{"as_of":"2026-08-15T07:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d6782dedf60ee416977e30f4b6a18712c3fa2e4a8a979ecad3004ad274717853","coverage":[{"denominator":41,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":41,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-19T09:00:29.590067Z","state":"measured"},{"denominator":44,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":44,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T23:40:03.858916Z","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":"2026-07-02T19:57:19.696960Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.14694","snapshot_observed_at":"2026-08-04T23:40:03.858916Z","title":"The homology torsion growth of determinantal hypertrees.arXiv preprint arXiv:2506.14694, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.06559","last_updated":"2025-09-08T11:18:02Z","snapshot_observed_at":"2026-08-10T02:22:49.696751Z","submitted_at":"2025-09-08T11:18:02Z","title":"Using dense graph limit theory to count cocycles of random simplicial complexes","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T23:40:03.858916Z"},"links":{"cited_paper":"/paper/2506.14694","citing_paper":"/paper/2509.06559"},"observation_digest":"sha256:ecaa43872b50148fad27114b3c22268c89d1a43751dfb20cd6bb9d925878ac0c","observation_id":"ca9fcb52-32de-4030-9820-53c25080646a","resolution":{"observed_at":"2026-08-04T23:40:03.858916Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.14694","snapshot_observed_at":"2026-08-04T08:50:01.826965Z","title":"M´ esz´ aros","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.19563","last_updated":"2026-06-09T14:18:09Z","snapshot_observed_at":"2026-08-11T01:53:15.021014Z","submitted_at":"2025-10-22T13:17:36Z","title":"Local limits of determinantal processes","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T08:50:01.826965Z"},"links":{"cited_paper":"/paper/2506.14694","citing_paper":"/paper/2510.19563"},"observation_digest":"sha256:298e1c694eba881a9762523c148bdd140db4ed4af80cfe397b347a0b1c83e669","observation_id":"cc002b18-39b5-4126-bbc2-3161b5a800e9","resolution":{"observed_at":"2026-08-04T08:50:01.826965Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"cited_work":{"arxiv_id":"2506.14694","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.14694","snapshot_observed_at":"2026-07-02T19:57:19.696960Z","title":"The homology torsion growth of determinantal hypertrees","venue":"math.CO","work_id":"cf5fc758-a104-427c-8558-0721aaf821e4","year":2025},"citing_paper":{"arxiv_id":"2606.06993","last_updated":"2026-06-05T07:31:59Z","snapshot_observed_at":"2026-08-07T12:22:11.524098Z","submitted_at":"2026-06-05T07:31:59Z","title":"A mod $p$ determinant criterion for Cohen--Lenstra convergence of random $p$-adic matrices with prescribed zero patterns","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-27T21:12:25.854244Z"},"links":{"cited_paper":"/paper/2506.14694","citing_paper":"/paper/2606.06993"},"observation_digest":"sha256:9f7b15f8546fc3190e3fe817abb0f91cd002ee5ad6fd7d4e9e226890ea03bc39","observation_id":"f0ac2785-c831-4980-a2ef-ad3640ff9ad1","resolution":{"observed_at":"2026-07-02T19:57:19.698344Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.14694/citation-record","integrity":"/paper/2506.14694/integrity","json":"/paper/2506.14694/citation-record.json","paper":"/paper/2506.14694"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On homology torsion growth.Journal of the European Mathematical Society","venue":null,"work_id":"215d85ab-5d36-4bcf-9bcd-754a412b63cf","year":2024},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:9e870607f0889e1c981407edec4f10318b111ce90feb867af2022ab07d45ccc1","observation_id":"04033aaf-dbb6-4a5f-862e-c0de36048a8d","resolution":{"observed_at":"2026-05-19T09:03:03.308158Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Rank, combinatorial cost, and homology torsion growth in higher rank lattices","venue":null,"work_id":"707f91ee-a062-4561-ae13-acba4ea60320","year":2017},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:22a64b45019a49d84fd65aaea9390c5b71054a064d447cb5181c7d36c403825f","observation_id":"c963f171-aab5-406a-a597-36c6ce83bdcc","resolution":{"observed_at":"2026-05-19T09:03:03.230509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Benjamini-Schramm convergence and pointwise convergence of the spectral