Interventional Grounding: Identifiability and Misrepresentation via Counterfactual Witnesses in Two-Topos Grounding

Passive observation underdetermines grounding: multiple concept hypotheses can fit the same evidence, and failures need not constitute misrepresentation without intervention-driven counterexamples. We extend Two-Topos Grounding with an explicit intervention channel and define counterfactual witnesses linking actions to observation-side evidence. We prove (i) an interventional identifiability theorem: under separating probes, the candidate pool shrinks monotonically to a unique hypothesis (up to isomorphism), and (ii) a normativity theorem: broken counterfactual witnesses generate explicit counterexample witnesses that certify misrepresentation rather than mere incompleteness. TTGOS v0.2.2 provides an executable audit trail (action logs, candidate-pool traces, counterexamples) reproducing these guarantees. We discuss minimal assumptions, and we do not address optimal intervention policies or probabilistic/noisy interventions. This preprint is part of the Two-Topos Grounding (TTG) series.Software reference: TTGOS v0.2.2.