{"paper":{"title":"A cubical formalisation of topos causal models: intervention, sheaf gluing, and the intuitionistic do-calculus","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","math.CT"],"primary_cat":"cs.LO","authors_text":"Karen Sargsyan","submitted_at":"2026-07-17T05:05:31Z","abstract_excerpt":"Topos causal models recast causal inference inside a topos: a causal world is a presheaf, an intervention is a characteristic map into the subobject classifier, and reasoning is carried out in the intuitionistic internal language. We give the first machine-checked account of this 1-topos core, in Cubical Agda, over a previously verified probability monad and do-calculus. We build the classifier of sieves and realise the intervention $\\mathrm{do}(X := x_0)$ as a characteristic map with its classification theorem; prove the sheaf gluing of independent mechanisms, which the source asserts but nev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15629","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/2607.15629/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"}