{"as_of":"2026-08-12T03:58:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:4bb5345f629faf7dced6d4e89948f0c492d0fc250e4db1e2a381c98a77a4e73f","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:10:59.786709Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2507.16765/citation-record","integrity":"/paper/2507.16765/integrity","json":"/paper/2507.16765/citation-record.json","paper":"/paper/2507.16765"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:11:00.049876Z","title":"Barry, Riordan Arrays: a Primer , Logic Press, 2017","venue":null,"work_id":"d057abe7-e856-447e-9cc3-50f65b81c760","year":2017},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.738538Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:e831525a4d2f975db81a379975228ad7ceb51650d45e58307bb4e78fc746b9b2","observation_id":"71a26788-7610-454d-b3e9-8281fb8f0975","resolution":{"observed_at":"2026-08-06T15:11:00.052227Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1910.00875","last_updated":"2019-10-02T11:01:32Z","snapshot_observed_at":"2026-08-12T01:53:52.568143Z","submitted_at":"2019-10-02T11:01:32Z","title":"Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials","version":1},"cited_work":{"arxiv_id":"1910.00875","doi":null,"metadata_source":"pith","pith_arxiv_id":"1910.00875","snapshot_observed_at":"2026-08-06T15:10:59.911348Z","title":"Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials","venue":"math.CO","work_id":"deb2d4a3-0ae2-474c-8b8a-9c6e4c9822e7","year":2019},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.741946Z"},"links":{"cited_paper":"/paper/1910.00875","citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:08e5f3ceef6e6fd009c478a4d3cbccef03cc08c500f1500aba155f267f8ed8b7","observation_id":"a1a10d6f-394c-4f1d-8081-a56bce83086a","resolution":{"observed_at":"2026-08-06T15:10:59.915015Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:11:00.038896Z","title":"Barry, Notes on Riordan arrays and lattice paths, https://arxiv.org/abs/2504","venue":null,"work_id":"e54a6594-260d-448f-b49b-06da21038941","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.744970Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:1836739cf2c05d4bbd7f997138ef1e93996098576485e665cd52f8cd4f74eeca","observation_id":"a2c5390c-b464-41da-b1aa-bbd849138734","resolution":{"observed_at":"2026-08-06T15:11:00.044384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2112.11595","last_updated":"2022-03-28T04:05:15Z","snapshot_observed_at":"2026-07-06T12:21:20.815242Z","submitted_at":"2021-12-22T00:30:54Z","title":"Pseudo-involutions in the Riordan group","version":4},"cited_work":{"arxiv_id":"2112.11595","doi":null,"metadata_source":"pith","pith_arxiv_id":"2112.11595","snapshot_observed_at":"2026-08-06T15:10:59.899240Z","title":"Pseudo-involutions in the Riordan group","venue":"math.CO","work_id":"83f225d8-fde8-4f47-9c12-4174d6e4fed4","year":2021},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.747334Z"},"links":{"cited_paper":"/paper/2112.11595","citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:1f70224a165bf87a425bd472d9b200977463ef0a4d79480010c6060b3920bd18","observation_id":"ea663c88-1183-4977-8d30-1e04f9fbe626","resolution":{"observed_at":"2026-08-06T15:10:59.902965Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:11:00.032618Z","title":null,"venue":null,"work_id":"ab56acd7-e990-4751-a5fa-f6dcd521c919","year":2012},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.749881Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:be0e4d10870ed000207b1287bf6c44e5fe06f17af8a7ad4fd36ad2d75aa2e22a","observation_id":"768f7daf-f510-43f3-8f85-8a675a75001d","resolution":{"observed_at":"2026-08-06T15:11:00.034810Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:11:00.025745Z","title":", 465 (2015), 15–42","venue":null,"work_id":"7bc9b766-53fb-42b0-a689-0204b54e91f1","year":2015},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.752272Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:ba47554daa4313962d5e6de71b3fcede93658656c0d9813a7f9bfdbbaf99ccc3","observation_id":"18003eac-7ab2-403d-af6e-52a7ee652df4","resolution":{"observed_at":"2026-08-06T15:11:00.028243Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:11:00.018287Z","title":null,"venue":null,"work_id":"7c1e3e9f-f83a-4534-a8ae-c101d92ac86d","year":2005},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.754607Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:e17025d8333d216b8ccf78b1730e7eb04fe4eef9154f094dc4c13fa519bfc845","observation_id":"cdd65526-01b1-474d-9e37-2d6be7b9b7c4","resolution":{"observed_at":"2026-08-06T15:11:00.020683Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:11:00.011466Z","title":null,"venue":null,"work_id":"854ad7ba-1073-4228-88d9-ef995103c08f","year":2001},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.757497Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:55c314b336939ee6b3b13b4b4aa1a03691016c355525ae82dc740dd13198f863","observation_id":"437dc932-5818-49c0-9a46-027586cbf4e5","resolution":{"observed_at":"2026-08-06T15:11:00.014003Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:11:00.004258Z","title":"Merlini, D","venue":null,"work_id":"0b7d6a52-5045-4481-882c-22532b8bd594","year":1997},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.759999Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:7d9c49058033a68cc8bc8da0a7428d7ad6fc001c7acd67a7b021406e527799f0","observation_id":"13282f54-4f94-45a1-bedb-07225b863d2e","resolution":{"observed_at":"2026-08-06T15:11:00.006830Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.996420Z","title":"Shapiro, R","venue":null,"work_id":"cfa5ca38-9f79-4525-8126-c7d25d52db2d","year":2022},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