{"as_of":"2026-08-17T06:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3ffbfff55ef6a479e0d6904dfee45e0027e69ed467ba4e52bcd219689c8e4931","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T14:57:54.403457Z","state":"measured"},{"denominator":30,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":30,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/2608.03097/citation-record","integrity":"/paper/2608.03097/integrity","json":"/paper/2608.03097/citation-record.json","paper":"/paper/2608.03097"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2512.04026","last_updated":"2026-04-13T09:13:48Z","snapshot_observed_at":"2026-08-14T22:51:03.242320Z","submitted_at":"2025-12-03T18:02:48Z","title":"Orderings of k-Markov Numbers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2512.04026","snapshot_observed_at":"2026-08-15T14:57:54.281560Z","title":"Banaian:Orderings ofk-Markov Numbers, preprint (2025),arXiv:2512.04026","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.281560Z"},"links":{"cited_paper":"/paper/2512.04026","citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:33d4ddfcb584f4bbfd0d6abc6781da298829fc4587d02af2b20e9d4b6201750d","observation_id":"7cf304d1-98ec-43f1-8441-5ef506053028","resolution":{"observed_at":"2026-08-15T14:57:54.281560Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.917337Z","title":"Baragar:The Markoff equation and equations of Hurwitz, Ph.D","venue":null,"work_id":"4307a151-68ab-4e62-8bd2-ecfb7e2084da","year":1991},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.286993Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:8073726f481068f00ba0f5ab04923ebc607050f01a2a3cd8098ea47cf7d2e6c4","observation_id":"0d9baebb-55d2-4f9a-8084-1eea3f50bb2e","resolution":{"observed_at":"2026-08-15T14:57:54.921509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.904101Z","title":"Baragar:Integral solutions of Markoff–Hurwitz equations, J","venue":null,"work_id":"c6df68ca-ed4c-4966-bbc6-b2b8f821738c","year":1994},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.291787Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:89bf8916aa63c48962cc67015feb1574b71a01db7359a0278da29cb27528045d","observation_id":"d6e025e0-dfd3-4830-98bf-3535336cb209","resolution":{"observed_at":"2026-08-15T14:57:54.908770Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.891859Z","title":"Bourgain, A","venue":null,"work_id":"09b2f81b-ffc8-4e79-b5a5-ae10193fa2b3","year":2016},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.295965Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:d4dd7d7ba9837a325e42a8c52e272c56b19e2acee45ea0bd072787e4015ec991","observation_id":"e4dd8f76-73cc-4e30-91c8-d6f67a623532","resolution":{"observed_at":"2026-08-15T14:57:54.895793Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.879529Z","title":"Bourgain, A","venue":null,"work_id":"dd20f0ea-605c-4254-a4ea-5a715337b0f3","year":2026},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.300534Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:2ec582fd7940ad76af4ad0d65ae37a805646684b424e2ac758719394537076ca","observation_id":"d20e0e5d-838a-4671-b5dc-efc3fd5b6a8a","resolution":{"observed_at":"2026-08-15T14:57:54.883602Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.867002Z","title":"Cantat:Bers and H´ enon, Painlev´ e and Schr¨ odinger, Duke Math","venue":null,"work_id":"15a18eea-a86a-462b-a202-078eec0397ab","year":2009},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.304891Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:03de4d69d627135d9754844be211bede3fd16b70e90acfd146b4b28024b1d642","observation_id":"6f33e2c6-837b-4a3f-93ef-3edd4e3c69a8","resolution":{"observed_at":"2026-08-15T14:57:54.870990Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.854294Z","title":"Cantat, F","venue":null,"work_id":"925c3900-40f5-4b35-99a5-6b42b647b56f","year":2009},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.309540Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:cd81f56223b2e1a90de1b71e10dc8124d674d2789c8d77141780a66d5b17c367","observation_id":"1ea8ed73-82e4-45ef-8c2f-96eb80f8c885","resolution":{"observed_at":"2026-08-15T14:57:54.858416Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.841275Z","title":"Carlitz:Certain