a2f4-6ca0b4ce976b","year":2015},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.387903Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:af665bf9c0948a767e94fe2487d779b15bc0a759ccf129460cab559f2277e8bf","observation_id":"9c2e038d-0dad-47bf-b799-1ebc3df47c3f","resolution":{"observed_at":"2026-08-14T14:00:14.690183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.664385Z","title":"Lassalle, Two integer sequences related to Catalan n umbers","venue":null,"work_id":"749a6ed1-1ee9-44eb-9d83-31528741bfc8","year":2012},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.394337Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:e5ffe37bb9346260850aabf4c2c1e836fc4f53b3f73612515a46502518393c11","observation_id":"f99fbb45-739a-4801-babd-b38befe8da67","resolution":{"observed_at":"2026-08-14T14:00:14.670396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.639797Z","title":"Linton, N","venue":null,"work_id":"8b922cb6-fab6-474a-99d4-feac07893efb","year":2010},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.401388Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:e296f141fe710e548d4148aeb9cf33f8015a768adb13f7f6bd4d0d9c45fcd057","observation_id":"5b916c7c-1ced-41e1-8bf1-9d933eac10b4","resolution":{"observed_at":"2026-08-14T14:00:14.650458Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.617728Z","title":"Petrov and A","venue":null,"work_id":"7a38ceff-3bef-4917-acd2-3c433dace3fc","year":2018},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.406589Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:6b5c38bcee76728db3ed68c2b7d328f704e0b9f8926f5139f4471c7c713d81d5","observation_id":"4bd70e44-a1ad-4060-875f-b067e226d7d0","resolution":{"observed_at":"2026-08-14T14:00:14.624572Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1808.01907","last_updated":"2018-08-16T14:32:03Z","snapshot_observed_at":"2026-08-14T18:44:07.786878Z","submitted_at":"2018-08-06T13:52:19Z","title":"A bijection between ternary trees and a subclass of Motzkin paths","version":2},"cited_work":{"arxiv_id":"1808.01907","doi":null,"metadata_source":"pith","pith_arxiv_id":"1808.01907","snapshot_observed_at":"2026-08-14T14:00:14.484751Z","title":"A bijection between ternary trees and a subclass of Motzkin paths","venue":"math.CO","work_id":"51137fe5-de8f-4068-b316-cfa9d1c24e21","year":2018},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.411555Z"},"links":{"cited_paper":"/paper/1808.01907","citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:e641081fd62c6376a11d468a7d3e117d35d749417c2f777b88815a0c7c02251e","observation_id":"c4e88273-5e3e-4f7f-ae6a-9df17eabe724","resolution":{"observed_at":"2026-08-14T14:00:14.492940Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.597104Z","title":"West, Permutations with restricted subsequences an d stack-sortable permutations, Ph.D","venue":null,"work_id":"054313a5-a558-46f6-bd39-f68004e94041","year":1990},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.416618Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:8ddc45e9f0337243259e53d2e8aea8567e13e78a4618f266ed2ae7623cd817f5","observation_id":"a224baf0-7488-4a7b-a064-9b30f00f5ede","resolution":{"observed_at":"2026-08-14T14:00:14.603381Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.571949Z","title":"Whitworth","venue":null,"work_id":"67c5f4b7-4b6c-4f78-b3e9-de4286667027","year":null},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.421146Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:bd7cda3ff332f961be7d2c5e6a5b7ac4a2393927a54db608644ec0a343f27a02","observation_id":"e3fc63c6-122b-4259-b6bf-3aa4018315c8","resolution":{"observed_at":"2026-08-14T14:00:14.577474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:00:14.552020Z","title":"Zeilberger, A proof of Julian West’s conjecture that the number of two-stack-sortable permutations of length n is 2(3n)!/ ((n + 1)!(2n + 1)!)","venue":null,"work_id":"30232a84-5336-4a8c-9fd5-3d058ae2609c","year":1992},"citing_paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations","version":4},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T14:00:14.426587Z"},"links":{"citing_paper":"/paper/1908.04025"},"observation_digest":"sha256:8099ca55ddf33798d7ca72bd8203b346d6ab293ff8e83f65191651c5aac41525","observation_id":"7e793781-cc9e-42bb-a7f6-52d30ff8eb18","resolution":{"observed_at":"2026-08-14T14:00:14.558776Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.04025","last_updated":"2021-08-30T17:52:06Z","latest_version":4,"primary_category":"math.CO","snapshot_observed_at":"2026-08-16T03:25:31.215051Z","submitted_at":"2019-08-12T06:54:40Z","title":"Lattice Paths and Pattern-Avoiding Uniquely Sorted Permutations"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":2,"verified_fuzzy":22},"total_outbound_references":26},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:1908.04025."}