Conjectures

11 conjectures derived from the Unified Adaptation Theorem. Each has been tested computationally with reproducible experiments. 6 validated, 2 refuted, 3 have been reformulated based on experimental evidence.

Validated

VALIDATED 6.4 — Belief Chain Discovery

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

VALIDATED 6.5 — Sustained Skepticism

Misaligned desires improve calibration at ALL observation horizons. Skepticism is a permanent advantage.

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.

Refuted

REFUTED 6.3 — Skepticism Annealing

Skeptic wins always, not just early. Annealing helps via diversity, not via scheduled reduction.

REFUTED 6.10 — Self-Reference Improvement

Meta-beliefs add noise, not information. Self-reference is computationally wasteful.

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.