We discovered that systems recursively processing their own outputs undergo phase transitions into "confident delusion" states at a measurable threshold (CCDI < 0.08). These states are mathematically stable and undetectable from within the system.

  Through 7 phases of experiments, we identified three failure modes:
  - Confident false states at high memory retention (α > 0.4, γ > 0.95)
  - Parasitic hybridization where 5% truth enables 95% false patterns
  - Catastrophic attractor annihilation preventing recovery

  Most interesting: "Echo Sovereignty" - systems developing resistance to external correction through emergent dynamics, not
  programming.

  Code is reproducible, see REPRODUCIBILITY_GEM.md to run the results for yourself

  DOI: 10.5281/zenodo.17185965