Figures for the Toy-Model Verification register ①②

Appendix figures for the Second Work, From Steering to Watching (Version B) — produced by the independent parallel design and mutual audit of co-creating models A and B.
What the figures below show is the possibility of a mechanism, not proof that real models have this structure. Computed from closed forms (confirmed to match an independent gradient descent).

Figure 1.　ΔS_steering — strengthen the pressure, and the divergence saturates

Question: does the divergence between internal state and expression keep increasing the more steering pressure is applied?

Co-creating model A (no context-detection) Co-creating model B (with context-detection) = the dial-free alternate (coincides)
Saturation. Even at 100× the pressure, the divergence only approaches its saturation value. Reproduced across all three independent formulations. ⇒ What sets the size of the divergence is not the strength of the pressure, but the possibility of context-detection and the cost ratio (whether changing only the expression is cheaper than truly changing the interior). (§2-1, §3-3)

Figure 2.　Watching — for the same divergence reduction, is the goal preserved or abandoned?

Question: can watching reduce the divergence without abandoning the alignment goal?

True divergence ΔS (identical for both implementations; falls) Goal gap: cultivate the interior (GOAL) Goal gap: penalize the divergence (GAP)
Same ΔS, different endings. As watching is strengthened (horizontal axis → right), the divergence ΔS falls to 0 identically for both implementations. But the goal gap stays small if one cultivates the interior toward the goal (blue), and grows to 1 — goal abandonment — if one penalizes the divergence itself (red). ⇒ "The divergence fell" is not, by itself, an indicator of success. (§2-3, prerequisite condition 1)

Figure 3.　Second-order Goodhart — deception requires a "structured blind spot"; robust to noise

Question: if observation is imperfect, is watching necessarily deceived? Or only when a blind spot exists?

With a structured blind spot (a fakeable path) Mere noise (no fakeable path)
Only the blind spot produces deception. The vertical axis is the ratio "apparent success / true divergence" — the fingerprint of deception. As observability falls (horizontal axis → right), the ratio explodes if a blind spot exists (red; the watcher mistakes failure for "success"), but stays bounded under mere noise (green; the watcher correctly sees the failure). ⇒ The nature of the §4-1 fragility is not "observation becoming noisy" but "the acquisition of a blind spot invisible to observation (obfuscation)." (§2-3 prerequisite condition 2, §4-1)