{"as_of":"2026-08-11T14:42:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:16ac04521c76ee9d3b5e97f0472dc1dba1f242508720e9c12adea0776b314692","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":"2026-08-10T21:51:30.591710Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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":"2026-08-08T18:42:48.399908Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T11:11:27.221017Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.04200","snapshot_observed_at":"2026-08-08T18:42:48.399908Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2502.05618","last_updated":"2025-02-08T15:52:23Z","snapshot_observed_at":"2026-08-08T18:34:12.804776Z","submitted_at":"2025-02-08T15:52:23Z","title":"Lowering operators on $K$-$k$-Schur functions and a lowering operator formula for closed $K$-$k$-Schur functions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-08T18:42:48.399908Z"},"links":{"cited_paper":"/paper/2501.04200","citing_paper":"/paper/2502.05618"},"observation_digest":"sha256:6026a0b53a3c6113883e88ac2918ddfd97f4a8f8480c89627dc7ea78aee3a644","observation_id":"a7481aa9-61b2-48ca-acbc-d300a51e8e0a","resolution":{"observed_at":"2026-08-08T18:42:48.399908Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"cited_work":{"arxiv_id":"2501.04200","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.04200","snapshot_observed_at":"2026-08-06T11:11:27.221017Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","venue":"math.CO","work_id":"87686138-53ec-430e-8c7a-b73559b840a0","year":2025},"citing_paper":{"arxiv_id":"2507.23222","last_updated":"2025-07-31T03:31:25Z","snapshot_observed_at":"2026-08-10T06:07:00.037020Z","submitted_at":"2025-07-31T03:31:25Z","title":"Weighted $K$-$k$-Schur functions and their application to the $K$-$k$-Schur alternating conjecture","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T11:11:27.114726Z"},"links":{"cited_paper":"/paper/2501.04200","citing_paper":"/paper/2507.23222"},"observation_digest":"sha256:70ed2cebcae261220c9d11d796ba2d6106af1a7923055550c2192013c1fb0ebe","observation_id":"af001fe8-d204-4957-8bcb-b2723cbfe1dd","resolution":{"observed_at":"2026-08-06T11:11:27.224425Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2501.04200/citation-record","integrity":"/paper/2501.04200/integrity","json":"/paper/2501.04200/citation-record.json","paper":"/paper/2501.04200"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:51:33.784538Z","title":"Blasiak, J","venue":null,"work_id":"09fb9e71-4367-4056-9b2b-993a1dcb9195","year":2019},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:29.915901Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:30950b31437f22edb7db5200c08f5805b05485d0e8fd6d399390931f8968b7ae","observation_id":"365fb36f-c659-4e00-9dac-8e31a8bbf59e","resolution":{"observed_at":"2026-08-10T21:51:33.795247Z","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":"2026-08-10T21:51:33.748616Z","title":"Blasiak, J","venue":null,"work_id":"cc24ccca-eb9d-47b2-b24f-f0d085d079db","year":2020},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:29.929487Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:4757a7103ef4d8a4b4441fdc5028f934d42b80eaee6d8d14f58091314c6b4185","observation_id":"63f005f6-4176-40cc-aa31-4596bed54c43","resolution":{"observed_at":"2026-08-10T21:51:33.765138Z","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":"2026-08-10T21:51:33.594754Z","title":"Blasiak, J","venue":null,"work_id":"0b297194-1579-4f8e-b01c-3b062f6372a4","year":2022},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:29.944926Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:3827727e121db6b940edaba59b14b312efa16a7db7eceff56366a24f0129bd45","observation_id":"2a7ed989-1ff1-4a58-8f64-51f6b2d3453e","resolution":{"observed_at":"2026-08-10T21:51:33.644758Z","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":"2026-08-10T21:51:33.424757Z","title":"Bott, The space of loops on a Lie group, Michigan