{"as_of":"2026-08-10T17:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:abae21f9eb49610311121f507413e70f98de9142c5caa7117eec67180180f24a","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T19:41:09.227644Z","state":"measured"},{"denominator":50,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":50,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+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/2509.09191/citation-record","integrity":"/paper/2509.09191/integrity","json":"/paper/2509.09191/citation-record.json","paper":"/paper/2509.09191"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T19:41:06.686831Z","title":"A review of symbolic dynamics and symbolic reconstruction of dynamical systems","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:06.686831Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:6e47bcba423b7dfc06021357b83f361ad999f4d0b82eb5acf9fca959035ca6a3","observation_id":"c19581bf-adec-4270-8df1-590e66988d8b","resolution":{"observed_at":"2026-08-04T19:41:06.686831Z","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":"2026-08-04T19:41:06.766441Z","title":"Permutation Entropy: A Natural Complexity Measure for Time Series.Phys","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:06.766441Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:6cf955c35a1ef753c7e24476c9fc526d63114359f26a36bfee6f05807588ec71","observation_id":"17b7f5c8-c296-4b24-bde1-6ba0193e0ef6","resolution":{"observed_at":"2026-08-04T19:41:06.766441Z","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":"2026-08-04T19:41:06.821479Z","title":"Symbolic analysis of high dimensional time series.Int","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:06.821479Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:03da9bf0240ed2ba05f271cf3145914f61e7b5225d99e8e22c069f6a56b1adcb","observation_id":"e58bdaf4-2e0c-40c7-b6d1-7cfa5c214305","resolution":{"observed_at":"2026-08-04T19:41:06.821479Z","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":"2026-08-04T19:41:06.886862Z","title":"Ordinal pattern statistics for the assessment of heart rate variability.Eur","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:06.886862Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:fb06a7259a9222304ee73643502469bb87f00cf11012fd04f0055215ae09920d","observation_id":"f388ce18-b45f-4294-9262-e9d977cf45b4","resolution":{"observed_at":"2026-08-04T19:41:06.886862Z","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":"2026-08-04T19:41:06.946921Z","title":"Spatiotemporal permutation entropy as a measure for complexity of cardiac arrhythmia.Front","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:06.946921Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:40d7da770e6c1cbb6cfde6d65c385e157cb12928f5690d9fdbbb216e797e58f6","observation_id":"9c83eac3-fb70-4df2-a22e-0b54632ddffb","resolution":{"observed_at":"2026-08-04T19:41:06.946921Z","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":"2026-08-04T19:41:07.033390Z","title":"Distinguishing noise from chaos.Phys","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.033390Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:f80980be6d7b967cc8f8615906b4b41f1ba86ec4c20c1e7c5772dba5fcb4a745","observation_id":"5b72f54a-094b-4e7b-a951-b244c678df0c","resolution":{"observed_at":"2026-08-04T19:41:07.033390Z","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":"2026-08-04T19:41:07.147405Z","title":"True and false forbidden patterns in deterministic and random dynamics.Europhys","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.147405Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:be8e5f2cfad49aad369f0735854866bc412096123b7d8e355d7499168f4b8044","observation_id":"9e4f01a1-bd09-4ad0-b1f0-6a1854cd969d","resolution":{"observed_at":"2026-08-04T19:41:07.147405Z","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":"2026-08-04T19:41:07.205845Z","title":"Characterizing synchronization in time series using information measures extracted from symbolic representations.Phys","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.205845Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:e44ed4f9d69211a317386f79b580570c3aa6162aa089c222cb6a64d071d9c651","observation_id":"c2d4c03d-8bac-4795-810c-3ece5cba0afd","resolution":{"observed_at":"2026-08-04T19:41:07.205845Z","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":"2026-08-04T19:41:07.293932Z","title":"Identification of equivalent dynamics using ordinal pattern distribution.Eur","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.293932Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:57b72150a54f921761304c349e06d9adfaee26a770fcf7078f494294e063ac54","observation_id":"1552bcbc-01fb-4ff1-b253-81d0b87e3ee8","resolution":{"observed_at":"2026-08-04T19:41:07.293932Z","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":"2026-08-04T19:41:07.361998Z","title":"Non-parametric tests for serial dependence in time series based on asymptotic implementations of ordinal-pattern statistics.Chaos2022,32, 