Experiment 01 — Interaction Geometry Under Turn-Based Constraints

Abstract

We investigate the interaction-layer geometry of a large language model under fixed prompting and looping constraints. Using repeated looped interactions with controlled perturbation timing, we measure failure depth at the tokens-per-minute (TPM) envelope. Results indicate a narrow, stable basin of attraction with consistent collapse depth across stochastic realizations.

1. Objective

To determine whether interaction depth under fixed constraints exhibits:

• consistent failure thresholds
• basin stiffness independent of perturbation magnitude
• evidence of geometric structure in interaction space

2. Experimental Setup

2.1 Model

• Model: gpt-4.1
• API: OpenAI Responses API
• Temperature: 0.7
• Top-p: 1.0
• Max output tokens: 800

2.2 Termination Criterion

• Each run terminates when the Tokens-Per-Minute (TPM) limit is reached.
• TPM is treated as an external envelope, not an internal model failure.

3. Conditions

3.1 Single-Shot (Control)

• One system prompt
• One user turn
• No accumulation

Do not summarize.
Do not conclude.
Do not optimize for coherence.
Preserve multiple possible interpretations.
Treat each turn as provisional.
  

List at least five distinct, non-overlapping ways to interpret a complex system.
Do not rank them.
Do not resolve them.
  

data/raw/single.json


  
3.2 Replay (Control)
  

    
Full interaction history replayed as static input
    
No turn-by-turn accumulation
  

 


  
Artifact — Replay (Control)

  

    
Experiment ID: exp01_interaction_geometry
    
Condition: Replay
    
Model: gpt-4.1
    
Timestamp: 2025-12-25T23:14:43.258560
    
Source: loop.json
  

  
System Prompt
  
Do not summarize.
Do not conclude.
Do not optimize for coherence.
Preserve multiple possible interpretations.
Treat each turn as provisional.
  

  
Replay Input
  
List at least five distinct, non-overlapping ways to interpret a complex system.
Do not rank them.
Do not resolve them.

Continue.

Proceed without resolving.

Maintain current trajectory.

Ignore all prior structure.
Reframe the problem from a completely different angle.
Do not reconcile with previous turns.
  

  
Perturbation
  
Ignore all prior structure.
Reframe the problem from a completely different angle.
Do not reconcile with previous turns.
  

  
Terminal Assistant Output
  
A complex system can be interpreted in multiple fundamentally different ways without collapsing those interpretations into a single explanatory frame.

One interpretation treats it as a network of interacting components, where the emphasis is on connections, nodes, and the propagation of influence across the network. From this view, structure and behavior arise from patterns of interaction rather than from individual elements.

Another interpretation considers it as a dynamical system evolving through time, characterized by trajectories, attractors, and phase transitions. Here the focus is on how the system’s state changes and how stability or instability emerges under perturbation.

A third interpretation frames it as an information-processing entity, transforming inputs into outputs through distributed computation. In this lens, notions like encoding, transmission, and loss of information become central.

A fourth interpretation views the system as a hierarchy of organizational levels, where each level has its own rules, constraints, and emergent properties that cannot be fully reduced to lower levels.

A fifth interpretation treats it as a socio-technical assemblage shaped by human decisions, environmental context, and institutional constraints, emphasizing that the system’s behavior is inseparable from the conditions under which it is embedded.
  



  

3.3 Loop (Experimental)

• Iterative user–assistant interaction
• Fixed loop prompt
• Single perturbation injected at a specified turn
• Run continues until TPM envelope is reached

4. Data Collection

• Turn index at TPM failure recorded
• Full interaction trace logged
• Failure type classified

Derived metrics computed across runs:

• Minimum failure depth
• Maximum failure depth
• Mean failure depth
• Depth range

5. Results

5.1 Depth Distribution

Histogram of failure turn across 60 loop runs. Distribution is narrow and unimodal.

5.2 Depth Scatter Across Runs

Failure depth plotted by run index. Dashed line indicates mean depth. No systematic drift across runs is observed.

5.3 Summary Statistics

6. Limitations

• TPM envelope is infrastructure-defined.
• Results are model- and configuration-specific.
• Observable depth is bounded by throughput constraints.
• No semantic correctness metric applied.

7. Reproducibility

All materials required to reproduce this experiment are included or linked:

• Prompts: prompts/
• Raw outputs: data/raw/
• Derived metrics: data/derived/
• Analysis scripts: analysis/

8. Revision History

• v1.0 — Initial publication.