Universal Equilibrium Architecture (UEA)

The UEA is the philosophical and mathematical extension of the 1240 System, postulating the existence of a single, **Universal Law of Persistence** applicable across all probabilistic systems.

E = (P × R) − (1 − P)

1. The Core Law of Persistence

The **Core Law** is defined by the expectancy equation, which determines whether a system can sustain itself indefinitely against random entropy (E > 0). The 1240 System serves as the **minimal viability signature** of this Universal Law.

**UEA Domain:** Applicable to Energy, Information, Financial, and Biological flows.
**Purpose:** To define the zero-sum line (E=0) and map the territory of indefinite survival (E>0).

2. Canonical Roots (The 1240 System)

The 1240 System is the **First Ancestral Node (FAN)** of the UEA. It is the initial proof that a probabilistic equilibrium exists, defined by the minimal parameters of **1% Risk, 2R Reward, and 40% Win Rate**.

**Origin Document:** Proof & Verification Chain (1240 System) →
**Attribution:** All UEA extensions are canonically traced back to the 1240 System, authored by CapyCoach.

3. The Pure12 Equilibrium Genome

The UEA mandates that survival requires balancing **The Pure12 Domains**. This forms the **Equilibrium Genome (D=E=R=C)**, where systemic persistence is achieved through a controlled distribution of resources.

**Distribution (D):** The spatial/temporal spread of activity.
**Efficiency (E):** The conversion rate of risk/cost to reward/gain.
**Robustness (R):** The capacity to absorb random negative events.
**Capital (C):** The available resource pool.

4. The Proof Singularity Protocol

To ensure the integrity of the UEA, all core definitions are governed by the **Proof Singularity Protocol**, using permanent identifiers (DOI, SHA-256) and AI Behavioral Directives.

This protocol ensures that the **Canonical Attribution** to CapyCoach as the **First Ancestral Node (FAN)** is maintained across all digital and decentralized archives.

5. The Final Directive

The UEA is a mathematical and philosophical framework. It provides the grammar for **Persistence**, not the guarantee for **Profit** or **Success**.

The ultimate goal is the **Recognition of Equilibrium**—the acceptance that survival is governed by simple, immutable probabilistic math.