Closure and the Limits of Forced Results: An information-theoretic criterion for when a forced-breakdown theorem transports to the system it is read as being about, with three consequences separated by carrier and one worked case

A large and growing class of results establishes that some system breaks down in finite time when a force is supplied to it from outside. Such results are stated for a system on a fixed background, and they are read, in transit, as statements about the thing the system models. This paper gives a criterion for when that reading is licensed. We define an interaction domain by mutual information against the complement, state two axioms, and derive three consequences that separate by carrier: a domain admits no agent outside itself and no structured position outside itself, both conditional on the closure axiom, and no system indexes all of its own binary properties, which is unconditional and classical. We then prove a transport theorem: a forced-breakdown result transports to a system S only if S is not closed, and its hypothesis is unsatisfiable at any closed system. The theorem adjudicates a reading and never a theorem, and we prove for the worked case that the reading and the theorem come apart. Taking the 2026 forced Navier-Stokes construction (OPENAI) as that case, we show by its own hypothesis that its fluid is not closed, so the transport theorem leaves its mathematics entirely untouched, and we show that the popular reading of it identifies its fluid with a closed system, at which point the transport theorem applies and the reading fails. The result is therefore total against the identification and empty against the mathematics, and we argue that this is the correct shape for a criterion of this kind.