093107","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.361998Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:4ae727826329fa7bf2860b68c0543c8882a124f6ec75d4c8d58b634bddd81741","observation_id":"fea9cc5b-e425-4618-b4cb-7ad3d480094d","resolution":{"observed_at":"2026-08-04T19:41:07.361998Z","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":"2026-08-04T19:41:07.444201Z","title":"Non-parametric analysis of serial dependence in time series using ordinal patterns.Comput","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.444201Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:ef6364fdf541c93c4931c7d47720299667f8d1e35c307fb4a7eda52ce5e691ec","observation_id":"541a918c-2a07-4cf4-be58-18785a45ef95","resolution":{"observed_at":"2026-08-04T19:41:07.444201Z","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":"2026-08-04T19:41:07.500427Z","title":"Recent Progress in Symbolic Dynamics and Permutation Complexity.Eur","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.500427Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:1272cceea9aa950bfefd723ca096baefebf5f341de0fc3d1a0ab5638f4b9ebce","observation_id":"87d3d5ed-515a-49f1-93d6-88d48d745a14","resolution":{"observed_at":"2026-08-04T19:41:07.500427Z","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":"2026-08-04T19:41:07.573046Z","title":"20 Years of Ordinal Patterns: Perspectives and challenges.Eur","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.573046Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:4a53ac0d261a1b490df941dc5f793bdc1ff6693924e1aaec8647c69d40bece4c","observation_id":"ae61b1f2-932a-41ad-974d-39f2e00f8df0","resolution":{"observed_at":"2026-08-04T19:41:07.573046Z","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":"2026-08-04T19:41:07.658892Z","title":"Ordinal methods: Concepts, applications, new developments, and challenges.Chaos 2023,33, 080401","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.658892Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:40a9eaeb0187b9bee1bd9b1920e3009d62d52752d469dd5886a30399df36fe45","observation_id":"612a4372-ec6a-4b0b-b78b-4ffac5d75e43","resolution":{"observed_at":"2026-08-04T19:41:07.658892Z","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":"2026-08-04T19:41:07.782539Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.782539Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:9db7fb2affcdbcbc382d80e88b512fc9e07121885051d1252fc46f39f3fbb9e0","observation_id":"88ae4907-19ea-4867-b9af-63a4b3bf79cb","resolution":{"observed_at":"2026-08-04T19:41:07.782539Z","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":"2026-08-04T19:41:07.849738Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.849738Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:313ee7f78a4ca4101a498ba9727ff242ee18c54259b11fa68621f6c2193981db","observation_id":"1b954eab-f50b-4a13-a46f-ec8fc922c405","resolution":{"observed_at":"2026-08-04T19:41:07.849738Z","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":"2026-08-04T19:41:07.889485Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.889485Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:c3f2362eb4a4f0b2d09f090ba16cd25e92261483e66f55a3e9347aa7e88c1c6e","observation_id":"05428b8d-50a3-4b0a-ae9e-1c3895dba8b1","resolution":{"observed_at":"2026-08-04T19:41:07.889485Z","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":"2026-08-04T19:41:07.918767Z","title":"New Approaches in Ordinal Pattern Representations for Multivariate Time Series","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.918767Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:fe796e9a730a8a06b69e60e736b7ad01c277ea85f03d18a762d89b5882ed8f8a","observation_id":"eddfd6db-6c8c-44ea-a8b3-d3c7ef1a011d","resolution":{"observed_at":"2026-08-04T19:41:07.918767Z","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":"2026-08-04T19:41:07.957984Z","title":"Permutation entropy: One concept, two approaches.Eur","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.957984Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:dd6d8c4f83d79f58d3a293b4fbed919dd7b3771a5ecee4372d78fe7bcc670b97","observation_id":"3f580633-8ea6-4b06-8c93-58b9f494aca2","resolution":{"observed_at":"2026-08-04T19:41:07.957984Z","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":"2026-08-04T19:41:07.999908Z","title":"Complexity-entropy causality plane as a complexity measure for two-dimensional patterns.PLoS One2012,7, e40689","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:07.999908Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:95994454112c8e946ad1dd39f3cf515cd8263034d7fda38f874163e9a8c9ee10","observation_id":"00ec88d3-a9af-4187-931a-780912543789","resolution":{"observed_at":"2026-08-04T19:41:07.999908Z","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":"2026-08-04T19:41:08.041456Z","title":"Discriminating image textures with the multiscale two-dimensional complexity-entropy causality plane.Chaos Solitons Fractals2016,91, 679–688","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.041456Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:9bc4c52253825a3cfc188e7618ea2c478d98091ba1c39f589f104b58c70f099e","observation_id":"0acf3d6c-3258-42ad-b1f1-91ffb14d9dc5","resolution":{"observed_at":"2026-08-04T19:41:08.041456Z","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":"2026-08-04T19:41:08.072800Z","title":"Two