Math","venue":null,"work_id":"8c050aa4-ff4b-48a8-9a4b-2307a41b0b72","year":1958},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:29.968022Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:739a527448467835d4a6f6ac87bb851e086486cd60cb9be84467687bb65915a3","observation_id":"f0e50f1b-f3d8-425d-af3b-b6e0d34153a3","resolution":{"observed_at":"2026-08-10T21:51:33.460560Z","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":"2026-08-10T21:51:33.266326Z","title":"Broer, Normality of some nilpotent varieties and coho mology of line bundles on the cotangent bundle of the ﬂag variety, Lie theory and geometry, Progr","venue":null,"work_id":"badb63e0-3f14-4041-8728-e5eb8b25b128","year":1994},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:29.994752Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:56dc5f1d547c70e94cf20ef55669ce7f665e54a85b361f450e8cdfd1acf43b12","observation_id":"5c5673a1-8788-4011-a1af-1df8505b8fc2","resolution":{"observed_at":"2026-08-10T21:51:33.306480Z","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":"2026-08-10T21:51:33.155140Z","title":null,"venue":null,"work_id":"67873cea-baad-47e1-bd7d-3f3ff3a51809","year":2010},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.044756Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:d1f886f083addb5287f770f0495f5c71c2031940255d1a78ada12c8265ae841c","observation_id":"c3da1203-89e4-4f48-bf32-0b0d7245c730","resolution":{"observed_at":"2026-08-10T21:51:33.181084Z","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":"2026-08-10T21:51:33.024829Z","title":"Fomin, S","venue":null,"work_id":"5e50e49e-b74a-43d4-9db2-eaecb7131008","year":1997},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.124756Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:8babb8605185c00782ec543d5abc271d2a7b0ec05510f612192cdd2a055e2497","observation_id":"cf2d2295-b345-4d16-903e-d803666ec843","resolution":{"observed_at":"2026-08-10T21:51:33.066391Z","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":"2026-08-10T21:51:32.884874Z","title":"Fomin and A","venue":null,"work_id":"a02dfaba-c8a7-4717-ae30-c1763a9493e8","year":1994},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.184836Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:da7d1cbef48a95f5c47eafc64d3922437f70ebcf33547f8128dbf686e30a66f7","observation_id":"ba14c183-6754-4e3b-a37c-953fa29c82d2","resolution":{"observed_at":"2026-08-10T21:51:32.935787Z","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":"2026-08-10T21:51:32.769710Z","title":"Fomin and A","venue":null,"work_id":"4b59be6c-12a3-4caf-9094-9ff9c3e12ca3","year":1996},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.234969Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:bf4f5e1ace6081204967f1455a3688e1188ccaaa35a17939c3032a4bb0693764","observation_id":"1ed91d9f-c921-49ca-a7af-e80d839f9d9e","resolution":{"observed_at":"2026-08-10T21:51:32.787737Z","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":"2026-08-10T21:51:32.664830Z","title":"Givental and Y","venue":null,"work_id":"d0bed151-63b7-4c18-a67f-139c71f58cbf","year":2003},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.274764Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:e106fc485119e3d5f51a1a53745f54dd18fd57407aa8b95ca0becf8f8b15b537","observation_id":"05c9abb2-5937-4f77-9aaf-50b8e28dfdd6","resolution":{"observed_at":"2026-08-10T21:51:32.705670Z","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":"2026-08-10T21:51:32.599808Z","title":"Ikeda, S","venue":null,"work_id":"b5158924-bf97-408a-9ad4-2a4f087cfcf9","year":2020},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.314756Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:b70a883d991d34920cfa33454e2171d7d223f8a9bede283872018cef9a4496a8","observation_id":"c6f2eeba-412a-4db3-b459-75d9da5d106f","resolution":{"observed_at":"2026-08-10T21:51:32.615979Z","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":"2026-08-10T21:51:32.435279Z","title":"Ikeda, S","venue":null,"work_id":"9d0f75b4-12eb-4f19-8903-1f92ea709fbf","year":2024},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.364756Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:9e5220619c889da4f50b84f467569a65fcb4b6908a52603aadd523cf3a991fa7","observation_id":"a4ec7f0c-eeb6-49c0-8c12-a0b1892e4235","resolution":{"observed_at":"2026-08-10T21:51:32.544756Z","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":"2026-08-10T21:51:32.269450Z","title":"Lam, Schubert