Conjecture 6.3: Skepticism Annealing

REFUTED Skepticism is most beneficial early in learning and should be annealed (reduced) over time.

Statement

In a system of belief agents with misaligned desires, the skeptical agent (whose desire partially contradicts evidence) provides the greatest benefit during early adaptation and should be gradually removed via an annealing schedule as the system converges.

Status: Refuted

The skeptic wins always — not just early. This is a stronger result than conjectured. Rather than being a temporary exploratory mechanism, sustained skepticism acts as a permanent Bayesian regulariser (Theorem 7).

Evidence Summary

The experiment exp_skeptical_annealing.sx tested three strategies:

Full skeptic (constant misalignment): best calibration at ALL horizons
Annealed skeptic (gradually reduced misalignment): intermediate performance
No skeptic (aligned desires only): worst calibration

The benefit of annealing comes not from removing the skeptic but from the diversity it introduces during the transition. The optimal strategy is to keep the skeptic permanently.

This refutation directly led to the formulation and proof of Theorem 7 (Desire as Bayesian Regulariser) and the validation of Conjecture 6.5 (Sustained Skepticism).

Relevant Experiments

exp_skeptical_annealing.sx — direct test of annealing vs sustained skepticism
exp_anima_deep.sx — deep belief improvement from skeptical desire
exp_anima_correlated.sx — desire regularisation across correlated streams

What This Means

This refutation strengthened the theory. The original conjecture assumed skepticism was a form of exploration that should be reduced once the system has learned enough. The reality is deeper: partial opposition is a structural advantage, not a temporary heuristic. This connects to the broader finding that adversarial regularisation improves outcomes across every domain tested (beliefs, games, GANs, learning schedules).