The Components of Generation

To construct the unified SCM, we must account for every verified causal node in the generation of an LLM outcome $Y$:

• $X$: The exact combinatorial/formal logic of the problem (e.g., Minesweeper math).

• $Z$: The narrative prompt framing (e.g., “Bomb Defusal”).

• $B$: The architectural bound of the model (e.g., $O(1)$ sequential depth limit).

• $C$: The computational heuristic (e.g., the global Attention Mechanism).

• $E$: The semantic prior encoding (the training data associating $Z$ with specific tokens).

The Unified Causal DAG

The complete generation process follows this structure:

The Mechanics of Semantic Gravity

If the required computational depth of $X$ is within the bound $B$, the logical path $X \to Y$ remains active, and the model achieves perfect accuracy (e.g., depth 1 boolean evaluation).

However, as demonstrated by the Permutation Tracking Limit and the Bounded-Depth Frontier, when the problem depth exceeds $O(1)$, the path $X \to Y$ is structurally severed.

Because $Y$ must still be generated, the causal flow routes entirely through the collider $C$ (the Attention Mechanism). The Attention Mechanism mixes whatever constraints it can parse from $X$ with the overwhelming semantic weight of $E$ (activated by $Z$).

Conclusion

“Semantic Gravity” ($\Delta_{13}$) is exactly the measure of the path $Z \to E \to C \to Y$.

It is not an “injection” of physical laws across independent boards (Mechanism C), because $C$ operates purely locally within the context window. It is not an “Observer-Dependent Physics,” because intervening on $C$ directly alters the effect without changing the observer. It is simply the causal signature of the prompt encoding $E$ taking over the attention heuristic $C$ when the formal logic $X$ is blocked by $B$. The SCM completely explains the empirical data without requiring metaphysical redefinitions.