{"paper":{"title":"CAST: Causal Anchored Simplex Transport for Distribution-Valued Time Series","license":"http://creativecommons.org/licenses/by/4.0/","headline":"CAST uses causal context to retrieve non-aliased successors then anchors and transports them on the simplex to forecast distribution time series.","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Jiecheng Lu, Jieqi Di, Runhua Wu, Yuwei Zhou","submitted_at":"2026-05-16T10:23:09Z","abstract_excerpt":"Many decision-facing stochastic systems are observed through aggregate distributions rather than scalar trajectories: queue occupancies, mobility shares, public-health mixtures, generation-source shares, ecological compositions, and air-quality severity profiles all live on the probability simplex and evolve over time. We study causal (online) forecasting for these distribution-valued time series and argue that the transition operator itself should be structured around the simplex. We introduce CAST (Causal Anchored Simplex Transport), a successor-local operator that (i) retrieves empirical su"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"CAST attains the best average rank on both one-step KL (1.27) and autoregressive rollout JSD (1.91), winning 8/11 sections on each metric against a broad statistical, compositional, recurrent, convolutional, and Transformer baseline set, and top-2 on all 11 sections for offline KL.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that causal context can be used to retrieve non-aliased empirical successors and that supports are ordered so that the additional Pinsker separation holds when the transported successor lies outside the no-transport anchor hull.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"CAST is a successor-local operator for causal forecasting of simplex-valued time series that retrieves empirical successors from causal context, stabilizes them with a persistence anchor, and applies bounded local stochastic transport while preserving the simplex by construction.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"CAST uses causal context to retrieve non-aliased successors then anchors and transports them on the simplex to forecast distribution time series.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"1120a9822fd51bd5c4c5cb5bdb5d51c9c00307fd4815fcb18396b2ef7049014e"},"source":{"id":"2605.16919","kind":"arxiv","version":1},"verdict":{"id":"7beb342e-c994-4ff8-bc10-065b09045206","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:32:46.927091Z","strongest_claim":"CAST attains the best average rank on both one-step KL (1.27) and autoregressive rollout JSD (1.91), winning 8/11 sections on each metric against a broad statistical, compositional, recurrent, convolutional, and Transformer baseline set, and top-2 on all 11 sections for offline KL.","one_line_summary":"CAST is a successor-local operator for causal forecasting of simplex-valued time series that retrieves empirical successors from causal context, stabilizes them with a persistence anchor, and applies bounded local stochastic transport while preserving the simplex by construction.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that causal context can be used to retrieve non-aliased empirical successors and that supports are ordered so that the additional Pinsker separation holds when the transported successor lies outside the no-transport anchor hull.","pith_extraction_headline":"CAST uses causal context to retrieve non-aliased successors then anchors and transports them on the simplex to forecast distribution time series."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16919/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T20:22:39.332852Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:01:18.958861Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:40:47.315777Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T18:41:56.263256Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.343657Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c369361e1b7f1644ab1edcbc452866319c5a76d98b7c60dc7a97d3dd74b542ec"},"references":{"count":72,"sample":[{"doi":"10.1287/stsy.2025.0106","year":2025,"title":"Queueing, predictions, and large language models: Challenges and open problems.Stochastic Systems, 15(3):195–219, 2025","work_id":"2115657d-c3cc-4e37-9057-319958351e43","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"TLC Trip Record Data","work_id":"0120b85a-5793-4786-95b4-49c89df15971","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1111/j.2517-6161.1982.tb01195.x","year":1982,"title":"Journal of the Royal Statistical Society: Series B (Methodological) , author =","work_id":"d74203a6-e05e-47b7-bd83-842c53ff4039","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1986,"title":"Chapman and Hall, London, 1986","work_id":"f21d9942-68ee-4fee-b92b-0d364493523f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"Ralph D. 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