.762133Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:562abe45fa36583f7d29eb65d195edd35dffa7b95780e022e8debc66092e6e1c","observation_id":"249b70e4-43a9-46b0-9a80-978aa1dfa751","resolution":{"observed_at":"2026-08-06T15:10:59.999093Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.988409Z","title":null,"venue":null,"work_id":"f8cd1891-8273-4f5e-8d2b-901afb1e80c3","year":1991},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.764582Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:56ff623d704f791e49851e52184765239ba882d50e15eff5cdd0ba5dc261450c","observation_id":"c2ac42b2-7976-4f0d-b7e3-052201ca7e42","resolution":{"observed_at":"2026-08-06T15:10:59.991844Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.981163Z","title":null,"venue":null,"work_id":"577cfe40-9631-43ed-9d85-3f8338c2616b","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.766962Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:b435e65dd25c843765586c721d4badad1b30d996fd09fb4a6dbf8697611ea567","observation_id":"bc4ba507-f4e4-4187-a39c-428be33a7bdf","resolution":{"observed_at":"2026-08-06T15:10:59.983773Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.972701Z","title":null,"venue":null,"work_id":"734d61f1-9c27-4962-8763-e0f485a803d6","year":2025},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.769062Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:99306a70ee9c2b330c2830491f03444c6ccb7f68f94049174dcdcb0cf2fbd306","observation_id":"6aa18134-e15a-4941-87e2-ec5eb5d129ab","resolution":{"observed_at":"2026-08-06T15:10:59.975778Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.964498Z","title":null,"venue":null,"work_id":"bbe7eefa-afa8-4f62-b6b6-fbd58d37fd80","year":2003},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.771475Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:ea783056fa0fc06133190a0a76f6569efaffd9e65ae242ed1d34a050fac36dd5","observation_id":"9e338763-2a56-46de-9258-2daa989c7eed","resolution":{"observed_at":"2026-08-06T15:10:59.967336Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.956682Z","title":null,"venue":null,"work_id":"057a944d-14e9-41cb-a797-b586582b7e50","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.773593Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:8fe5bcc16f52b33096c118cf3c3d2c2283bec7745b1c280a654285abcadfb7a3","observation_id":"1e38a067-211d-4acb-994d-04364de85e3e","resolution":{"observed_at":"2026-08-06T15:10:59.959574Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.950352Z","title":null,"venue":null,"work_id":"e326bdbb-ab2d-4a12-b143-f3bfe2e3fb81","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.775570Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:cc2167137032870272b6df1d00dd79a69c89b4f0f3a321f251d8aed49267cd60","observation_id":"fa1efb3d-9bcb-4a7b-a044-69ba86fac21e","resolution":{"observed_at":"2026-08-06T15:10:59.952637Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.943949Z","title":null,"venue":null,"work_id":"e380bde6-fa52-4b03-b4d9-0b403cd4eb33","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.777822Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:66f83d273e45bee526cb4b1f73bcb245945a4d36e91aa621b5e0f2f6610dadb4","observation_id":"5eccd79c-828a-4cdd-9d65-c2e60c238bf9","resolution":{"observed_at":"2026-08-06T15:10:59.946136Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"math/0508094","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T15:10:59.884718Z","title":"Swart and A","venue":null,"work_id":"d867e788-3046-4e57-8844-87f899cd19b7","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.780301Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:65f3d781dc783cbee03159e6b2d15df2093c995eb5a5fa1aef4b826938434ff4","observation_id":"4eccd6f5-b483-498f-9306-2831e4b639ca","resolution":{"observed_at":"2026-08-06T15:10:59.890226Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.936245Z","title":null,"venue":null,"work_id":"34d0682f-5bf8-4220-b468-3202afba5916","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.782527Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:51f807ab943aebb16eebad5a908888192c827c8c2ee187d1ab691a05ed6451a0","observation_id":"a9e38f29-9087-4e24-851b-bfbb1b4fd92a","resolution":{"observed_at":"2026-08-06T15:10:59.939020Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.928898Z","title":null,"venue":null,"work_id":"fc0bad37-ae06-4866-828c-9eb3974d48d9","year":null},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.784489Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:178bfb42eb53298f409bdf81b60fc0c21792d7cf7fbe280fd926d7e7a75032bc","observation_id":"d62809cd-1119-4075-ac04-d2b615aebe39","resolution":{"observed_at":"2026-08-06T15:10:59.931494Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T15:10:59.921305Z","title":"Yura, Hankel determinant solution for elliptic sequence, Linear Algebra Appl","venue":null,"work_id":"d12dfc71-d3ac-4497-bdcd-72c7e0a40fc8","year":2015},"citing_paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T15:10:59.786709Z"},"links":{"citing_paper":"/paper/2507.16765"},"observation_digest":"sha256:2a0c5ed111e2c2e82b52c795984d5e211c42e6fb092a18347c993042c0730e7f","observation_id":"0960fe09-4e02-4d59-85e1-7dc5163c0ee6","resolution":{"observed_at":"2026-08-06T15:10:59.923916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.16765","last_updated":"2025-07-22T17:06:53Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-07T00:08:25.143169Z","submitted_at":"2025-07-22T17:06:53Z","title":"Elliptic Curves, Riordan arrays and Lattice Paths"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":3,"verified_fuzzy":6},"total_outbound_references":21},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2507.16765."}