CHRONO-ARCH — Results & Benchmarks

01 — Phase Transition Detection

All Phase Transitions Detected with Early Warning Signals

Transition Type	EWS Detection	Collapse Threshold	Lead Time	Status
Stable → Critical	Variance ↑ 340%	S(t) ≈ 0.50	~25 years	✓ Early
Critical → Collapse	AC₁ ↑ 180%	S(t) < 0.35	~15 years	✓ Early
Collapse → Recovery	τ_relax ↑ 220%	Post-collapse	~10 years	✓ Detected
Average	—	—	~16.7 years	All ✓

02 — Stability & Resilience Metrics

0.5439

Avg Stability (Stable)

Rigid-Declining trend

0.5252

Avg Stability (Moderate)

Balanced-Resilient

0.5073

Avg Stability (Fragile)

Adaptive-Volatile

+0.3764

Fragile Δ Improvement

Best long-term gain

03 — Perturbation Experiments

0.4973

All systems converged

After noise injection

2 collapses

Fragile system

Adaptive-Volatile recovered in 3y

0 collapses

Stable system

Rigid-Declining declined -0.385

+0.410

Fragile improvement

Despite 6 collapse events

04 — New Taxonomy

Old Name	New Name	Characteristics	Risk Profile
Stable	Rigid-Declining	High initial, negative trend	Low risk, negative reward
Moderate	Balanced-Resilient	Consistent, best baseline	Low risk, moderate reward
Fragile	Adaptive-Volatile	Fast recovery, positive trend	High risk, high reward

The Fragility Paradox: Systems with higher volatility and repeated collapses achieved BETTER long-term outcomes than initially stable systems.

05 — Phase Classification

Phase	Condition	Behavior	Resilience
Phase I — Stable	S(t) ≫ θ_c	Converges to attractor basin	Resilient to moderate shocks
Phase II — Critical	S(t) ≈ θ_c	Sensitivity diverges; EWS rise	Fragile; elevated collapse risk
Phase III — Collapse	S(t) < θ_c	Transition to new attractor	Recovery requires strong shocks