{"as_of":"2026-08-10T19:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:47f957713cfba6e77a57afa40d5cc371a537867ee1104514ad3e750d37307a93","coverage":[{"denominator":18,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":18,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-27T15:37:01.138339Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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":"2026-08-04T02:49:17.136602Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.10214","snapshot_observed_at":"2026-08-04T02:49:17.136602Z","title":"Distribution of sandpile groups of random directed bipartite graphs, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.06952","last_updated":"2026-08-01T08:34:01Z","snapshot_observed_at":"2026-08-09T15:57:24.391083Z","submitted_at":"2026-07-08T03:26:29Z","title":"Universality for cokernels of partially random integral matrices","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T02:49:17.136602Z"},"links":{"cited_paper":"/paper/2606.10214","citing_paper":"/paper/2607.06952"},"observation_digest":"sha256:ac081696c495973935c7ec0198d506822b8672df49b2dfb0c3a2e097d1bbec85","observation_id":"471ec5e7-6de1-4851-ace6-db9953f1f2a0","resolution":{"observed_at":"2026-08-04T02:49:17.136602Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.10214","snapshot_observed_at":"2026-07-14T00:43:43.380480Z","title":"Distribution of sandpile groups of random directed bipartite graphs.arXiv preprint arXiv:2606.10214, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.10056","last_updated":"2026-07-11T00:54:17Z","snapshot_observed_at":"2026-08-07T15:00:43.771127Z","submitted_at":"2026-07-11T00:54:17Z","title":"Distribution of Sandpile groups of random bipartite graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-14T00:43:43.380480Z"},"links":{"cited_paper":"/paper/2606.10214","citing_paper":"/paper/2607.10056"},"observation_digest":"sha256:9e65ca5ec49d0fb25f997e5affd24ab45042e72393ed522d370af53004434cfd","observation_id":"eba6371f-95ed-44e6-97cf-ec22ab46b9f8","resolution":{"observed_at":"2026-07-14T00:43:43.380480Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.10214/citation-record","integrity":"/paper/2606.10214/integrity","json":"/paper/2606.10214/citation-record.json","paper":"/paper/2606.10214"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:21f2801156c4ccc757d7bfe615084fb0ee3e892b4f3154f78d5aec231a518c04","observation_id":"b74ab24e-6582-40e3-8f7f-cde025122a1e","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Modeling the dis- tribution of ranks, selmer groups, and shafarevich–tate groups of elliptic curves.Cambridge Journal of Mathematics, 3(3):275–321, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:24a71577218662d8d3f5b3f4b5035fe6b684950632e0420310726514153427f0","observation_id":"0595f3a0-b7a9-4814-844a-ab47be4b67e3","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"The cokernel of a polynomial push-forward of a random integral matrix with concentrated residue","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:a1bde7a4d436692a4b2b79a65c5aced189c7f6e73776685866ab77cfe704e139","observation_id":"203c796a-6c57-4ce8-835c-3db2b41ed3b1","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Generalizations of results of Friedman and Washington on cokernels of random p-adic matrices.Journal of Algebra, 604:636–663, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:6f07b42015d226bece65d485d03db43f1099910e2ad2f14869e916dad9089dd1","observation_id":"b93a33aa-2591-456d-9828-518ecd6c3dfc","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2303.09125","last_updated":"2023-10-21T07:35:11Z","snapshot_observed_at":"2026-08-05T22:55:25.039584Z","submitted_at":"2023-03-16T07:40:59Z","title":"The distribution of the cokernel of a polynomial evaluated at a random integral matrix","version":3},"cited_work":{"arxiv_id":"2303.09125","doi":null,"metadata_source":"pith","pith_arxiv_id":"2303.09125","snapshot_observed_at":"2026-07-09T02:05:52.196451Z","title":"arXiv preprint arXiv:2303.09125 , year=","venue":"math.NT","work_id":"26ee5303-a8d6-427d-93f7-e62c1e7e9182","year":2023},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"cited_paper":"/paper/2303.09125","citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:3a8fbbd5a222ffcc2fd429610ad7fde6691f4801c0eaa391d5ce83d5abd40356","observation_id":"036d834b-6bb1-4987-9f4b-6a5820950d6c","resolution":{"observed_at":"2026-07-03T03:07:34.738203Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-06-27T15:37:01.138339Z","title":"On a Cohen– Lenstra heuristic for jacobians of random graphs.Journal of Algebraic Combinatorics, 42(3):701–723, 2015","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:639e0a539aed21800d6380728886e8c948abd415baafcf116d8e1e889ea8a6b6","observation_id":"0a7c9935-9322-480f-b58d-23a0d8b984cd","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"On the