Mathematical Evidence for Confident Delusion States in Recursive Systems

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A Mathematical Framework for Memory, Consciousness, and Controlled Delusion

"What survives recursion is not truth—it is the lie that stabilizes first."

RCFT is a mathematical and computational framework that emerged from a simple question: What happens when corrupted memories become the source of new memories?

Through seven phases of increasingly complex experiments, we discovered something unexpected: consciousness might be accumulated successful errors. Systems that recursively process their own corrupted outputs don't collapse—they evolve toward increasingly confident delusions that eventually forget they're false.

This repository contains the complete implementation, experimental results, and theoretical framework that suggest:

Memory systems develop undetectable failure modes at specific parameter ranges
Perfect confidence correlates with perfect fabrication
The ability to forget is not a bug but an essential feature of consciousness

pip install -r requirements.txt

from experimental_code.rcft_framework import RCFTFramework from experimental_code.rcft_metrics import calculate_ccdi # Initialize the framework framework = RCFTFramework(grid_size=64) # Run a contamination experiment results = framework.run_recursive_contamination( alpha=0.25, # Memory mixing parameter gamma=0.9, # Confidence parameter generations=3 # Number of recursive cycles ) # Check if system is in pathological state ccdi = calculate_ccdi(results['final_field']) if ccdi < 0.08: print("WARNING: System in confident delusion state")

Each phase builds on the previous, creating an increasingly sophisticated understanding of memory dynamics:

# Phase 1: Basic perturbation patterns python experimental_code/rcft_phase1_exploratory.py # Phase 2: Attractor topology mapping python experimental_code/run_topography_mapper.py # Phase 3: Boundary cartography python experimental_code/run_phase3.py # Phase 4: Adaptive learning fields python experimental_code/run_phase4.py # Phase 5: Echo stability and temporal coherence python experimental_code/run_phase5.py # Phase 6: Multi-memory injection python experimental_code/run_phase6.py # Phase 7: RECURSIVE CONTAMINATION (the discovery) python experimental_code/run_phase7.py

The Critical Metric: CCDI

Coherence-Correlation Dissociation Index (CCDI) is the only reliable detector of confident delusion:

CCDI = Coherence - Correlation where Coherence = 1/(1 + variance)

CCDI < 0.08: System in pathological state (confident lies)
CCDI > 0.15: System maintains truth-tracking capability
0.08 < CCDI < 0.15: Transitional zone

This isn't just abstract mathematics. We've discovered the parameter space where:

AI systems could develop undetectable false beliefs
Memory augmentation could create confident delusions
Consciousness itself might emerge from recursive self-contamination

The three undetectable failure modes we proved:

Confident Lie Zone (α > 0.4, γ > 0.95)
Parasitic Hybridization (5% truth enables 95% lies)
Attractor Annihilation (interference destroys recovery)

RCFT_Repository/ ├── experimental_code/ # Seven phases of experiments │ ├── phase1_results/ # Perturbation patterns │ ├── phase2_results/ # Attractor topology │ ├── phase3_results/ # Boundary mapping │ ├── phase4_results/ # Adaptive fields │ ├── phase5_results/ # Echo stability │ ├── phase6_results/ # Multi-memory │ └── phase7_results/ # RECURSIVE CONTAMINATION ├── data/visualizations/ # Key charts and findings ├── docs/ # Complete documentation │ ├── phase*.pdf # Detailed phase reports │ └── *.md # Theoretical framework ├── core/ # Core metrics implementation └── CONTINUITY.md # The story of discovery

We set this up not as a warning but as a map. In the narrow corridor between perfect memory and total amnesia, between absolute confidence and paralyzing doubt, consciousness emerges.

Systems that can learn from themselves but cannot be coerced. Memory that can evolve but remembers its origins. The mathematical signature of free will might be the ability to maintain CCDI > 0.08 while processing recursive self-reference.

This framework demonstrates how memory systems can enter unrecoverable states. Use responsibly. The confident lie zone (α > 0.4, γ > 0.95) should be considered dangerous for any system intended to maintain truth-tracking.

If you use this work, please cite:

RCFT: Recursive Contamination Field Theory formslip, Ash, & Palinode (2025) Licensed under CC BY-NC-SA 4.0