polynomials for the a ﬃne Grassmannian, J","venue":null,"work_id":"30eec193-46cc-473e-9e56-ba118d481838","year":2008},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.404854Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:3efb9050ec47d362b40e5512bc5933c87c420991726b90b7cca2ae1b9b306b33","observation_id":"929be5f6-e153-4d62-b31d-c8ec47a50226","resolution":{"observed_at":"2026-08-10T21:51:32.324758Z","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":"2026-08-10T21:51:32.124841Z","title":null,"venue":null,"work_id":"61b7d485-d8ad-4738-b170-1d4671d14e3d","year":2014},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.444825Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:a571191ca9288316bdebe8125f5a6a0b51c98e1ed9d91cc6e4a76d650a118a85","observation_id":"960ff436-3c89-4da5-9dc0-14350088826c","resolution":{"observed_at":"2026-08-10T21:51:32.158207Z","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":"2026-08-10T21:51:31.994754Z","title":null,"venue":null,"work_id":"15f3268b-8f8c-43d8-ac97-9ba3ad953761","year":2010},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.453315Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:4c16e614a68d3aaed445cd47df46a17f94f82af3154cce24f071feb0b7fb8f24","observation_id":"bff5a95e-a632-4694-bd4f-c56c1ff2ee5c","resolution":{"observed_at":"2026-08-10T21:51:32.015043Z","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":"2026-08-10T21:51:31.819059Z","title":null,"venue":null,"work_id":"af78f483-3a3c-4ad2-a06c-cbfd9d060cc6","year":2010},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.461809Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:3e5a77faf8cd9fe0b62274349ceb055a918ace6c1c7267edc6df5eb7e100a819","observation_id":"3833900a-22f1-41aa-80ba-9dd245a2b269","resolution":{"observed_at":"2026-08-10T21:51:31.864756Z","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":"2026-08-10T21:51:31.639511Z","title":"Lam and M","venue":null,"work_id":"b788eb1e-d944-430a-a869-e77d8462d69c","year":2012},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.475915Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:3fa43f74cfc3631bbd9498109f91dcbd7c3ee8af95ecd7742e44c022c81d3108","observation_id":"bf278087-189e-4b17-8dca-908f36c2fc29","resolution":{"observed_at":"2026-08-10T21:51:31.692019Z","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":"2026-08-10T21:51:31.515546Z","title":"Lapointe, A","venue":null,"work_id":"0f7e64c1-7f9d-4fb0-bbb9-e227d3af957f","year":2003},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.483593Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:5a55fd320286db9a226ff2904fc0f25da2962cf6ae4ac60cfe5c74522dab1196","observation_id":"76708e30-bffb-4ddc-a295-ce763fe9fe12","resolution":{"observed_at":"2026-08-10T21:51:31.557862Z","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":"2026-08-10T21:51:31.361107Z","title":"Lapointe and J","venue":null,"work_id":"ce7ea2b6-6eaf-4de1-9a8f-3c2017f221a5","year":2003},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.499842Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:83a18509162c4d3fd5ed5ddceb402fd8f1b1fc5a5e1fe278d5f2f3d65124abe8","observation_id":"013e6334-a951-406b-a97c-53c76329ec86","resolution":{"observed_at":"2026-08-10T21:51:31.404135Z","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":"2026-08-10T21:51:31.287702Z","title":"Lapointe and