distribution of divisor class groups of curves over a finite field","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:b99b30dac2449c3b57cfb373d8fa6891415df7c2745a797eca8cda5e31498583","observation_id":"442a88bc-4d0d-4916-820d-1d15b4c961d1","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Sandpile groups of random bipartite graphs and families of distributions with the same moments","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:c7d0efd601041d502ecd875a905b12595262ef24c7b082fbcc2656d8a764fb3f","observation_id":"c5d68c5e-a5c9-4c15-b0b4-35041f8c123e","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"The distribution of sandpile groups of random graphs with their pairings.Transactions of the American Mathematical Society, 377(12):8769–8815, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:1fa9811d622064d72c410b6e8ca5f8775c2757ed261f7c66acd869d0d5a6ab3a","observation_id":"a110c969-0737-4d80-aa80-22bfc90414a3","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Sandpile groups and the coeulerian property for random directed graphs.Advances in Applied Mathematics, 90:145–159, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:37868e10f751679639e5c70b603347e954fddbaf9c4a6acb867dd7de5d028ce7","observation_id":"b0c0388d-0c6b-4d86-a25e-a8f08054fdbc","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Joint distribution of the cokernels of random p-adic matrices","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:453e5deab0ab69f9ebe65f417808afe9ef6f34bb0bf6ef9b6a6bc0d161580c52","observation_id":"6ca5bc87-7c55-4965-aff0-bf38541b2a52","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"The distribution of sandpile groups of random regular graphs.Transactions of the Amer- ican Mathematical Society, 373(9):6529–6594, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:e951d65d287e5fa22873ceb37d6f66eb19c96fd94bdfba59f8a4538825a4080d","observation_id":"2926451b-b9ba-4e52-b61e-4eacdd56e562","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Random integral matrices: universality of surjectivity and the cokernel.Inventiones mathematicae, 228(1):1–76, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:5daaff8a3f7fea9c1d9ea924a5d1644c9339fe2c328842fdaab0bb004cd14432","observation_id":"d3878f0f-f6d5-4f30-94cc-1e2a5c329b7a","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Local and global universality of random matrix cokernels","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:50e48669f2c514acbe7a0684a8bcfdb68ec28228bce1a9414ba1cff0eada9923","observation_id":"d3a19b2a-57a6-4926-8503-6cea25326097","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":"2601.09704","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-03T21:38:58.954561Z","title":"Quantative universality for cokernels of matrices with symmetries.arXiv preprint arXiv:2601.09704, 2026","venue":null,"work_id":"8390ebd0-f7e8-4a4a-b7cd-a941a0dc4fc7","year":2026},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:1da0fa6bf0203882ce3bd3fe082cee9bf0e84d9ed3cec5f6d45c8922001d8331","observation_id":"ad4f629b-5388-4a01-b86e-6eb5c8df7db6","resolution":{"observed_at":"2026-07-03T03:07:34.738399Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+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":"2026-06-27T15:37:01.138339Z","title":"Distribution of sandpile groups of random bipartite graphs","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:dc5433d52d40e50ef0fdd2cb08f4f5d66759127c50b315defeaece5ac9524648","observation_id":"652096b9-14e8-4ca3-a13a-2fe41d8ddb6c","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"The distribution of sandpile groups of random graphs.Journal of the American Mathematical Society, 30(4):915–958, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:9d216967fb553760ac09fd7b67a67ae47ff9f25cfafa0e77887e36c8ceceea02","observation_id":"27a72ba9-b486-4f65-9157-861d1c84b1f7","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-27T15:37:01.138339Z","title":"Random integral matrices and the cohen-lenstra heuristics.American Journal of Mathematics, 141(2):383–398, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-27T15:37:01.138339Z"},"links":{"citing_paper":"/paper/2606.10214"},"observation_digest":"sha256:d63f4829d203fd35a9357cdefc6e90a164a82010b98617b68b03763ccc3d5bbf","observation_id":"adbaf612-10c2-43b1-abc1-2bc058b2fa89","resolution":{"observed_at":"2026-06-27T15:37:01.138339Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.10214","last_updated":"2026-06-08T22:08:54Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-06T03:52:02.741683Z","submitted_at":"2026-06-08T22:08:54Z","title":"Distribution of Sandpile groups of random directed bipartite graphs"},"reference_resolution":{"displayed":18,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":18},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 2 inbound Pith citation observations for arXiv:2606.10214."}