Conjectures

11 conjectures derived from the Unified Adaptation Theorem. Each is tested computationally with reproducible experiments: 5 validated, 3 reformulated on the evidence, 3 explored and open.

Validated

VALIDATED 6.4 — Belief Chain Discovery

Interaction matrix recovers causal ordering among belief agents without prior topology.

VALIDATED 6.6 — Optimal Forgetting

Meta-gradient descent recovers near-optimal forgetting rates: λ*=0.99 stationary, λ*=0.93 changing.

VALIDATED 6.7 — Transfer Learning Threshold

Clear crossover at |p_A - p_B| ≈ 0.15 where transfer becomes harmful.

VALIDATED 6.8 — Group Structure Discovery

Interaction matrix discovers coalition topology: within-group α=0, between-group α=0.785.

VALIDATED 6.9 — Structural Stability

Perturbations to converged systems recover equilibrium within O(10) adaptation cycles.

Explored

EXPLORED 6.3 — Skepticism Annealing

Whether a partially contradicting desire should be reduced over time. Sustained, annealed and absent skeptics compared at several horizons; open.

EXPLORED 6.5 — Sustained Skepticism

Whether a partially contradicting desire keeps a calibration advantage at every horizon. Explored in the anima runs; open.

EXPLORED 6.10 — Self-Reference Improvement

Whether a meta-belief about one's own accuracy improves calibration. No benefit measured in the runs to date; open.

Reformulated

REFORMULATED 6.1 — Convergence Ratio Universality

Universality holds within equivalence classes defined by spectral radius and subsystem count, not globally.

REFORMULATED 6.2 — Soft Phase Transition

Convergence probability is a sigmoid of σ(M) centred at 1, recovering sharp transition in the linear limit.

REFORMULATED 6.11 — Hybrid Lyapunov

Monotone decrease between consolidation events with bounded jumps. Convergence when contraction exceeds jump magnitude.