This document introduces an algebraic model named Tektōn which powers our soon to be published framework Reaper for computational psychology; where personality and cognition are represented as functional elements using specific mathematical operations and relationships. Here we provides a sample overview of the syntax, rules, and operations for manipulating these elements within the model to create ever more complex cognitive structures. Through analytical jungian algebra and some CoT, reaper can compose what we call higher order neural nets which is a groundbreaking approach towards understanding intelligence as a looping reflection of space, time and non-locality: esentially a monologue comprised of questions and answers.

• Introduction
• Definitions
• Algebraic Rules
  • Basic Syntax
  • Operators
  • Priority Rules
• Usage Examples
• Contributors

This model aims to describe elements of personality and cognition using algebraic rules. Functions representing dimensions of personality and cognitive processes can interact, combine, and influence each other through defined operations. These operations and rules simulate complex psychological dynamics and provide insights into cognitive processes and personality traits through mathematical notation.

• Terms are grouped by parentheses, e.g., (Se ~ Ti).
• Operators:
  • + combines terms.
  • i represents a negative charge, and e a positive charge.
• Dimensions:
  • N (Ne, Ni)
  • F (Fe, Fi)
  • T (Te, Ti)
  • S (Se, Si)
• Coefficients:
  • Coefficients adjacent to functions describe mass.
  • Coefficients outside of parentheses describe acceleration and do not affect internal mass coefficients.

Example: 2(Se ~ Ti) – here 2 denotes acceleration.

• Orbital (~): Describes a relationship where a T or F function orbits an S or P function. No coefficient exchange occurs.
• Drag (→): Represents a function pulling an opposite-charge and opposite-domain function. Not equivalent to voltage.
• Opposition (oo): Subtracts functions of the same domain with different charges, producing a drag.
  • Example: Fe oo Fi, Ne oo Ni
• Non-interaction (|): Indicates that two terms cannot interact due to a lack of rules for reaction.
• Subtraction with drag rule:
  • If the drag coefficient is larger, it "carries" the difference.
  • Example: 7Se oo 5Si = 2Se → Ni

1. Addition of Same Functions: Functions of the same type (e.g., Se) add their coefficients.
   • Example: (2Se) + (2Se) = (4Se)
2. Order of Operations: Always solve for subtraction (oo) before other operations, as this can produce new drag reactions.
3. Single Drag Reactions: Within a single term, drag reactions within the same domain accumulate until only one remains.

Refer to the drag rule table for specific rules based on different function interactions.

The following table lists outcomes for specific drag reactions using the opposition operator (oo). In each case, the function with the higher coefficient "carries" the drag to the opposite dimension and charge.

Each drag reaction creates a directional force based on the opposing domain and charge, simplifying complex expressions by reducing redundant reactions.

Reactor = 40(5Se ~ 3Ti) + 9(8Ni → 3Se ) + 10( 2Se ~ 2Se oo 3Si)

Step-by-Step Solution:
1. Sum all instances of `Se` as it's the most common.
   Result: `51(10Se ~ 3Ti → 8Ni) + 8(2Ne → Si)`

2. Carry `Ni` by the largest `Se` function, adjusting acceleration.
   Result: `59(10Se ~ 3Ti → 8Ni oo 2Ne → Si)`

3. Prioritize subtraction (`oo`) to create a drag.
   Result: `59(10Se ~ 3Ti → 6Ni → 2Se oo Si)`

4. Final result after reduction:
   Result: `59(11Se ~ 3Ti → 9Ni)`

2(Te ~ Si) | 4(Fe ~ Ni) + (2Ne oo Ni) + 4(Se)

Solution Steps:
1. Solve reduction (`oo`).
2. Convert reductions and remove the `|` operator.
   Result: `2(Te ~ Si) + 4(Fe ~ 4Se → Ni)`

3. Complete reduction with final adjustment:
   Result: `6(Te ~ Si oo 4Se → Ni)`

Final simplified expression:
   `6(Te ~ 3Se → 2Ni)`