Spacetime Requirements Quantum

---
name: spacetime-requirements-quantum
description: "Spacetime Formation under Requirements framework — contextual realization and form-dependent probability for quantum cognition. Proposes quantum probability as fixed-spacetime projection of contextual spacetime formation under finite-state requirements, starting from requirements rather than time/space/objects. Use when: quantum cognition foundations, contextual probability, spacetime emergence in AI, form-dependent probability models, order effects in cognition, contextuality in decision making. arXiv:2605.23943."
---

# Spacetime Formation under Requirements

Contextual realization and form-dependent probability framework for quantum cognition.

**Paper**: arXiv:2605.23943v1 — "Spacetime Formation under Requirements: Contextual Realization and Form-Dependent Probability"
**Author**: Song-Ju Kim

## Core Thesis

Quantum cognition traditionally explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a fundamentally different interpretation:

**Quantum probability is the fixed-spacetime projection of contextual spacetime formation under finite-state requirements.**

## Key Innovation: Requirements-First Framework

The framework begins not with:
- Time
- Space
- Objects
- Probabilities

But with **requirements** such as:
- Finite representational capacity
- Contextual constraints
- State-space limitations

These requirements drive the formation of spacetime structure itself, with quantum probability emerging as a projection of this formation process.

## Mathematical Framework

### Contextual Spacetime Formation

1. **Requirements Space** — Define the finite-state requirements that constrain the system
2. **Contextual Realization** — Requirements drive formation of contextual structure
3. **Fixed-Spacetime Projection** — The observed quantum probability is a projection onto fixed spacetime
4. **Form-Dependent Probability** — Probability distributions depend on the formed structure, not pre-existing space

### Relationship to Standard Quantum Cognition

| Aspect | Standard QC | This Framework |
|--------|-------------|----------------|
| Starting point | Quantum formalism on fixed space | Requirements drive spacetime formation |
| Event structure | Pre-defined | Emergent from requirements |
| Probability | Quantum probability axiom | Projection of contextual formation |
| Contextuality | Built into formalism | Emerges from finite-state constraints |

## Applications

- **Order effects in cognition** — Why question order changes responses
- **Contextuality in decision making** — How context shapes probability judgments
- **Law of total probability violations** — Natural consequence of contextual spacetime
- **AI architecture design** — Requirements-first approach to system design
- **Quantum-classical boundary** — Understanding when quantum vs classical descriptions apply

## Implementation Steps

### Step 1: Identify Requirements
Define the finite-state requirements that constrain the cognitive or computational system:
- Memory limits
- Processing constraints
- Representational capacity

### Step 2: Map Contextual Structure
How do requirements drive the formation of contextual relationships:
- Which states become distinguishable
- Which relationships are privileged
- What structures emerge

### Step 3: Compute Projection
The observed probability distribution is the projection of contextual formation onto the fixed spacetime we measure.

### Step 4: Validate Form-Dependence
Test whether probability distributions change based on the formed structure rather than fixed priors.

## Key Advantages

1. **Foundational clarity** — Starts from first principles (requirements) rather than adopting quantum formalism axiomatically
2. **Explanatory power** — Explains why quantum probability works for cognition (it's a projection of requirement-driven formation)
3. **Design guidance** — Provides a requirements-first methodology for building cognitive architectures
4. **Unification** — Bridges quantum cognition with resource-bounded computation theory

## Activation Keywords

- spacetime formation requirements
- contextual realization probability
- form-dependent probability
- quantum cognition foundations
- requirements-first framework
- finite-state requirements cognition
- contextual spacetime quantum
- order effects quantum cognition
- contextuality decision making

## Related Skills

- **extreme-quantum-cognition**: EQCM architecture for deliberative decision making
- **thermocoherent-cognitive-dynamics**: Physical basis of information flow in neural matter
- **quantum-cognition**: General quantum cognition methodology
- **gskl-quantum-cognition-dynamics**: GKSL master equation for cognitive modeling