Axiom · Chain Position 94 of 346

BIMODAL OUTCOME

**Sign determines asymptotic fate (no neutral terminus).**

Connections

Assumes

  • None

Enables

  • None
Mathematical Layer

Formal Statement

Axiom ([[094_A12.2_Bimodal-Outcome|A12.2]]): For any soul state ψ with sign σ:

\lim_{t \to \infty} \Phi(\psi(t)) = \begin{cases} \Phi_{max} & \text{if } \sigma = +1 \\ 0 & \text{if } \sigma = -1 \end{cases}

The asymptotic fate is entirely determined by the sign. There is no other possibility.

Defeat Conditions

To Falsify This

  1. **Find a third attractor** — Demonstrate a stable equilibrium state that is neither Φ_max nor Φ_min. This would require a potential landscape with three wells, but the destiny equation has only two fixed points. The dynamics are bistable, not tristable.
  2. **Show continuous outcome distribution** — Prove that asymptotic Φ values form a continuum rather than clustering at two points. But the dynamical analysis ([[093_A12.1_Asymptotic-Behavior|A12.1]]) proves convergence to fixed points, not intermediate values. The distribution IS bimodal.
  3. **Demonstrate stable limbo** — Find souls that remain eternally at intermediate coherence without approaching either attractor. But intermediate states are unstable equilibria—any perturbation sends them toward one attractor or the other.
  4. **Prove sign-independent outcomes** — Show that σ = +1 and σ = -1 souls can reach the same attractor. This contradicts the sign-dependent dynamics: sign determines direction, and direction determines destination.