measure.preprint","venue":null,"work_id":"4391b837-7913-463c-9170-c499950a73ec","year":2013},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:021e131b1be33f63734cc5a192bef855fba275f50bdf0610d0cc4fc6bc1bf62b","observation_id":"2d161048-cd25-4af6-b7b0-835c814f3165","resolution":{"observed_at":"2026-05-19T09:03:03.170257Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"The continuum random tree I.Annals of Probability, 19(1):1 – 28","venue":null,"work_id":"2b6eaa20-7579-4d87-8898-f1c25e6375c6","year":1991},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:49147d0f84b09afca549f5885c431c858ba8bb0ee8c8ce16a78bd5e2edadff31","observation_id":"ffbc68c8-6f20-49db-9e5b-c2b4bae89077","resolution":{"observed_at":"2026-05-19T09:03:03.272518Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"The continuum random tree II","venue":null,"work_id":"329fd809-0e2e-4506-865d-7244f0b7da07","year":1991},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:1a8ff118fbc80912b215f0ce2db14295e9fa36a4fc8d363161967f0a04f4f59f","observation_id":"4b2705cf-0777-4b8b-a2ca-0a98dc9a901a","resolution":{"observed_at":"2026-05-19T09:03:03.381120Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"The continuum random tree III.Annals of Probability, pages 248–289","venue":null,"work_id":"8336b600-5ef3-4025-8e6a-49f91b2c87f7","year":1993},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:47f4709196df1a0ddb5563bdf08754ed91ab7cb653016b35c8fffcd29870ff7f","observation_id":"dcde6e19-3dec-4cd0-98f1-c6f7afd4346e","resolution":{"observed_at":"2026-05-19T09:03:03.353166Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"When does the top homology of a random simplicial complex vanish? Random Structures & Algorithms, 46(1):26–35","venue":null,"work_id":"ccd893ea-b170-4a2a-a439-100fa44c27a4","year":2015},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:bfbcd202c59dc511536e2e016f64909906c0b123f75f2804dfadb1f62ca91bcf","observation_id":"e950f1fa-4c05-4236-894c-f2dd24d638f8","resolution":{"observed_at":"2026-05-19T09:03:03.256486Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"The asymptotic growth of torsion homology for arithmetic groups.Journal of the Institute of Mathematics of Jussieu, 12(2):391–447","venue":null,"work_id":"aef73e01-a2db-4ddd-97d5-6c4be7d662da","year":2013},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:d083af72c4cd8edf046d69f989a0e7a237a2600c2d793dc8e4b2f7bf1728fba7","observation_id":"8ec94b93-3742-4708-95bf-2a3e86646658","resolution":{"observed_at":"2026-05-19T09:03:03.375609Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Non-standard limits of graphs and some orbit equivalence invariants.Annales Henri Lebesgue, 4:1235–1293","venue":null,"work_id":"3629af37-0245-494d-85d8-d88985788e3b","year":2021},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:a0f4637c84af336a5f29d29da318bbfe92967faabca8e152da93d49e34c93603","observation_id":"f8518b19-3edc-4ae0-8944-8f232bdde8cf","resolution":{"observed_at":"2026-05-19T09:03:03.186558Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Matchings in vertex-transitive bipartite graphs.Israel Journal of Math- ematics, 215(1):99–134","venue":null,"work_id":"b7bdf52e-0916-4fd8-bc08-5ac2adf74d1a","year":2016},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:1280abd167cd6afce59f38fe044cf77a2a1cba6c755f254cd87aae813464cc29","observation_id":"907cb8fc-dd03-415d-9401-1c4f85381587","resolution":{"observed_at":"2026-05-19T09:03:03.293502Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Simplicial matrix-tree theorems","venue":null,"work_id":"44e95ea0-5ebb-4178-bc78-e9fc3163973c","year":2009},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:1df4955c351af54ba7db28b3419443805d8bfa50df01158d9d6ceeec510004fb","observation_id":"3b458ff6-d772-4e42-8747-8e708a474911","resolution":{"observed_at":"2026-05-19T09:03:03.213397Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Geometry of growth: Approximation theorems forL2 invariants","venue":null,"work_id":"c071b5bd-2ae5-4cea-9d76-e949ab7f7dc7","year":1998},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:ad3670ba30b0d0b5ba200b49744e85be37146f393dce67a9cb5581f3f5f061a2","observation_id":"af447532-8bee-45a9-9272-1d68e9311d92","resolution":{"observed_at":"2026-05-19T09:03:03.237916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Growth of mod-2 homology in higher-rank locally symmetric spaces","venue":null,"work_id":"c5d8469d-ad1a-4125-9536-7394a0e2b2b9","year":2022},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:eefddc07b4b4390445bd79c9891188d6c605a59ab46fb330d27fbe5661736ff5","observation_id":"401e7fc8-7fdb-46a3-80b1-32117366e9ad","resolution":{"observed_at":"2026-05-19T09:03:03.401235Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Random