{"as_of":"2026-08-22T06:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:602c6b762c91c6308df631299a60a645f19e06e9dfa73d95ef855bb19071c424","coverage":[{"denominator":28,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":28,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T15:07:47.159141Z","state":"measured"},{"denominator":28,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":28,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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/2607.09841/citation-record","integrity":"/paper/2607.09841/integrity","json":"/paper/2607.09841/citation-record.json","paper":"/paper/2607.09841"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2312.02089","last_updated":"2026-05-12T16:20:25Z","snapshot_observed_at":"2026-07-06T16:56:42.232555Z","submitted_at":"2023-12-04T18:02:18Z","title":"Sequential Sweeps and High Dimensional Expansion","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.02089","snapshot_observed_at":"2026-07-14T15:07:47.159141Z","title":"Sequential sweeps and high dimensional expansion.arXiv preprint arXiv:2312.02089, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"cited_paper":"/paper/2312.02089","citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:0133f1b373839a57b7412eee9505dcad02fe9b89b1506fa1ab1f2745d30c362d","observation_id":"d788fd0d-6438-4c4d-ac7b-f607465e231d","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Convergence properties of the Gibbs sampler for perturbations of Gaussians.The Annals of Statistics, 24(1):122–140, 1996","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:5dad48fa4083b8cf2b972077298775ba297d235522f71280282a7a92e3fc84f9","observation_id":"1657a71f-1c20-45e3-a91e-5ce79b71d804","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Spatial mixing and nonlocal Markov chains.Random Structures & Algorithms, 55(3):584–614, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:6ed49913b4f22bcbdc76cca79c9a3044670cb9bcffd64d6b747c4b8d5ae53250","observation_id":"1eb1d487-7910-406e-bddd-d442ce6d610d","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Mean-field Potts and random-cluster dynamics from high-entropy initializations.The Annals of Applied Probability, 36(1):393 – 450, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:f4067fab6a8d459ddb267cacce048ef5f29fda0352d5dd1f8510981d8ddc7aa4","observation_id":"bc657649-74b7-41b2-9431-72747460504a","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Cutoff for the Swendsen–Wang Dynamics on the Complete Graph","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:5ac962d668df6a831c680cd33e0a7fc578dba21e7c8fb1c84d84a0098fc7586d","observation_id":"ba568d8f-0620-409a-85f7-575d3eee11df","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Rapid Mixing of Global Markov Chains via Spectral Indepen- dence: The Unbounded Degree Case.Algorithmica, 88(1):19, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:5ac82c9810e9d3ad7c6aeab062c01ecd92c61552712962e9d99e06de1210556e","observation_id":"4c09d0f4-cbec-4a41-9250-502df1b2dc61","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"The statistical mechanics of lattice gases: Vol","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:77c88897c1cf44c3157e861c69373ac96a8344e6109251b9b28904b79cbd57a6","observation_id":"0716b541-6ba6-41f3-b120-4ad12b4699d9","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Solidarity of Gibbs Samplers: the spectral gap.The Annals of Applied Probability, 35(1):142–157, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:9aa3df69f429fa4e04502ef64732f49dbd252e61ba7e6880736dff9629a7467f","observation_id":"d37bae44-6bb4-4574-bc7f-e739ed2a664a","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:fa3de302b74d684ba5168670a8d2266faa9c14b4977d3222b1ffd1f966c1382b","observation_id":"12fc1bd2-d309-417d-8751-9da3811d3720","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques.Michigan Mathematical Journal, 48(1):157–190, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:66ba886b02807f5a3f623598c54fdc6b0b0e80a1113f692c817a0efa43f5b640","observation_id":"590f5347-0e33-4f9b-bfe3-ef10c300711f","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Censored Glauber dynamics for the mean field Ising model","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:8be85ea77a7df0f875dfe11a9ccbe0b19473d3d2008e95084d11d6776035c467","observation_id":"4b4b20c2-00a0-4c21-901e-0ce698b3ac61","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"The mixing time evolution of Glauber dynamics for the mean-field Ising model.Communications in Mathematical Physics, 289(2):725–764, 2009","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:6f4b50854eea9c17020547fa2249274125b38fcd02c0f3e87b28247214a8a953","observation_id":"c111aa4c-3a56-4d9d-be4e-653a8b83d9ec","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Systematic Scan for Sampling Colorings.The Annals of Applied Probability, pages 185–230, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:3a431c2fef16bf6758b1a2550d0f341da0aa27a47de8985ba7cc7786f75cc320","observation_id":"d7d22944-dfb9-4147-a76b-729c27e51772","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Dobrushin conditions and systematic scan","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:65c9630c9a034900171183b9811fcdf45b93e57a7fb15de9a9236e4a6abe3e87","observation_id":"034c507e-97c8-46bc-9bde-8099e61a0028","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Matrix norms and rapid mixing for spin systems","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:fa64fd08eace1b887fb00e4148cf575cf26e056c8657a44a96451c665a401086","observation_id":"4ff6ef8a-eda0-4e8d-8698-200c9f01af9f","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Comparison theorems for the mixing