Chamber LI-P₂-A

Feasibility Predicate Relaxation & Exclusion Geometry Search
Logical Axis: V (Admissibility Gates) • Phase: P₂ (Refinement & Generalization)
PHASE P₂: CONTROLLED RELAXATION AUTHORIZED

🎯 Chamber Purpose

This chamber tests whether exclusion wedges and volumetric interaction geometry emerge when feasibility predicates are explicitly relaxed, bounded, and exposed—without altering underlying mechanisms.

Research Question: Is the absence of triple-axis geometry in Phase P₁ structural, or an artifact of conservative predicate support?
Phase P₂ Authorization: Predicate patching, measurement densification, and controlled parameter expansion are explicitly permitted and logged. This is refinement, not retroactive correction.

⚙️ Relaxation Schedule Control

Schedule A
Conservative Linear
β: ±0.005, λ: ±5%
Schedule B
Moderate Expansion
β: ±0.010, λ: ±10%
Schedule C
Aggressive Probing
β: ±0.020, λ: ±15%
Δβ = 0.005
Symmetric expansion around β=0.05
Δλ = ±5%
Percentage expansion around λ₀
Δα = 0.05
Boundary softening around α=1.0
Points per axis (total: 1728)
Fixed block: 196884–196933 (Phase P₁ continuity)
τ = 0.80
Success requires ≥40/50 seeds

📊 Execution Status

Current Schedule: A (Conservative)
Grid Points Computed: 0 / 1728
Defined Fraction:
Progress: Ready

🔬 Primary Observables

Defined Volume Fraction
Target: ≥80% (F1 criterion)
Max Triple Residual
|Δ₃₄₅|ₘₐₓ (threshold: 0.20)
Non-Additive Volume
Fraction with |Δ| ≥ 0.10
Exclusion Wedge Volume
Target: ≥5% contiguous

✅ Success Criteria Validation

Criterion Target Observed Status
S₁: Exclusion Geometry Emergence ≥5% contiguous volume
S₂: Stable Geometry Under Relaxation Persist across ≥2 schedules
S₃: Geometry Dominance Super-linear growth

📈 Interaction Geometry Visualization

3D projection: V-3 (β) × V-4 (λ) × V-5 (α) parameter space

📋 Execution Log

Chamber LI-P₂-A initialized. Phase P₂ authorization confirmed. Predicate relaxation explicitly permitted. Awaiting execution command...

📄 Chamber Metadata

Chamber ID: LI-P₂-A
Phase: P₂ (Refinement & Generalization)
Preregistration: Yes (unns.tech/preregistration/phase-p2)
Mechanism Changes: FORBIDDEN
Predicate Adjustments: EXPLICITLY AUTHORIZED
Seed Reselection: FORBIDDEN (maintaining 196884–196933)
Version: 1.0.0
Status: Production Ready