Causal Set Theory for Agent-Based Multiverse Knowledge Graph Generation

Abstract

We present a framework for dynamically generating interactive narrative multiverses using Causal Set Theory (CST) as the underlying mathematical structure. Documents become discrete spacetime events, reader choices determine causal relationships, and the emergent large-scale structure forms a coherent narrative universe with genuine relativistic properties.

1. Theoretical Foundation

1.1 Physical-Narrative Correspondence

Core Mapping:

1.2 Causal Structure

Partial Ordering Relation: For documents D₁, D₂ in the narrative multiverse, D₁ ≺ D₂ iff:

Causal Diamonds: Regions of story-space where certain document sequences are mandatory:

1
2
3
4
5

    D_future
   /         \
D_past ≺ D_present ≺ D_consequence
   \         /
    D_branch

2. Dynamic Graph Generation

2.1 Birth Process Dynamics

Document Generation Probability:

1

P(new_doc | causal_context) = f(ρ_local, θ_coherence, E_thematic)

Where:

Accretion Rules:

  1. Causal Completeness: If reader choice creates causal necessity, corresponding document must be generated
  2. Coherence Preservation: New documents minimize narrative stress tensor
  3. Thematic Consistency: Generated content preserves field configuration energy
  4. Temporal Ordering: New documents respect established causal precedence

Reader Choice Mapping:

1
2
3
4
5
6
7
8
9
10
11
12

def process_reader_choice(character_state, dialogue_input, context):
    # Extract causal parameters from roleplay interaction
    causal_vector = extract_causality(character_state, dialogue_input)
    
    # Determine which future documents become accessible
    accessible_futures = causal_cone(current_position, causal_vector)
    
    # Generate new documents if causal necessity requires
    if causal_gap_detected(accessible_futures):
        new_docs = generate_causal_completion(gap_region)
        
    return next_document_set

3. Emergent Spacetime Geometry

3.1 Narrative Manifold Structure

Discrete to Continuous Limit: As document density increases, the causal set approximates a smooth narrative manifold with:

Causal Horizons: Documents beyond the reader’s causal reach:

1

Horizon(reader_position) = {D : no causal path from reader choices to D}

3.2 Lorentz Invariance

Path Independence: The essential narrative structure remains invariant under reader path transformations:

4. Multi-Scale Coherence Dynamics

4.1 Coupled Field Equations

Narrative Lattice Evolution:

1

∂²g_μν/∂τ² = -Γ(∇coherence) - κT_narrative

Thematic Field Dynamics:

1

□φ_theme + V'(φ_theme) = J_reader_choices

Where:

4.2 Cross-Scale Coupling

Microscale → Macroscale:

Macroscale → Microscale:

5. Implementation Architecture

5.1 Agent-Based Generation Engine

Core Components:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30

class NarrativeCST:
    def __init__(self):
        self.causal_graph = CausalSet()
        self.coherence_field = NarrativeCoherence()
        self.thematic_field = ThematicField()
        self.generation_agent = DocumentAgent()
    
    def process_reader_interaction(self, roleplay_input):
        # Update causal structure
        new_links = self.extract_causal_relationships(roleplay_input)
        self.causal_graph.add_edges(new_links)
        
        # Check for causal completeness
        gaps = self.find_causal_gaps()
        
        # Generate necessary documents
        new_documents = []
        for gap in gaps:
            doc = self.generation_agent.create_document(
                causal_context=gap,
                coherence_constraints=self.coherence_field.local_state(gap),
                thematic_requirements=self.thematic_field.local_state(gap)
            )
            new_documents.append(doc)
        
        # Update fields
        self.coherence_field.propagate_changes(new_documents)
        self.thematic_field.evolve(new_documents)
        
        return self.get_accessible_documents(roleplay_input.reader_position)

5.2 Document Type Manifold

Coordinate Charts: Different document types occupy different regions of narrative spacetime:

Transition Functions: Smooth transformations between document types based on reader trajectory:

1
2
3
4
5
6

def document_transition(current_type, reader_vector, causal_context):
    # Calculate optimal document type for new causal position
    coherence_requirements = analyze_narrative_stress(causal_context)
    thematic_needs = analyze_field_configuration(causal_context)
    
    return optimize_document_type(coherence_requirements, thematic_needs)

6. Validation and Consistency

6.1 Causal Consistency Checks

Acyclicity Enforcement:

1
2
3
4
5

def validate_causal_structure(new_links):
    for link in new_links:
        if creates_causal_loop(link):
            return resolve_paradox(link)
    return True

Temporal Ordering: Ensure all generated documents respect established narrative chronology while allowing for multiple consistent interpretations.

6.2 Coherence Metrics

Narrative Stress Tensor:

1

S_μν = ∂²E_narrative/∂g_μν∂g_ρσ

Measures structural inconsistencies in the causal graph.

Thematic Field Energy:

1

E_theme = ∫(½(∇φ)² + V(φ) + φJ_reader)d⁴x

Quantifies philosophical consistency across the multiverse.

7. Emergent Properties

7.1 Narrative Thermodynamics

Entropy Growth:

Information Geometry:

7.2 Phase Transitions

Genre Shifts: Critical points where narrative structure undergoes discontinuous change:

8. Applications and Extensions

8.1 Interactive Storytelling

Personalized Multiverse Generation: Each reader creates their own branch of the causal set, with shared backbone structure but unique experiential paths.

Collaborative World-Building: Multiple readers contribute to same causal structure, creating emergent narrative complexity beyond any individual contribution.

8.2 Educational Applications

Science Communication: Complex scientific concepts naturally emerge through roleplay interactions, with technical documents generated on-demand based on reader curiosity.

Historical Simulation: Causal set structure can model historical events with multiple perspectives and counterfactual branches.

9. Future Directions

9.1 Quantum Extensions

Narrative Superposition: Multiple potential documents exist in superposition until reader choice collapses them into definite states.

Entanglement: Distant parts of the narrative multiverse exhibit quantum correlations through shared thematic coherence.

9.2 Machine Learning Integration

Causal Discovery: Use ML to automatically infer optimal causal structures from reader interaction patterns.

Predictive Generation: Train models to anticipate reader preferences and pre-generate likely narrative branches.

Conclusion

By treating interactive narratives as discrete spacetime manifolds governed by causal set theory, we create genuinely physics-based storytelling systems. The resulting multiverses exhibit emergent complexity, maintain consistency across scales, and provide rich, personalized experiences that evolve through reader interaction.

This framework bridges computational creativity, fundamental physics, and human narrative understanding, suggesting new approaches to both storytelling technology and our understanding of information, causality, and meaning in complex systems.

The story becomes a living universe that readers help optimize through their choices, creating unique contributions to an ever-evolving narrative cosmos.