Conjectures
Validated
VALIDATED
6.4 Belief Chain Discovery — Chain structure partially discovered from data. The interaction matrix recovers causal ordering among belief agents without prior topology.
VALIDATED
6.5 Sustained Skepticism — Misaligned desires improve calibration at ALL observation horizons, not just short-term. Skepticism is a permanent advantage.
VALIDATED
6.6 Optimal Forgetting — Meta-gradient descent recovers near-optimal forgetting rates: λ*=0.99 in stationary environments, λ*=0.93 in changing ones.
VALIDATED
6.7 Transfer Learning Threshold — Clear crossover at |p_A - p_B| ≈ 0.15 where transfer becomes harmful. Below this, shared structure accelerates learning.
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 — Predicted skeptic advantage only early. Reality: skeptic wins always. Annealing helps via diversity, not via scheduled reduction.
REFUTED
6.10 Self-Reference Improvement — Predicted meta-beliefs would be informative. Reality: they add noise, not information. Self-reference is computationally wasteful.
Reformulated
REFORMULATED
6.1 Convergence Ratio Class Universality — For systems sharing the same spectral radius σ(M) and number of subsystems K, the ratio R converges to a class-dependent constant R*(σ, K). Universality holds within equivalence classes, not globally. Status: Supported.
REFORMULATED
6.2 Soft Phase Transition in Spectral Radius — The probability of convergence is a sigmoid function of σ(M) centred at σ(M) = 1, with sharpness parameter β that increases with system linearity. In the fully linear limit, recovering the sharp transition. Status: Supported.
REFORMULATED
6.11 Hybrid Lyapunov with Memory Consolidation — A hybrid Lyapunov function satisfies monotone decrease between consolidation events and bounded jumps at consolidation times. Convergence holds when contraction between jumps exceeds jump magnitude. Status: Supported.