The Impossibility of Deeper Invariants Under the AMetric Boundary

This paper establishes that no deeper invariants exist beneath the AMetric Boundary. Once admissibility is enforced, the search for more fundamental, hidden, or pre-metric invariants is shown to be incoherent rather than incomplete. The analysis proceeds by exhaustion. It demonstrates that all proposed candidates for deeper invariants—structural symmetries, abstract information measures, meta-dynamical principles, or pre-geometric substrates—rely on illicit re-metricization, scope transport, or covert reintroduction of structure that the AMetric Boundary explicitly excludes. When these moves are removed, nothing remains that could function as an invariant. The result fixes the AMetric Boundary as terminal with respect to invariance. There is no admissible explanatory layer beneath it, and no further reduction is possible without violating admissibility. The paper introduces no constructive alternatives or investigative programs. It records an impossibility result that closes the search for deeper invariants at the meta-foundational level.