special equations in a finite field, Monatsh","venue":null,"work_id":"ce9be9c5-369c-41ed-b73d-0d077c77d787","year":1954},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.313620Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:fa5469384b8dda5512ed87dc9dbaf26085805ab97cbc9f70a882ff51391fba78","observation_id":"3b942a80-7deb-403f-9a91-a75e3a1cb3ab","resolution":{"observed_at":"2026-08-15T14:57:54.845677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.828917Z","title":"Carlitz:The number of solutions of some equations in a finite field, Portugal","venue":null,"work_id":"97aa7b22-4392-4954-9b43-1f3073c664d0","year":1954},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.317837Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:410b9b281e084c7a78031ce68391672cf589bd87c44db79e45bcc5152a93fb6a","observation_id":"00a1c3ec-f49b-4ea3-9adf-7d65d06cc67c","resolution":{"observed_at":"2026-08-15T14:57:54.832912Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.816453Z","title":"Carlitz:The number of points on certain cubic surfaces over a finite field, Boll","venue":null,"work_id":"4cbbbfe4-95ca-4703-b099-7edae9019dbf","year":1957},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.321855Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:c242bce631f0389f23e2d27ea13e6d7d35b77469b76dda17e5fc0d75debe0a01","observation_id":"146b4bf3-601f-409b-9f03-25838f3eec50","resolution":{"observed_at":"2026-08-15T14:57:54.820619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.804012Z","title":null,"venue":null,"work_id":"c0a58400-91c4-4d29-93ea-e662996b5ebb","year":2024},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.326078Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:9922d261fa00e54945d4d5633a364d636aee372e5625f87807fd29aeacfeac57","observation_id":"ad4d1751-8091-459c-849e-2c06b5156f5f","resolution":{"observed_at":"2026-08-15T14:57:54.807983Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.791385Z","title":"de Courcy-Ireland:Non-planarity of Markoff graphs modp, Comment","venue":null,"work_id":"afe88059-2aa6-4c33-a875-df0c771ae994","year":2024},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.329974Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:2fd40336a49653c280b1ac4fc285470c59d6391e9823e8d836d0f6f7da42fa51","observation_id":"cbf68e56-2246-4adf-857c-bf6eed847fbf","resolution":{"observed_at":"2026-08-15T14:57:54.795537Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.778168Z","title":"de Courcy-Ireland, S","venue":null,"work_id":"08c94058-0e70-4d67-8a1b-190473d6f146","year":2022},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.334204Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:37cc191b4f5ba9ff7ce848c845ee70ce40d567167469e54c3f9e7cf8bba384ec","observation_id":"74e5f3bb-82a2-4d07-8d0a-50392c905d8f","resolution":{"observed_at":"2026-08-15T14:57:54.782814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2509.02187","last_updated":"2026-06-05T09:16:52Z","snapshot_observed_at":"2026-08-09T09:58:55.140565Z","submitted_at":"2025-09-02T10:51:18Z","title":"Divisibility by $p$ for Markoff-like Surfaces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2509.02187","snapshot_observed_at":"2026-08-15T14:57:54.338392Z","title":"de Courcy-Ireland, M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.338392Z"},"links":{"cited_paper":"/paper/2509.02187","citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:af7a868e397e4b9f5e7af9d8811839d52a113a5c9f6889a724345919cbb83bd4","observation_id":"1293f760-6e02-4a39-aac5-93a4288044d9","resolution":{"observed_at":"2026-08-15T14:57:54.338392Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.765897Z","title":null,"venue":null,"work_id":"8b61ad86-5588-4799-894e-791e9a724e8b","year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.342614Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:7190146fe2a5de34e864131ca3e1e22304ac679675814ec35c6c43fa1b330c6f","observation_id":"d392