labelled trees and their branching networks.Journal of the Australian Mathematical Society, 30(2):229–237","venue":null,"work_id":"efb815c9-7aa5-448b-905f-6704b448ce5e","year":1980},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:a28d360ffb4bb4101e00d5a0d29c45edd0f9af8bb6182d6f19d04249d6c92e80","observation_id":"bb8623af-f7de-4c84-9abc-de05415770bb","resolution":{"observed_at":"2026-05-19T09:03:03.162512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"The threshold for integer homology in random d-complexes","venue":null,"work_id":"0d6af8a3-c30b-4606-bd48-4f5c41b11015","year":2017},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:263b7de7763722f551b377ff53bd648dd48cbe3cff4461eddbecdac6bbc88085","observation_id":"f6079cae-f919-464c-9be3-69c8b166a382","resolution":{"observed_at":"2026-05-19T09:03:03.303679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Determinantal processes and independence.Probability Surveys, 3:206–229","venue":null,"work_id":"33fbc78f-f6b9-45b0-9581-c25942ed4c0a","year":2006},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:e56c6fb142ac2991476310170a7a1555ee385e9017ff88aa4f9506edb300e619","observation_id":"56cc66bf-6219-4501-8277-013698ba53b5","resolution":{"observed_at":"2026-05-19T09:03:03.249821Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Cohen–Lenstra heuristics for torsion in homology of random complexes","venue":null,"work_id":"4198415b-931b-4597-84a7-514249d0308f","year":2020},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:08e1ef01e5216adde99328d5d66968750b8ad274ec3fe09fe88ed713868a109e","observation_id":"9081db21-3f1d-4a63-affc-65759c87cd36","resolution":{"observed_at":"2026-05-19T09:03:03.199756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Topology and geometry of random 2-dimensional hypertrees","venue":null,"work_id":"55251b01-4916-4490-b86c-1ffdde7273ed","year":2022},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:abc750e20fbf5d7acbe0c92edb01e086f55df0952128df2f75f795d569860103","observation_id":"99e1e226-a1ea-4431-8889-642239503f2b","resolution":{"observed_at":"2026-05-19T09:03:03.242119Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Inside the critical window for cohomology of random k-complexes","venue":null,"work_id":"899750c4-e412-4ba5-8e4e-80b3f7ffa956","year":2016},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:0aad82135e32c826d878d44389b87b56b99e25ca5bdd697ffb574f38803e2f2c","observation_id":"7f747cff-e7a3-476b-8b2f-dd89f964ef8c","resolution":{"observed_at":"2026-05-19T09:03:03.227111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Enumerationof Q-acyclicsimplicialcomplexes","venue":null,"work_id":"1939e85c-b856-44dd-b99e-85499a17f420","year":1983},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:4791d4118547345cc3ba481ecf6d9893a8257cf0e2da5898d736967b6ea6fc2d","observation_id":"bdd1764d-9f90-49cc-8184-82671a1a5975","resolution":{"observed_at":"2026-05-19T09:03:03.155950Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2505.11700","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-03T21:38:58.993073Z","title":"Distribution of the cokernels of determinantal row-sparse matrices","venue":null,"work_id":"f97059e7-006c-4ac8-945d-bbe6f9367796","year":2025},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:d6371a35f44858cfd9db10f7ea7e6ace818d8386eb0292c0d529a1517cdb076a","observation_id":"3cb47319-b8f6-488f-8cdb-0692255ce167","resolution":{"observed_at":"2026-05-19T09:02:15.082804Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Homological connectivity of random 2-complexes","venue":null,"work_id":"c9aab0cf-d28d-4c82-9ea5-1e7b4312d15d","year":2006},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:50776c0d972effbb030532774442e2434244d8deaf9a984988c552ea7dfecd50","observation_id":"3aed77f6-7fd7-49d4-88e0-4333e6b10e89","resolution":{"observed_at":"2026-05-19T09:03:03.266295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"On the phase transition in random simplicial complexes","venue":null,"work_id":"9ccc0efb-0c2c-4a90-bcb8-beb10e59ca89","year":2016},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:938e533db8ae610c8c02b96d7d6719ad4e7cbe25484161bf1df96590fed883fe","observation_id":"46ec6b76-e0fb-4740-9159-7208e9fe770f","resolution":{"observed_at":"2026-05-19T09:03:03.192991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Enumeration