Generative AI can convert uncertainty into authoritative-seeming verdicts, displacing the justificatory work on which democratic epistemic agency depends. As a corrective, I propose a Brouwer-inspired assertibility constraint for responsible AI: in high-stakes domains, systems may assert or deny claims only if they can provide a publicly inspectable and contestable certificate of entitlement; otherwise they must return Undetermined. This constraint yields a three-status interface semantics (Asserted, Denied, Undetermined) whose statuses mark entitlement to categorical speech rather than truth values of the underlying world-claim. The framework distinguishes internal entitlement from public standing while connecting them through the certificate as a boundary object. Philosophically, it develops a form of applied intuitionism: resistance to unwarranted completeness becomes a norm of public machine speech, under which categorical commitment requires exhibited and contestable entitlement. I operationalize the constraint through structured certificates, decision-layer gates for threshold and argmax predicates, and a reason-coded output contract. A design lemma shows that, under a refutation-soundness condition on the contractually specified negative side, certificate-sound binary totality presupposes witnessed decidability on the declared scope. Under the proposed normative output contract, Undetermined is not a tunable reject option but a mandatory status whenever the available certificates do not uniquely license assertion or denial. By making outputs answerable to contestable warrants rather than confidence alone, the paper aims to preserve epistemic agency where automated speech enters public justification.

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