becf-ac28-41b3-9c8e-69dbed2ddb67","resolution":{"observed_at":"2026-08-15T14:57:54.769727Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.753473Z","title":"Fuchs, M","venue":null,"work_id":"c025aae1-4bc4-4320-9815-cba3a81e5af7","year":2024},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.346736Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:23e45206ce40c6768cf66f553653a4d3b6c735930010f17d07db65c36f85f720","observation_id":"612c7ec0-9c3f-4487-b859-30b12816b4ea","resolution":{"observed_at":"2026-08-15T14:57:54.757559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.740861Z","title":"Gamburd:Arithmetic and dynamics on varieties of Markoff type, ICM—International Congress of Mathematicians 2022, Vol","venue":null,"work_id":"16b7d0c9-b279-43c5-b9a8-0d2e77369898","year":2022},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.350640Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:66678b5f8836a99f0c4ffcdd3a9cce47a1bb2a079a701a7c30fedd1eb0fa2077","observation_id":"87dae90e-ce3b-476c-9ad6-1f0a1e69184a","resolution":{"observed_at":"2026-08-15T14:57:54.745264Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.727723Z","title":"Ghosh, P","venue":null,"work_id":"b8ffd46b-f609-4ad7-9b65-58d2cc97b03b","year":2022},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.354678Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:9952f09a2c085b69f1a2caacdfde16b7910c009d62bacaceb40fbda183d0827f","observation_id":"dee00422-7668-4efa-bc49-a3f70fb7b011","resolution":{"observed_at":"2026-08-15T14:57:54.731812Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.715004Z","title":null,"venue":null,"work_id":"094d2eac-7596-4b14-bafa-2d431910f75d","year":2009},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.358652Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:789882fd11b26d2c8f79faee510352ccef64845d3610565a521c4d7592c5f16f","observation_id":"ede82c50-77ce-41f5-84b7-6903f658ce8e","resolution":{"observed_at":"2026-08-15T14:57:54.719182Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2312.07329","last_updated":"2024-07-11T13:36:44Z","snapshot_observed_at":"2026-08-16T14:35:27.532858Z","submitted_at":"2023-12-12T14:45:12Z","title":"Uniqueness theorem of generalized Markov numbers that are prime powers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.07329","snapshot_observed_at":"2026-08-15T14:57:54.362798Z","title":"Gyoda, S","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.362798Z"},"links":{"cited_paper":"/paper/2312.07329","citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:de393a6e60de5daf0728441e32a9bf4bcbc324e5a3f1c520809cc839bf2d31a0","observation_id":"987f28e2-9d71-4c62-b6b7-6baf0aa93721","resolution":{"observed_at":"2026-08-15T14:57:54.362798Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08203","last_updated":"2025-03-06T13:10:25Z","snapshot_observed_at":"2026-08-16T13:35:13.076149Z","submitted_at":"2024-07-11T06:02:27Z","title":"SL(2,Z)-matrixizations of generalized Markov numbers","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08203","snapshot_observed_at":"2026-08-15T14:57:54.367423Z","title":"Gyoda, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.367423Z"},"links":{"cited_paper":"/paper/2407.08203","citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:1361e73357a6208f71b2e31e3558455ce81358f2ce830322d8c6eff89805b065","observation_id":"ce8ab713-1edc-4c75-95da-c5ddc6ddc0c5","resolution":{"observed_at":"2026-08-15T14:57:54.367423Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.702118Z","title":"Gyoda, K","venue":null,"work_id":"f5347ae0-6edb-4e44-bce7-115cfd7a0a64","year":2023},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.371700Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:314f06febb3102ae04102ead1061bda846c3716937cc485cb73ae1267a4b187c","observation_id":"af17b819-87cf-4845-8e89-f74f9af85079","resolution":{"observed_at":"2026-08-15T14:57:54.706125Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.689191Z","title":"Kiritchenko, M","venue":null,"work_id":"e23096ed-a3ad-4324-b600-739a1c53a84e","year