and randomized constructions of hypertrees","venue":null,"work_id":"0bb91c49-2b8a-4aca-86bb-0feffddbb821","year":2019},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:53de0df31c4a24c35bdd0ea7ed510c0d87f269ed7fc2af892f9ff6990bee583f","observation_id":"08dc3bb3-df98-4ab5-9c3b-e6ad0478e21d","resolution":{"observed_at":"2026-05-19T09:03:03.232582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"ApproximatingL2-invariants by their finite-dimensional analogues.Ge- ometric & Functional Analysis GAFA, 4:455–481","venue":null,"work_id":"4cb83d39-eb6b-46f5-a634-1cc282700805","year":1994},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:73894370ceedbd0d02310de3cfc7f40289bd07397555e2497f5bd790593c61f4","observation_id":"7c5fe13f-1af8-4211-856a-52f19cf36aca","resolution":{"observed_at":"2026-05-19T09:03:03.251392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Integral homology of random simplicial complexes","venue":null,"work_id":"85c8d5e0-c462-4a67-862a-a73dc32d084c","year":2018},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:ee6f0f8bc3ae3dd34e30eb79588a3d4bde36567650366059caad534ec7aa02da","observation_id":"6e2563f6-ac2a-4f6f-b7fd-6740ec5e4ec6","resolution":{"observed_at":"2026-05-19T09:03:03.267188Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Determinantal probability measures","venue":null,"work_id":"26c620cc-14de-497c-962d-e0d4611810b8","year":2003},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:c5cea9942b8876d2c8955c93a174f61d2b2affc71665095e83f44f54f79c54c5","observation_id":"139d4aa6-8dbd-44dd-a329-6cda03a138f4","resolution":{"observed_at":"2026-05-19T09:03:03.208765Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Asymptotic enumeration of spanning trees.Combinatorics, Probability and Computing, 14(4):491–522","venue":null,"work_id":"88722e45-2620-42e2-9af0-b015bf1beca0","year":2005},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:6ee829235c0c6370d0e1ac68137232911990866fbc448663b3ca739a1e828165","observation_id":"7ebc512a-5cb2-4ed5-b16e-ddc2144be95b","resolution":{"observed_at":"2026-05-19T09:03:03.218414Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Random complexes and ℓ2-betti numbers","venue":null,"work_id":"ef3879f4-ee0a-46e6-9e34-954da167ee87","year":2009},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:802aa4d8602cbb1e6c5109f6225bb3c7279558e03a5961ed045c661108813525","observation_id":"ae5a3841-8a6f-4807-a62b-7a8dbac8223f","resolution":{"observed_at":"2026-05-19T09:03:03.261851Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Identities and inequalities for tree entropy.Combinatorics, Probability and Computing, 19(2):303–313","venue":null,"work_id":"d9d332d1-7c2c-4ba7-9fb1-e1c952b2a884","year":2010},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:0b406bdb6fb9b240fa04a33faf42f9bd7dcb38ec228f401ae21f1fda0a7a8bc1","observation_id":"b4b09fa9-72f8-425c-ad36-39bac531df5c","resolution":{"observed_at":"2026-05-19T09:03:03.390169Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Cambridge University Press","venue":null,"work_id":"57f2136c-6b9b-4682-b40e-6b3389b98c6f","year":2017},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:cff9cfe407250b581cf7b3eeab5cd103864813ad8c90cb0550f4a1f5564e2d74","observation_id":"1ef56739-59e3-477e-97de-33e13291d21c","resolution":{"observed_at":"2026-05-19T09:03:03.282845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Homological connectivity of random k-dimensional complexes","venue":null,"work_id":"f1332f68-cb52-46c4-90da-f7a9931175f1","year":2009},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:3f66c7ae96bee8c33ea2a81d04ee02883279096d5bb7fc354163c1325001b336","observation_id":"d9760aa9-f7c8-4035-a840-e02ea14dc47a","resolution":{"observed_at":"2026-05-19T09:03:03.333345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"The local weak limit of k-dimensional hypertrees.Transactions of the American Mathematical Society, 375(9):6127–6154","venue":null,"work_id":"e4176e86-7786-4e0f-8a5f-1a65a0f6ca5f","year":2022},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:feb0e3af789c7e63645e8515548c259722335e0dc0bfc6cb2d03f3a6122a51f2","observation_id":"5aa7aa4f-87ac-4191-ab9a-aaf3466ddf30","resolution":{"observed_at":"2026-05-19T09:03:03.288297Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2404.02308","last_updated":"2024-04-02T21:08:43Z","snapshot_observed_at":"2026-08-13T00:38:56.803792Z","submitted_at":"2024-04-02T21:08:43Z","title":"The $2$-torsion of determinantal hypertrees is not Cohen-Lenstra","version":1},"cited_work":{"arxiv_id":"2404.02308","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2404.02308","snapshot_observed_at":"2026-07-02T19:57:19.703430Z","title":"The2-torsion of determinantal hypertrees is not Cohen-Lenstra","venue":null,"work_id":"5c515d84-0057-415e-9f6a-8f5200219243","year":2024},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"cited_paper":"/paper/2404.02308","citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:815b23111049216b5b958949b88d5438f6546a3bb1cfde3305bec6aa248afb2c","observation_id":"aaf5809d-0267-4381-8dde-9e9112b173b0","resolution":{"observed_at":"2026-05-19T09:02:15.076859Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Coboundary expansion for the union of determinantal hypertrees","venue":null,"work_id":"a4c501b3-4d03-4a77-843c-1549b81b58a1","year":2024},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:2d7ab2ef7746705b10d79bae7be0d99a751902aac96c180902950fb877eb55c6","observation_id":"9dea2389-08d3-484a-814b-6760d4b5225c","resolution":{"observed_at":"2026-05-19T09:03:03.298482Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Bounds on the mod 2 homology of random 2-dimensional determi- nantal hypertrees.Combinatorica, 45(2):17","venue":null,"work_id":"c67b5b82-18b2-4724-b11e-e16df200d3a6","year":2025},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:bd7fd04b27c830bda21282c3a74b84168c5ca93488b5fa97bb35e67aac5ed2f9","observation_id":"aba71408-8c45-41fe-91d4-a60b5e477e81","resolution":{"observed_at":"2026-05-19T09:03:03.370858Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Cohen–Lenstra distribution for sparse matrices with determinantal biasing","venue":null,"work_id":"ae4ee6ca-979b-4e2c-a63e-234cfffae6d2","year":2025},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:5ebadd7704999cda6e80eaa052ed819ec793ab7b5d3113a0cece69444088a0bb","observation_id":"86ff101d-e3ac-474f-896c-de37f01e3fc3","resolution":{"observed_at":"2026-05-19T09:03:03.396228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"The integer homology threshold in Yd(n, p)","venue":null,"work_id":"fd6eb1c7-1d61-4e86-b287-a7ffbc6caa12","year":2023},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:30151221a6ef042d1bb56956638bdd02df8c30afa859d701bb5779826d0864ad","observation_id":"35b63848-d4c8-41cd-becd-3154132d818a","resolution":{"observed_at":"2026-05-19T09:03:03.295452Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Distribution of labelled trees by diameter","venue":null,"work_id":"00eda3de-f083-48be-b78c-7c3b0ad62bf5","year":1982},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:ebaae10d2418d93d04fdb0d5231ad912edfec7d2b1e34e9ba4a48832f9d310ba","observation_id":"627e0758-60a7-4d76-82c2-c7f08f22eec4","resolution":{"observed_at":"2026-05-19T09:03:03.385301Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Sofic groups and diophantine approximation.Communications on Pure and Applied Mathematics, 61(8):1155–1171","venue":null,"work_id":"3d32c39a-3521-42d9-8500-6b81f5b77e15","year":2008},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:1e8afc07269992d116e4720d61c27cc47be4abcaf3692cf6196609e25435b565","observation_id":"8c6688e1-d151-4b5b-8f2f-aef986c405f7","resolution":{"observed_at":"2026-05-19T09:03:03.358882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-06-05T21:23:00.469572Z","title":"Simplex links in determinantal hypertrees.Journal of Applied and Computational Topology, pages 1–26","venue":null,"work_id":"25a5042a-37f3-451b-8af2-54450cad3433","year":2024},"citing_paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-05-19T09:00:29.590067Z"},"links":{"citing_paper":"/paper/2506.14694"},"observation_digest":"sha256:9ceae11d0b55dc40b4167357b9d944c2d4367682e8187beeaad38629f57cf4e2","observation_id":"f3dbef6f-5164-4fd2-add6-ea37618fa54b","resolution":{"observed_at":"2026-05-19T09:03:03.365704Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.14694","last_updated":"2026-04-23T19:25:11Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-08T16:16:05.942461Z","submitted_at":"2025-06-17T16:32:41Z","title":"The homology torsion growth of determinantal hypertrees"},"reference_resolution":{"displayed":41,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":2,"verified_fuzzy":39},"total_outbound_references":41},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 3 inbound Pith citation observations for arXiv:2506.14694."}