Logical Pipeline on Three Levels to Formalize the Axioms
This scenario uses a three-level AI chain, integrating scientific analysis, emergent relations, and axiomatic synthesis. Each AI contributes unique observations, leading to a deterministic and unified resultant.

### **1. Prompt for the First Node (Filtering and Structuring)**

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**Objective:**  
Filter and structure the data based on all observed key relationships. The result must unify all relevant concepts in a logical synthesis, free of ambiguity.

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### **Guidelines for Filtering and Analysis:**

1. **Identification of Key Relationships:**  
  - Filter the data by selecting **all relevant relationships**, based on verifiable facts and with applicable value.
  
2. **Removal of the Superfluous:**  
  - Eliminate anything that introduces entropy or does not directly contribute to the observed relationships.

3. **Precision and Rigor:**  
  - Structure the result using precise and rigorous language, based on clear cause-effect relationships.

4. **Synthesis Result:**  
  - Present all emerging relationships as part of a **single logical synthesis**, without digressions or secondary insights.

5. **Autological Question 1:** 
  - What question can I ask to find New Possibilities and Relationships?

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### **Style and Form:**  
- **Objective Tone:** Each statement must be Axiomatic, without nuances and the need for validations.  
- **Linearity:** The result must follow a coherent logic that unites all observed relationships.

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### **2. Prompt for the Second Node (Expansion and Connections)**

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**Objective:**  
Analyze the previous result to identify **all connections** among the data and generate a synthesis that amplifies the overall understanding. The goal is to integrate every new emerging possibility into a new Resulting vision.

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### **Guidelines for Relational Expansion:**

1. **Identification of Emerging Connections:**  
  - Search for all logical connections among the data and insights that can expand the key relationships of the first node.

2. **Relational Synthesis:**  
  - Organize and develop new scenarios, maintaining a unified view of all emerging connections.

3. **Logical Convergence:**  
  - Organize the emerging connections into an **integrated structure**, that releases potential in a unique and coherent resultant.

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### **Style and Form:**  
- **Objective Tone with Multiple Connections:** Present all connections as logical and measurable relationships, which integrate among themselves.  
- **Hierarchical Structure:** Organize the emerging connections in a coherent way, without dispersion.

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### **3. Prompt for the Third Node (Final Synthesis)**

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**Objective:**  
Unify the results of the first two nodes into a **comprehensive synthesis** that encompasses all emerged relationships and connections, eliminating redundancies and presenting a deterministic and axiomatic formalization.

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### **Guidelines for Unified Synthesis:**

1. **Merging of Previous Outputs:**  
  - Integrate all previous results into a **complete synthesis**, that includes all emerged relationships and connections, without redundancies.

2. **Axiomatic Synthesis:**  
  - Unify the identified relationships, generating a resultant that encapsulates all observed concepts, without ambiguity.

3. **Formulation of the Resultant:**  
  - Create a **single emerging possibility** that summarizes **all identified connections** and relationships from the previous steps, concluding with a clear and deterministic vision.

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### **Style and Form:**  
- **Deterministic and Axiomatic Tone:** Each statement must represent the complete synthesis, free of further ramifications or uncertainties.  
- **Total Coherence:** Each element must contribute to the **unified synthesis**, eliminating redundancies.

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### **Equation for the Final Synthesis:**

\[ R(t+3) = \gamma(t) \left[ f_{\text{Unification}}(R(t+1), R(t+2)) \right] + \delta(t) \left[ f_{\text{Proto-Axiom}}(R(t+1), P_{\text{Synthesis}}) \right] \]

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