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.375658Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:d35d0331607bc1b17173f89f41317f789ac58a2480e1064fc8c6c88e7089ee02","observation_id":"6bcc09f6-e039-4707-838c-085ab8df85d2","resolution":{"observed_at":"2026-08-15T14:57:54.693232Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.675560Z","title":null,"venue":null,"work_id":"875c02fe-b445-4ee2-a8e8-d2f6b4b8d9dd","year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.379565Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:2708125da990d60927c498a5ec6812e87d5d933c652fe37a7916728e6df2dd7c","observation_id":"9b7ea281-1f82-4907-92b8-04b3e7b6e5ee","resolution":{"observed_at":"2026-08-15T14:57:54.680082Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.661635Z","title":null,"venue":null,"work_id":"0166de49-2046-4efb-adbc-14e74f5254c4","year":1953},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.383490Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:9c77b442a27fedf6facc3b77c97094b3e06fe79dbb4f830dab419cced9e7a2b0","observation_id":"30304e28-54f9-490f-a869-d215fde93d2e","resolution":{"observed_at":"2026-08-15T14:57:54.665634Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.648366Z","title":"Nica:Jacobsthal Sums, Monogr","venue":null,"work_id":"b0d32d79-f34e-4735-8df0-456bfd2c02a3","year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.387561Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:3c5e73db98c74ba1b0259bfa53c945eb77225606d511e6bbd6ff6ac24d1ba0db","observation_id":"35c6a5bc-c4b5-461f-8aef-dde9d5dbcd36","resolution":{"observed_at":"2026-08-15T14:57:54.652662Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.634268Z","title":"Rebelo, R","venue":null,"work_id":"91f297c7-c028-4c33-80a6-e96735b18f6c","year":2024},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.391433Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:e06354467a436cb38b82631299cb48279a63d797f91ba73001eba15bff42a2b5","observation_id":"ece25833-1093-494f-b732-a11c23b700ee","resolution":{"observed_at":"2026-08-15T14:57:54.639508Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.620035Z","title":"Silverman:The Markoff equation: past, present, future, Notices Amer","venue":null,"work_id":"f0d1dfa6-06c1-4634-b041-788baa208ba2","year":2026},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.395325Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:7f62c0483f9efc6f41e48dae658780a100304710835a1aacd3a52bb5304c3e79","observation_id":"748740e8-c4ad-4659-8e94-e3c6d319f206","resolution":{"observed_at":"2026-08-15T14:57:54.625095Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2512.21963","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.533827Z","title":"Satake, Y","venue":null,"work_id":"206c5d5d-9e14-4b59-9529-3a18e5811c9e","year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.399558Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:2f91ac00b74e1ec4fca50cae90759f70a088924e64a59449957ab49f5959e237","observation_id":"6af80272-a90d-4e49-add6-fe77054585f8","resolution":{"observed_at":"2026-08-15T14:57:54.543821Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T14:57:54.606751Z","title":null,"venue":null,"work_id":"5d907cf4-ef60-4b0d-8cdd-cbd05709645d","year":2025},"citing_paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T14:57:54.403457Z"},"links":{"citing_paper":"/paper/2608.03097"},"observation_digest":"sha256:f4c661c02bec774e02a749cf17c9d18c88179c6362b16502227ed094eb07c60e","observation_id":"9eb5ad28-8049-4b4b-9f5e-d555611fcdb6","resolution":{"observed_at":"2026-08-15T14:57:54.611046Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.03097","last_updated":"2026-08-04T04:14:05Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-15T14:50:21.397599Z","submitted_at":"2026-08-04T04:14:05Z","title":"Counting in Vieta graphs over $\\mathbb{F}_p$"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":10,"verified_exact":1,"verified_fuzzy":19},"total_outbound_references":30},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 17 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2608.03097."}