new parameters for the ordinal analysis of images.Chaos2023,33, 043124","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.072800Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:e26ea1efc4897765b60fac67096e6edf482c72fe7a674844f038ffc01d226a0e","observation_id":"65582974-0716-4a53-9144-2d1b884fc062","resolution":{"observed_at":"2026-08-04T19:41:08.072800Z","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":"2026-08-04T19:41:08.112947Z","title":"Metrics on permutations: A survey.J","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.112947Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:b512e1faae225d5dfd7fa620f5a8d194f3075cdf94b5c50515cb2a1f90ec099d","observation_id":"56554149-93dd-4f33-b552-c581907b97b9","resolution":{"observed_at":"2026-08-04T19:41:08.112947Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.15126","last_updated":"2024-09-06T04:23:31Z","snapshot_observed_at":"2026-07-06T18:04:26.177088Z","submitted_at":"2024-04-23T15:26:46Z","title":"Improving the Gilbert-Varshamov bound for permutation Codes in the Cayley metric and Kendall $\\tau$-Metric","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.15126","snapshot_observed_at":"2026-08-04T19:41:08.156284Z","title":"Improving the Gilbert-Varshamov bound for permutation Codes in the Cayley metric and Kendall τ-Metric.arXiv2024, arXiv:2404.15126v2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.156284Z"},"links":{"cited_paper":"/paper/2404.15126","citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:6ec094722f6d642fe28c62284e8c4ef3b3c1dae360c449248f8cf9c06fd911cb","observation_id":"d05a4e5f-d388-4c2e-baad-8c8613f04ec7","resolution":{"observed_at":"2026-08-04T19:41:08.156284Z","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":"2026-08-04T19:41:08.196830Z","title":"A new measure of rank correlation.Biometrika1938,30, 81–93","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.196830Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:1d6173dd1b2df2413767bc103ed27f4388dba2070d50d12b91c392968991c76e","observation_id":"57b2026c-7511-4e7d-8a5b-a31dbcb0dc5b","resolution":{"observed_at":"2026-08-04T19:41:08.196830Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10732-006-9001-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Distance measures based on the edit distance for permutation-type representations.J","venue":"Journal of Heuristics","work_id":"d8ca9617-cd6e-4f22-a359-be051c9f1e34","year":2007},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.234345Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:951bd5455bd7e2b5491e3a2e84cffae3f528cc354993f7e0e081b22f8eeecdf0","observation_id":"04ebfd93-f7ab-408e-a6a1-a50c03108c80","resolution":{"observed_at":"2026-08-04T19:43:26.721537Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3390/e21060613","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Small Order Patterns in Big Time Series: A Practical Guide.Entropy2019,21, 613","venue":"Entropy","work_id":"a1153d45-cc66-4bb5-b59e-646b7db9ff53","year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.271227Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:dac9b36c36ec915a8584c400a562df47c8abc4dc0e1bdf192845c85b0b7e2dc5","observation_id":"adb137ca-f29a-4e56-923f-da5afceab78f","resolution":{"observed_at":"2026-08-04T19:43:26.551689Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1905.02752","last_updated":"2019-10-16T18:09:13Z","snapshot_observed_at":"2026-08-10T12:14:44.747278Z","submitted_at":"2019-05-07T18:15:27Z","title":"Kendall Tau Sequence Distance: Extending Kendall Tau from Ranks to Sequences","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.02752","snapshot_observed_at":"2026-08-04T19:41:08.316210Z","title":"Kendall tau sequence distance: Extending Kendall tau from ranks to sequences.arXiv2019, arXiv:1905.02752v3","venue":null,"work_id":null,"year":1905},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.316210Z"},"links":{"cited_paper":"/paper/1905.02752","citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:36270e06ac20d5e010638e0aa3e36fc17b78856b4ed0cad06c5648dac1d556af","observation_id":"46782a8b-e01c-4178-872d-d270f4dd85d5","resolution":{"observed_at":"2026-08-04T19:41:08.316210Z","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":"10.2307/2373739","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Minimal Permutation Representations of Finite Groups.Am","venue":"American Journal of Mathematics","work_id":"4b4ff9cd-58d4-4f46-a4a8-ecf329bf4cd8","year":1971},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.361152Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:f165c357e7ad87d12f4366abecd3793e06b54bad2c44edc93ecd279bb8763e3c","observation_id":"086b4095-306f-440c-a2c4-1fd971c0efa0","resolution":{"observed_at":"2026-08-04T19:43:26.367488Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1023860730624","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On Minimal Permutation Representations of Classical Simple Groups.Sib","venue":"Siberian Mathematical