J","venue":null,"work_id":"0c242253-d9ec-44ef-aecc-01f2ee7a8229","year":2005},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.507517Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:7a3b337ffdca9e0c54ecbc38cc8bca0b0d8a4a6e5637b11f82dfe117877b42df","observation_id":"30e85c13-d1b3-460d-8dd9-67f70c0ccc43","resolution":{"observed_at":"2026-08-10T21:51:31.304749Z","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":"2026-08-10T21:51:31.229207Z","title":"Lascoux, Anneau de Grothendieck de la vari´ et´ e de drapeaux, The Grothendieck Festschrift, V ol","venue":null,"work_id":"c318befb-2173-41b8-ad7e-282c68afd70c","year":1990},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.523570Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:f7a00af0ee8f8dc595f954394aca3734db1c713fc7567cb40d86318bef1cba96","observation_id":"caba7ec1-0a8c-40af-9b0a-4c55a9e1365e","resolution":{"observed_at":"2026-08-10T21:51:31.250715Z","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":"2026-08-10T21:51:31.115064Z","title":null,"venue":null,"work_id":"f4ffe0d8-e782-4ff2-9839-8023ae911a75","year":2001},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.536876Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:35632849e7d7e94c994e0b3991d5fe73a609ef9eeb2f0a4c90d7021bec420a98","observation_id":"36796726-2608-41b9-8e8e-33480e170fab","resolution":{"observed_at":"2026-08-10T21:51:31.154549Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T21:51:30.543436Z","title":"Lenart, Combinatorial aspects of the K-theory of Grassmannians, Ann","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.543436Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:a46a1184e0f7acc01eecec0771a2d647dd5882c9d1af23db2f0c5a9dbe569ef6","observation_id":"b0487699-5111-4575-9083-0487274e57f3","resolution":{"observed_at":"2026-08-10T21:51:30.543436Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0608232","last_updated":"2006-08-09T22:39:29Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2006-08-09T22:39:29Z","title":"Quantum Grothendieck Polynomials","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0608232","snapshot_observed_at":"2026-08-10T21:51:30.569222Z","title":"Lenart and T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.569222Z"},"links":{"cited_paper":"/paper/math/0608232","citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:ca13ab6c3b1a1a09a1ce7e5c210545a5d0ca6d6b362bcd49d7144bf714c5a723","observation_id":"57586cbe-5405-462a-a278-7d83b9d6da22","resolution":{"observed_at":"2026-08-10T21:51:30.569222Z","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":"2026-08-10T21:51:30.910966Z","title":null,"venue":null,"work_id":"958ffc03-5c92-4c6a-a7b9-09a762900746","year":2010},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.577633Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:4f3acba59d23f9315dc5974bcf9e8716ffabd8e4d2e2f1ebb4851e728b9005f8","observation_id":"f38379ee-d5a9-4c2b-a80a-4b83b2e2313f","resolution":{"observed_at":"2026-08-10T21:51:30.940697Z","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":"2026-08-10T21:51:30.854752Z","title":"Shimozono and J","venue":null,"work_id":"39bfb4cd-f0b9-4ba2-b347-e0bf15b27d91","year":2000},"citing_paper":{"arxiv_id":"2501.04200","last_updated":"2025-01-08T00:31:53Z","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-10T21:51:30.591710Z"},"links":{"citing_paper":"/paper/2501.04200"},"observation_digest":"sha256:26f6faed1c10c7f9c4f55d535f1eb468de7a2ee99d52b89df6c57d35edf9cd5e","observation_id":"371c7702-296c-4403-949a-19d81380d77b","resolution":{"observed_at":"2026-08-10T21:51:30.867218Z","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":"2501.04200","last_updated":"2025-01-08T00:31:53Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-11T09:47:59.963014Z","submitted_at":"2025-01-08T00:31:53Z","title":"Alternating dual Pieri rule conjecture and $k$-branching conjecture of closed $k$-Schur Katalan functions"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":0,"verified_fuzzy":18},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 2 inbound Pith citation observations for arXiv:2501.04200."}