{"as_of":"2026-08-13T22:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3b412ff2d8b2bb4712995066e5a5f825260958f9c45f6da53c6e60559e1cf31d","coverage":[{"denominator":43,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":43,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-29T21:49:02.906756Z","state":"measured"},{"denominator":43,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":43,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2605.25711/citation-record","integrity":"/paper/2605.25711/integrity","json":"/paper/2605.25711/citation-record.json","paper":"/paper/2605.25711"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T21:49:02.906756Z","title":"10, 2111–2122","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:565f6a27a82d3b9d41a471f85a6abfc7011196adfcc9372d3ad97ef4dafea671","observation_id":"1351a81a-5052-40d3-bf6d-be5b4af502d0","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:79dbfd03c15dd196d2805f1c58cbdc1108e124d74eaeff816964109db5a4dc1a","observation_id":"6bf19a45-58a0-4725-a439-a480b35fdfd9","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:62fd0b533395fe5a5f40f9d761a0b3a676f3ae0aa0d5fbb8461355e8751f55b3","observation_id":"c55a7f4b-575d-483f-8076-6e6e48f0fb52","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"II , Journal of Mathematical Analysis and Applications 68 (1979), no","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:daa040830fda65d8d6ee6ab55b051ab91f77287a90cd700075e6c2617731d9e5","observation_id":"48ac78d1-ee83-4a3c-b0c5-97cdbad6f81d","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"3, 419–453","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:90bdc6230028a9c8898a4ddda84ea75eb5d58e53e54131a2fe8536e047a02524","observation_id":"a5dd10d9-9bf2-4bcc-9e1f-a41a2d4982d6","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:99cec5946d0bf1d98e7e2760ab57c1965c6a0e17c1699812595667ee4176ca4c","observation_id":"8a235993-afb0-49b8-9290-433f32cd7699","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.13855","last_updated":"2026-05-31T06:51:37Z","snapshot_observed_at":"2026-08-13T14:37:07.025015Z","submitted_at":"2022-08-29T19:53:09Z","title":"Determining a Points Configuration from a Subset of the Pairwise Distances","version":4},"cited_work":{"arxiv_id":"2208.13855","doi":null,"metadata_source":"pith","pith_arxiv_id":"2208.13855","snapshot_observed_at":"2026-06-29T21:53:59.392934Z","title":"Benjamini and E","venue":"math.MG","work_id":"8cdc386e-4d09-43d3-9e97-1c0a8c08e588","year":2022},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"cited_paper":"/paper/2208.13855","citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:56651875dc04928100ca9adf30e7144418ee16177aa869856261adc9be176992","observation_id":"7c07032c-13a3-4a5c-9360-9de3c3866014","resolution":{"observed_at":"2026-06-29T21:53:59.394092Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-06-29T21:49:02.906756Z","title":"Gortler, Anthony Nixon, Meera Sitharam, and Louis Theran, Maximum likelihood thresholds via graph rigidity , The Annals of Applied Probability 34 (2024), no","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:a13b80a9224cb43a9f3a39e367e0a3be959edee522fb4271be3d710ef508695e","observation_id":"158c8a47-9baa-4ef3-86e8-3ba69462d295","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"73, Cambridge University Press, Cambridge, 2001","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:60bf1ba24963e22fe2592f9d6a67bdb9240f5a50e767a8d79d5e3e8a11f10473","observation_id":"d89d5c59-9e4e-4b28-ba16-e56ad090e00f","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"3, 332–352","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:5cfb2b65673ecb39d383c1e29cc2421dae0b24a88cc68083f81fd221c8c4a1b4","observation_id":"c9623764-ba3b-4f34-ac97-4149d7fa3158","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"3, 1097–1121","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:151c1978a5f82225262db77fa35dd1dff7e3035c0ae03091761d33ef85eb1edb","observation_id":"960408e0-9cb1-45c5-9c84-82e1d0ade180","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:8f438c97d00401b76103c03499c5df63198c38fe3007315ca8a2513aa974bf5c","observation_id":"9f6b03b4-d08a-4d8c-b906-88f784725c4c","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2510.05838","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T21:53:59.399387Z","title":null,"venue":null,"work_id":"3f774320-93c5-4078-964b-78f44f8293d7","year":2025},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:1730deaf04e0361c1e16eeb314d08556aa9651ae88826ef6a582eecf531f92c6","observation_id":"ec7bf600-855e-4ad9-a743-792fc9f4b36b","resolution":{"observed_at":"2026-06-29T21:53:59.400737Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-06-29T21:49:02.906756Z","title":"I , Publicationes Mathematicae Debrecen 6 (1959), 