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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 never proves; and machine-check the Kripke-Joyal forcing clauses of the internal language. In the modal layer we find and repair a gap: the three standard Lawvere-Tierney axioms do not force a closure operator. With the missing law restored, we exhibit the double-negation topology as a concrete instance and show that interventions and Pearl's rules a","title":"A cubical formalisation of topos causal models: intervention, sheaf gluing, and the intuitionistic do-calculus","url":"https://arxiv.org/abs/2607.15629","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.15629v1 Announce Type: cross \nAbstract: 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. 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