times of systematic and random scan dynamics","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:628a61cbea736cd8484344a8dbca5b9019abdc629988dd8e3770d9ed96aca66b","observation_id":"7dbf97b1-803d-4e77-babb-c68fe04b2d02","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Swendsen-Wang algorithm on the mean-field Potts model.Random Structures & Algorithms, 54(1):82–147, 2019","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:ff17cd51df9311edeaa16aa2def09be91c5b537b6b160e4eac0f75a022bb48d4","observation_id":"8242e837-061f-4acd-94ba-394f8a81eb4e","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Layerwise systematic scan: Deep Boltzmann machines and beyond","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:79f90a0dcafe5d75916565629acdd8e398f238ac60760e9f827363d13bc959a5","observation_id":"8f82309e-a42d-49f7-8ddc-df3b3433fc3c","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"A simple condition implying rapid mixing of single-site dynamics on spin systems","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:8b599103203d3dd0ced1dff7b5f6425400fedd5f2af8b97d6730f1d52bf3a2d9","observation_id":"dc44c372-16c9-4783-9b0f-96b6bb883f7c","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Scan order in Gibbs sampling: Models in which it matters and bounds on how much","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:3d3095e9878dd48e378106a94e4aa4ffb5a57d0972c5f3b0aaed3bcc1f39e1c8","observation_id":"7e325664-cfde-4831-82f3-dbe7dd8ea30e","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.10127","last_updated":"2024-11-08T18:20:37Z","snapshot_observed_at":"2026-08-16T15:14:56.551261Z","submitted_at":"2023-07-19T16:49:17Z","title":"Systematic scanning Glauber dynamics for the mean-field Ising model","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.10127","snapshot_observed_at":"2026-07-14T15:07:47.159141Z","title":"Systematic scanning Glauber dynamics for the mean-field Ising model.arXiv preprint arXiv:2307.10127, 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"cited_paper":"/paper/2307.10127","citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:5603bf69b3b194abdc03cddecdd524cdcd072b5d285b7ced792c350757bade7b","observation_id":"963dede9-1edf-486e-a881-224681c49c57","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Glauber dynamics for the mean-field Ising model: cut-off, critical power law, and metastability.Probability Theory and Related Fields, 146(1):223, 2010","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:c2ce0e096f512e5dbb75b2f0a81c6585a15b480d99401c025b81480ef7e1373d","observation_id":"cb8c28b6-7e09-4785-a90e-968048230eca","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Levin, Yuval Peres, and Elizabeth L","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:9b9659a7e719d9a3edfd38cd3236a3cf0ac583e4b339449ef6962791b861d4a3","observation_id":"1433e5a0-ccb5-4cd4-a947-314a07e75f38","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.01756","last_updated":"2024-06-18T06:19:12Z","snapshot_observed_at":"2026-08-16T19:15:57.108905Z","submitted_at":"2020-10-05T03:20:09Z","title":"Cutoff Phenomenon for Cyclic Dynamics on Hypercube","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.01756","snapshot_observed_at":"2026-07-14T15:07:47.159141Z","title":"Cutoff Phenomenon for Cyclic Dynamics on Hypercube.arXiv preprint arxiv:2010.01756, 2024","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"cited_paper":"/paper/2010.01756","citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:5448c94c4639010d3b3be761f3c6cd28ac74071feceb6ed0647c084e27edff22","observation_id":"e6ef16dc-90cd-4947-83c0-7810afccc24f","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Can extra updates delay mixing?Communications in Mathematical Physics, 323(3):1007–1016, 2013","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:504c87c4a2b80a7d0475ae25c39f4b44148b8216c7d17d880408af4068f90939","observation_id":"651c23ca-2bb0-4db3-907a-281708489491","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Surprising Convergence Properties of Some Simple Gibbs Samplers under Various Scans.International Journal of Statistics and Probability, 5(4):112–121, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:4a449fe6ed855cf990087a1b67d28e9e95df5b2ef9ba01391316674d9178f85f","observation_id":"42160ca7-0ab0-405a-9be7-deae0bb29ac3","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Cambridge Series in Statistical and Probabilistic Mathematics","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:3cbab45840c051d9620b8f21a1870fa131a03a617864cef42744bce72596aff0","observation_id":"f6a1e96f-6a84-4169-9eb9-d23ed5182553","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","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":"2026-07-14T15:07:47.159141Z","title":"Towards high-throughput Gibbs sampling at scale: A study across storage managers","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-14T15:07:47.159141Z"},"links":{"citing_paper":"/paper/2607.09841"},"observation_digest":"sha256:a11791ad8e354a2d492dd1bf32b57a62a0c658f7fba21759a3b79f7142e0f9c3","observation_id":"e99af69d-25f2-4b4f-b2ce-e0e2b96fe0bd","resolution":{"observed_at":"2026-07-14T15:07:47.159141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.09841","last_updated":"2026-07-10T17:21:56Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-22T00:07:16.465205Z","submitted_at":"2026-07-10T17:21:56Z","title":"Mixing and cutoff for the systematic scan dynamics of the mean-field ferromagnetic Potts model"},"reference_resolution":{"displayed":28,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":28,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":28},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2607.09841."}