290–297","venue":null,"work_id":null,"year":1959},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:8df3edb84f0e70914a23801919b05dd39eebd74125c44661bab76e3134f7fab8","observation_id":"3647fcc1-35ff-4bb5-9789-7489637a4253","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:edc7534183e72e185918bb69d38f566795b9dff6fe682e4fcdfef74aeb4a2a31","observation_id":"58ffbf19-347c-4ad3-b120-3dc4a7045e45","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:c4f1620c30c082972707204188a15de3178240cf0df76d80235ea33b698b999e","observation_id":"201b070e-8e97-4b9b-b70e-c6743004780c","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"32 YUV AL PELED","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:a9c482b4d210e377b009fca06343916c991cb12e72dfd4b957a93b6d77008688","observation_id":"629ba95e-4e1c-4648-a4ec-9307a48be858","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"4, 2709–2720","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:c213b827ef4dc75e8ba17562afd199fe677ef7dca25359dfb07f8549f64bdb29","observation_id":"130a3fdf-28c0-4e8e-8f7b-184da783059a","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"2, American Mathematical Society, Providence, RI, 1993","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:1f159b8c95c574927f65816e13bc6b8693c3ac840607c6a38f96cc4765282e12","observation_id":"a47b721c-fed7-436f-a217-e115f45a99e5","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"1, 386–407","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:b47a39ed19ed29064f81d00887d7f375cafad2bdb09e6d7630b0d40485a185fc","observation_id":"d0866f62-8078-4682-9433-210d0010c5b6","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"2, 154–166","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:45c30fe09b2d0dc9ed7fb81de6c7ce0489c95d81efeed27072038cc1e79187fe","observation_id":"bca1a6a7-147e-4e87-aa6a-76823e5e71a6","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"Luczak, A simple solution to the k-core problem, Random Structures & Algorithms 30 (2007), no","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:b589bcc80486293fdaed224a7eb9fd85a0746c03f740dc609b20dc86e67b0018","observation_id":"fb91a605-efb5-4ecd-9552-e4ba3009fdd0","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:f7b227237824a433e8028dd7a6cbbb0546d964b1484e0a69014411926fa796bf","observation_id":"f4008625-4a69-4a5c-b12f-868ca9852df2","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2510.25689","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T21:53:59.390484Z","title":null,"venue":null,"work_id":"ea124ab0-78ce-47c5-9c5e-8b90d741e3c5","year":2025},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:8e6b10d5ebbc4e0d09d1f18f8972e4f8df818b7567765ad6de4ffa34ec815e9b","observation_id":"cb3e673e-b5e4-4fb4-9ba8-e90747661960","resolution":{"observed_at":"2026-06-29T21:53:59.391727Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-06-29T21:49:02.906756Z","title":"3, 2367–2392","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:a47770a19a55e816619aa123affaf77c6837e20d26bce7bbf6bb53f61e5dff32","observation_id":"52368ef7-f125-4777-b7bf-284fac449176","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"1237–1252","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:e5cfcec072bed814a2e9af2a1bf64755833b78870f07bc95e85e632d6c3427e9","observation_id":"a249b0b1-8dc6-4b2c-aa9d-ff8d65ecd831","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1302.2767","last_updated":"2013-11-02T14:02:46Z","snapshot_observed_at":"2026-07-06T03:06:13.141215Z","submitted_at":"2013-02-12T12:15:20Z","title":"Coherence and sufficient sampling densities for reconstruction in compressed sensing","version":2},"cited_work":{"arxiv_id":"1302.2767","doi":null,"metadata_source":"pith","pith_arxiv_id":"1302.2767","snapshot_observed_at":"2026-06-29T21:53:59.401872Z","title":"Coherence and sufficient sampling densities for reconstruction in compressed sensing","venue":"cs.LG","work_id":"a0225b94-3660-496d-8029-3b99ef70a037","year":2013},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"cited_paper":"/paper/1302.2767","citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:a3196bce27a80a4b501ff8925e655377fb700cebc6093c3568588d0080e63321","observation_id":"ce9b556b-3073-487d-bd49-cb3fe4bf7b6c","resolution":{"observed_at":"2026-06-29T21:53:59.403243Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-06-29T21:49:02.906756Z","title":"Power, The rigidity of infinite graphs, Discrete & Computational Geometry 60 (2018), no","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:d884834e21dc7db8ef9dcf4b07350ca98cb2cee61c3acc11a91b610f7e0c18c2","observation_id":"d1067e81-a2f7-44f5-b345-34e50fbffd1e","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:9765cc442ee9c16b6b92adbf596b8daaa6414dc64e0cb896982073796845ea0c","observation_id":"9bb3c1e6-6856-4ca4-9a48-b4845f063e61","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2602.23713","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T21:53:59.400784Z","title":null,"venue":null,"work_id":"7d1e6a39-4007-43dd-b774-4e93ad5fe96f","year":2026},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:035edce008e9ed2f4f6a32b09d8226aa1fdaeb319ec9643b68888d3c2fbd8a87","observation_id":"681e7261-b495-4ed5-8667-13448e6019ca","resolution":{"observed_at":"2026-06-29T21:53:59.402052Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-06-29T21:49:02.906756Z","title":"1, e70279","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:3725e81bf369347c75fe634e126672730830a41d3806807f75ec8ca6c81b5a90","observation_id":"f283ec7e-8c1f-4a6a-99a4-5591cbb81fe2","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"4, 331–340","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:b63aed1d66369916b36c5112ba9f962e7b35820188d6120c86bdfa9a08bc3968","observation_id":"b52208f6-9c88-45c3-a42e-eb7416d405cf","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"Raz, Sharp threshold for rigidity of random graphs, Bulletin of the London Mathematical Society 55 (2023), no","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:5e4097c4c41024bae25f05578a755d597cb924592654b676a4a0ed3c65226724","observation_id":"39593523-2b58-46d8-90c2-2e3668e9e32e","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"3, 745–773","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:22ef759c0dc39607763806fd965b39029d8fb05ef50a55005d6e7c605168cf59","observation_id":"121e2170-4c61-4dcc-b21b-c93e2ca341c5","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"1, 61–68","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:92dd3c78e6822501a33d20bd0315106cb5672f89e8920943616fa5ab1971c3bd","observation_id":"fe689e56-4a27-4399-8123-dbe4399c07ed","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"6, Springer, 2025, pp","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:f05e98ae8948dc3e45efc46c7bf0f0d5ad5221994076fd9cc5cebb89b3b84cf3","observation_id":"84c4aaab-25b2-49a7-8370-887fc29fe2e1","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"Owen and Stephen C","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:f4e8797aecf601d3b526553c58a98c7ab0c59f68c43d3d7d048e233fdb5094a1","observation_id":"b244b8b9-bc7b-45b9-a8a1-b1e4c172e0b9","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.13127","last_updated":"2024-12-17T17:45:23Z","snapshot_observed_at":"2026-08-13T19:20:58.720393Z","submitted_at":"2024-12-17T17:45:23Z","title":"On the Rigidity of Random Graphs in high-dimensional spaces","version":1},"cited_work":{"arxiv_id":"2412.13127","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.13127","snapshot_observed_at":"2026-06-29T21:53:59.396717Z","title":null,"venue":null,"work_id":"c24ba40a-6527-45dd-a9ea-fcc10225d0d9","year":2024},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"cited_paper":"/paper/2412.13127","citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:e90a6b844d67d37a966ae09ce08f0e70602f5b5c3b15d4c637db7e7af5834f86","observation_id":"5afbe8d2-edac-4574-82ba-19b2eeffc62b","resolution":{"observed_at":"2026-06-29T21:53:59.398337Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-06-29T21:49:02.906756Z","title":"1, 111–151","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:e983d8480679d1db9686ab2934815bb0743b5485ccf444db9833266df6288f48","observation_id":"d9592650-b899-42b2-ab17-7b5641e06ccf","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"I: Functional analysis, revised and enlarged ed., Academic Press, New York, 1980","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:826392a84f03311c42b02f1d1e378554455b7d4a01a9f6701df7913b8a711587","observation_id":"7c195128-0d83-425b-ba02-0ccb0359a0b8","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:8067ebf4dcb8633412e5c845cb0eab9c29d619a02742174c7bf04e28680ceaee","observation_id":"8d7e42c9-467b-47cf-98de-75980748a505","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:3ba56fdce1d617eee32f86fc8579641d243aa60df95d7a0f653fff41561d6e5c","observation_id":"37bae101-d8a4-49b8-a0f6-74305976b27e","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","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":"2026-06-29T21:49:02.906756Z","title":"1, 238–261","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-06-29T21:49:02.906756Z"},"links":{"citing_paper":"/paper/2605.25711"},"observation_digest":"sha256:5e65e0227b8b2d207d21cb05ecb413028db6f66f8b1c151fe8105715ab149c46","observation_id":"424ce52c-473e-4be5-8252-6b6efc9ba1d4","resolution":{"observed_at":"2026-06-29T21:49:02.906756Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2605.25711","last_updated":"2026-06-10T09:46:53Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-08T05:35:00.424507Z","submitted_at":"2026-05-25T11:12:42Z","title":"On the $d$-rigidity phase transition in random graphs"},"reference_resolution":{"displayed":43,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":37,"verified_exact":6,"verified_fuzzy":0},"total_outbound_references":43},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2605.25711."}