An Enclosed Mode Is a Gauge Choice: Topology Relative to Reach in Certified Code World Models
A code world model accepted by a sampling gate can be exactly right on everything the gate can see and arbitrarily wrong beyond it. The paper characterizes what a certified model can know, and what its errors can cost, when the omission is an annular freeze mode enclosing an unreachable interior. On a minimal ring instrument the authors prove the extreme case (a wrong-topology filled-disc artifact unfalsifiable by any sampling gate and bitwise harmless at play) and measure, with LLM synthesis across three model families, how one knob (a channel of width gamma) walks the same artifact through three regimes: unfalsifiable-and-harmless, falsifiable-and-costly, and instantly falsified.
The paper introduces a formal framework for certified code world models, showing that acceptance by a sampling gate determines the model exactly only on the reachable query set; beyond reach is gauge. It proves an extreme case where a wrong-topology artifact is unfalsifiable by any sampling gate and bitwise harmless at play. Experiments with LLM synthesis across three model families show that a channel of width gamma transitions the artifact through three regimes: unfalsifiable-and-harmless, falsifiable-and-costly, and instantly falsified. Three principles organize the empirics: danger is topology relative to reach; repair is parameter-bound and sensor-bound; and no family recovers the r… (truncated in evidence).
The work formalizes certified model knowledge using a gate quotient: acceptance-with-certainty determines the model exactly on the reachable query set, while beyond reach is gauge. The minimal ring instrument demonstrates a wrong-topology filled-disc artifact that is unfalsifiable by any sampling gate and bitwise harmless at play. A channel of width gamma controls the artifact's regime: a planner-usable channel collapses the blind model's exploitation (play cost 1.09 to ~0 over a knee at gamma ~ 0.1), while a hidden channel with the same first Betti number keeps it at full strength (1.12). Repair is parameter-bound and sensor-bound; no family recovers the r… (truncated).
The findings highlight a fundamental limitation of sampling-based certification for code world models: models can be certified as correct on all observable queries while harboring arbitrary errors in unreachable regions. This has implications for safety assurance of AI systems in robotics and autonomous planning, where topology relative to reach determines whether hidden errors become exploitable. The observed regime transitions suggest that certification protocols must account for reachability and topology, not just sampled accuracy.
For organizations deploying certified AI models in safety-critical or autonomous systems, this research indicates that sampling-based certification may provide false assurance. Understanding topology relative to reach can inform better testing and certification strategies, potentially reducing risk of hidden model errors that become costly when reachability changes.
Next signals include whether the three model families can recover the missing topology under different parameter and sensor configurations, and whether the framework extends to more complex world models beyond the minimal ring instrument. The paper's truncated conclusion likely discusses open problems in certified model repair and the role of gauge choices in AI safety.