Escape, Cost, and Correlation at the Verification Floor of Gated Agentic Computation

This paper takes the verification floor of gated agentic systems — established statistically in A Fault-Tolerance Threshold for Gated Agentic Computation (DOI 10.5281/zenodo.20820968) and mechanistically in Generated Gates Inherit Their Generator's Blind Spots (DOI 10.5281/zenodo.20837102) — as given, and develops three of its consequences plus a practical framing. (i) A series-system escape identity gives the output-size analogue of the horizon ceiling: the probability that an n-unit output contains at least one escaped fault tends to 1 for any fixed per-unit escape rate, so "zero faults at scale" requires driving the per-unit floor to zero, not adding verification. (ii) A conditional cost comparison shows that, above the shared floor, reaching a target escape rate a distance δ above it costs O(log 1/δ) by gating versus O((1/δ)^(1/p)) by scaling the executor's own error down — formalizing the empirical "verify rather than scale" claim under stated cost models. (iii) A correlated-escape bound shows that, at fixed marginals, shared upstream provenance only clusters escapes, never raising the chance of at least one escape relative to independence, for any number of shared parents. Finally, the floor grounds a proposed ordinal assurance ladder and a typed-evidence non-collapse rule. The mathematics is classical and attributed to its sources; the contribution is the synthesis and one closed-form cost comparison. A self-contained Python script (simulate_floor.py) reproduces every numerical claim.