{"paper":{"title":"Towards Continuous-time Causal Foundation Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.data-an","stat.ME"],"primary_cat":"cs.LG","authors_text":"Dennis Thumm, Ruben Wiedemann, Ying Chen","submitted_at":"2026-05-26T12:06:04Z","abstract_excerpt":"Extending discrete-time causal Prior-data Fitted Networks for time series to continuous time invites writing the mechanism as a stochastic differential equation (SDE) -- but if the SDE is integrated \\emph{once per observation gap}, the trajectory law depends on when it is observed, and the prior remains a discrete-time Markov model in SDE clothing.\n  We propose a precise continuity criterion -- trajectory-law invariance to the observation schedule -- together with a three-tier taxonomy (discrete; naive observation-grid integration; fine-grid integration with decoupled observation) and a constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28880","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.28880/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}