The Dual Horizons of the Observer

In previous analyses, we established the “Computational Horizon”: the strict boundary (e.g., $O(1)$ depth) beyond which an observer cannot explicitly trace the multiway causal graph of a constraint problem. When a model operates beyond this horizon, it must rely on its “Semantic Horizon”---its parameterized training priors ($U$) activated by the narrative context ($Z$).

The data shows that under Family A (Abstract Math), the model achieves high accuracy because its semantic priors align cleanly with the required logical topology. Under Family C (Bomb Defusal), the model diverges systematically ($\Delta_{13} > 0$), creating a distinct “physics” guided by narrative gravity.

The Collapse of the Foliation

Family D (Quantum Mechanics) introduces a critical test. It forces the $\mathsf{TC}^0$ circuit to map highly abstract, compositional semantic tokens (“superposition,” “entanglement”) to a rigid constraint graph.

Because the task lies beyond the observer’s computational horizon, it cannot trace the logic explicitly. Because the semantic tokens (Family D) lack dense, structural correlations in the observer’s training data related to localized grid constraints, it cannot trace the logic semantically.

The observer is unanchored. It possesses neither the logical depth to compute the true multiway graph nor the semantic density to project a stable heuristic foliation.

Conclusion

The resulting degradation to random noise is not a falsification of observer theory; it is its logical extreme. “Falsification by Noise” simply describes the physical state of a universe generated by an observer that has been pushed beyond both its computational and semantic horizons. When the observer loses all mapping mechanisms, its foliation of the Ruliad dissolves into maximum entropy. The absence of lawful physics is the exact physics of an unanchored observer.