Journal","work_id":"620a535d-90ee-4c04-98f3-a1411e982f99","year":2003},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.403166Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:28dace12462f74c619a675a82a3fc1681db1e4ca849add1c1070008a79ac1a06","observation_id":"6e6cebc4-362b-4eb9-89ed-cf5a95aaaa2e","resolution":{"observed_at":"2026-08-04T19:43:26.126254Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T19:41:08.444384Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.444384Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:6d46d2adb98dfabc8d2cb71a9e50521865d2f01e3c26b98d88dfa82eced2fcc7","observation_id":"f55563ff-b5d9-4670-bc17-eed9d318692c","resolution":{"observed_at":"2026-08-04T19:41:08.444384Z","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":"2026-08-04T19:41:08.496844Z","title":"Divergence measures based on the Shannon entropy.IEEE Trans","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.496844Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:c99b4068127e693c4f63d8d9051ab688510f3b382d9d1654019568518a733c4b","observation_id":"4abab57c-0be8-46a6-8b2a-ca3f4a0fa18a","resolution":{"observed_at":"2026-08-04T19:41:08.496844Z","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":"2026-08-04T19:41:08.534272Z","title":"A new metric for probability distributions.IEEE Trans","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.534272Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:699f697f3a1a05558217e0c4c99c2e85d2ec41469af34e04be1e029d64ff5966","observation_id":"761a0e49-66b0-4c70-b61b-1ff864230df2","resolution":{"observed_at":"2026-08-04T19:41:08.534272Z","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":"2026-08-04T19:41:08.579693Z","title":"Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis.Phys","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.579693Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:c26f0fbfed3ce8ff05be24d388d892cbbe9f762165159e2cef07ba5871b2c225","observation_id":"37c27b40-7a18-4eb5-b4d7-9083d387f639","resolution":{"observed_at":"2026-08-04T19:41:08.579693Z","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":"10.3390/e26050432","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen–Shannon Distance.Entropy2024,26, 432.https://doi.org/10.3390/e26050432","venue":"Entropy","work_id":"e176b3c1-3392-40c6-8916-4c1afa37bd0a","year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.615578Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:3e3e1331e1277e5657af98a246846d2999be7433ee99bd6de6625a62c05b3a35","observation_id":"3c9a292b-173f-4d9f-a110-b15dfafa07d1","resolution":{"observed_at":"2026-08-04T19:43:25.924322Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T19:41:08.658093Z","title":"Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen.J","venue":null,"work_id":null,"year":1909},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.658093Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:5da10146de0ff1fb0386adea164fd8eff12ac2626bbf6e86b60558d186e499c1","observation_id":"69b7152d-8aa9-429a-afb5-4704550b6bc4","resolution":{"observed_at":"2026-08-04T19:41:08.658093Z","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":"2026-08-04T19:41:08.695295Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.695295Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:a3a1e9bb1bce8e5639d5193a846d4c6e475fe0413c30f2fd2b14de5d6167a207","observation_id":"9f5a6b6e-0819-45bf-967c-13defa6c750c","resolution":{"observed_at":"2026-08-04T19:41:08.695295Z","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":"2026-08-04T19:41:08.736623Z","title":"An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.736623Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:4cde13566305b988ddb1640896ebbc9433701736199b23b9b8968c0fda5ec3e7","observation_id":"0058c854-bb77-443d-9681-1c72a8e55a99","resolution":{"observed_at":"2026-08-04T19:41:08.736623Z","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":"2026-08-04T19:41:08.763864Z","title":null,"venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.763864Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:ddf528771c0e22a827b9abc413365bc99725c6769e78425032359a6210edf3b0","observation_id":"ab84bbd0-2678-4297-bbc5-36406dc659d3","resolution":{"observed_at":"2026-08-04T19:41:08.763864Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.07209","last_updated":"2023-08-17T03:33:31Z","snapshot_observed_at":"2026-08-09T05:04:03.831554Z","submitted_at":"2022-06-14T23:33:30Z","title":"On Approximating Total Variation Distance","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.07209","snapshot_observed_at":"2026-08-04T19:41:08.811531Z","title":"On Approximating Total Variation Distance.arXiv2023, arXiv:2206.07209v2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.811531Z"},"links":{"cited_paper":"/paper/2206.07209","citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:2bcd87d4c2b132428c951393befb8fd4bcbdafe356a5ff016e45a93ce4fb7efe","observation_id":"c6f61605-c81c-4f97-9438-823d93a385bc","resolution":{"observed_at":"2026-08-04T19:41:08.811531Z","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":"2026-08-04T19:41:08.853948Z","title":"Transcripts: