Witness-Separability Robustness Under Domain Perturbation
Purpose: Test whether factorization {G1, G2, G3, G4} remains structurally stable under controlled perturbations with identity-preserving witness tracking
Phase: P₃ (Factorization) • Builds on: Chamber LIII (Completeness)
🔧 Critical Fixes in v1.1.0:
Identity-Preserving Retention: Same mechanism pool across baseline and perturbations
Proper Dual-Relaxation Test: Evaluates combined relaxed predicates, not logical OR
Structural vs Parametric Separation: Distinct verdicts for collapse vs sensitivity
Sensitivity Metrics: Added dρ/dε slope and boundary thickness estimates
Surgical Scope: LIV does NOT search for new gates. It tests whether existing channels {G1, G2, G3, G4}
remain independently witness-separable when the SAME mechanism pool is subjected to domain deformation.
This validates factorization robustness through identity-preserving witness tracking.
⚙️ Configuration
P1: Encoding
P2: Operator
P3: Relaxation Geometry
P4: Sampling Distribution
Deformation magnitude
Fixed pool for ID preservation
R1 (ρ_min):
R2 (δ_max):
R3 (u_max):
R4 (μ_max):
ε grid: Comma-separated values for dρ/dε
Initializing...0%
📊 Baseline Witness Analysis
Gate
Witness Count (|W₀ᵢ|)
Baseline Density
Sample Witnesses
📐 Robustness Metrics (Identity-Preserving)
R1: Witness Retention Ratio
ρᵢ(ε) = |Wᵢᵉ| / |W₀ᵢ| where same IDs tracked
Gate
Pert.
ρᵢ
Status
R2: Channel Distinguishability
Oᵢⱼ(ε) = |Wᵢᵉ ∩ Wⱼᵉ| / |Wᵢᵉ|
R3: Dual-Relaxation Interference
uᵢⱼ(ε) = mechanisms viable only when both gates relaxed