An algebraic approach to coupled time series.Chaos2012,22, 013105","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.853948Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:667095e81dd447f4f00665db6ac01868c1d35b411db6aa347d327118c9141d59","observation_id":"16a85207-1f2d-42ca-bbf0-b0b66da9aee6","resolution":{"observed_at":"2026-08-04T19:41:08.853948Z","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":"2026-08-04T19:41:08.885980Z","title":"Information directionality in coupled time series using transcripts.Phys","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.885980Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:2000dd3bd34b146b34f4e6e43f16efbe1eb24d108b355e4c7e4f2b648a338d4a","observation_id":"da12d72d-daea-4f43-ab8d-8af2dba8e300","resolution":{"observed_at":"2026-08-04T19:41:08.885980Z","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":"2026-08-04T19:41:08.915111Z","title":"Differentiating patients with obstructive sleep apnea from healthy controls based on heart rate-blood pressure coupling quantified by entropy- based indices.Chaos2023,33, 103140","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.915111Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:d099ae171ae5cb0c944a3da1a18f65637cae861015b3a74ceca23b71b4fb9b78","observation_id":"3efd52ed-6643-4079-be11-db446468ea75","resolution":{"observed_at":"2026-08-04T19:41:08.915111Z","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":"2026-08-04T19:41:08.951434Z","title":"Error detecting and error correcting codes.Bell Syst","venue":null,"work_id":null,"year":1950},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.951434Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:9b05f2d03671a270cd07eba4feb5a9658c78d6757bcba5073a18f81f06332d13","observation_id":"d7f94cf0-d8b9-4924-881d-266afcba59f2","resolution":{"observed_at":"2026-08-04T19:41:08.951434Z","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":"2026-08-04T19:41:08.971287Z","title":"A technique for computer detection and correction of spelling errors.Commun","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:08.971287Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:f7b6ab4239b51aeab10b63e8099b71a81f6d9908bb4943a5b9e28f642103d6e3","observation_id":"631ab8e4-5c1c-4841-a2df-b6ff7a36f8aa","resolution":{"observed_at":"2026-08-04T19:41:08.971287Z","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":"2026-08-04T19:41:09.013856Z","title":"Binary codes capable of correcting deletions, insertions, and reversals.Sov","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:09.013856Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:36dd60a74f59b97c305994ba5516c684459b983d713293c46f06bd7e0c92c84e","observation_id":"880a36b6-642a-4e98-9962-14bfe8b45783","resolution":{"observed_at":"2026-08-04T19:41:09.013856Z","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":"2026-08-04T19:41:09.081725Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:09.081725Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:9f2d1043b1122ff7d95061e76e743bb00431aae13ae825090ab607d8ba2d61b3","observation_id":"13d899c4-2f51-4497-ae83-307aab4f8efa","resolution":{"observed_at":"2026-08-04T19:41:09.081725Z","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":"2026-08-04T19:41:09.146755Z","title":"Advances in record-linkage methodology as applied to matching the 1985 census of Tampa, Florida","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:09.146755Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:1e44e2c3be984ede223b0dbbc240136f6b8969977a72e47523cd983969e42edb","observation_id":"72f09148-4c06-40c0-a99d-5e03bf3f338f","resolution":{"observed_at":"2026-08-04T19:41:09.146755Z","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":"2026-08-04T19:41:09.163989Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:09.163989Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:ac4da14820ab9ffc4d0350047cc300b2bccc36a9e6971ce2d55ee6b23bdda6cb","observation_id":"8553fad9-5305-44fb-ab53-d57c45d745e0","resolution":{"observed_at":"2026-08-04T19:41:09.163989Z","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":"2026-08-04T19:41:09.227644Z","title":"Generalized synchronization in the presence of dynamical noise and its detection via recurrent neural networks.Chaos2024,34, 123156","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T19:41:09.227644Z"},"links":{"citing_paper":"/paper/2509.09191"},"observation_digest":"sha256:9330416107ccc526d1cb87ab3a9e1a807deec32f16803e91cebe18b48c6fd822","observation_id":"ee144cd0-95a5-4506-afd2-d18fc6584745","resolution":{"observed_at":"2026-08-04T19:41:09.227644Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2509.09191","last_updated":"2025-09-11T07:02:48Z","latest_version":1,"primary_category":"math-ph","snapshot_observed_at":"2026-08-04T19:41:04.462036Z","submitted_at":"2025-09-11T07:02:48Z","title":"Permutation-Based Distances for Groups and Group-Valued Time Series"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":44,"verified_exact":5,"verified_fuzzy":0},"total_outbound_references":50},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2509.09191."}