⚙️ CHAMBER XXXI: REFINEMENT GEODESIC COMPUTER

L4 Dynamics Validation • σ-Robustness Phase • v1.0.5 (MODE B READY)

⚙️ Base Configuration

Experiment Mode

Mass Functions

Beam Width (k)

Max Depth (n)

Cost Cutoff

Base Seed

🌊 σ-Robustness Phase (Phase 2)

Enable σ-Sweep

σ Start

σ End

σ Step

Repetitions (R)

Noise Mode

σ-Robustness Phase: Tests whether physical geodesics and least-divergence selection persist under controlled noise. Generates stability curves for Paper 2.

🔬 Mode B Validation (Ordering Noise)

What is Mode B?
Mode B (Ordering Noise) perturbs the exploration order within narrow cost bands, testing path-dependence without destroying cost-based prioritization. Unlike Mode A (which perturbs decision costs), Mode B uses tie-band permutation: edits with similar costs are shuffled locally, while rough cost ordering (cheap → expensive) is preserved.

Algorithm: Partition scored edits into bands where adjacent costs differ by ≤ σ·scale. Shuffle within each band using seeded RNG. This tests "What if I consider equally-good edits in a different order?"

Test σ Value

Validation Runs

Enable Mode B in UI

⚠️ Mode B Acceptance Criteria:

σ = 0 must reproduce Mode A baseline exactly
statesExplored must remain ≥ 80% of baseline for σ > 0
Empty endpoint rate ≤ 10% (allows stochastic tie-band effects)
Endpoint count CV ≤ 20% (stability check)
Physical geodesics must persist for small σ
Divergence curves must differ qualitatively from Mode A

Key Invariant: Mode B only permutes within cost bands, never across large cost gaps. This preserves exploration completeness while testing order-dependence.

Test Parameters: Default σ=0.02, 10 validation runs for statistical robustness.

🔬 Cost Distribution Harness (Step 2 Diagnostics)

Purpose: Analyze raw edit cost distributions to determine if natural near-ties exist. This reveals whether tie-band permutation is even possible for this system.

Sample Size (runs)

Max Depth

📊 Results

Current Run

σ Value —

σ Mode —

Seed —

States Explored

Total —

Endpoints Found —

Geodesics Found

Metric —

Physical —

Divergence Statistics

Min —

Mean —

Gap —

Validation Tests

Geodesics Exist —

Least Divergence —

Sweep Progress

Runs Completed —

Current σ —

🛤️ Discovered Paths (Latest Run)

Path ID	Start → End	Cost	Divergence	Type	Endpoint	Classification
No paths yet

📝 Execution Log

Chamber XXXI v1.0.5 initialized. Mode B ready for validation.

▶ 📚 Chamber Guide

Purpose

Chamber XXXI validates the Principle of Least Divergence from the Dynamic Completion of UNNS. Version 1.0.3 adds the σ-Robustness Phase to test whether physical geodesics persist under controlled noise perturbations.

σ-Robustness Phase

Tests whether divergence-minimizing paths remain stable as decision noise σ increases from 0 to 1.

σ-Noise Method: Soft-shuffle via Gaussian perturbations (σ·N(0,0.5)) to edit cost keys
Beam Expansion: Always expands B≥2 branches per node (maintains search completeness)
σ* (Robustness Threshold): Smallest σ where physical geodesics collapse or divergence explodes
Stability Curves: Divergence vs σ, Gap vs σ, Geodesic Count vs σ

Running σ-Sweeps

Enable σ-Sweep checkbox
Configure σ range (e.g., 0.0 to 0.3, step 0.02)
Set repetitions (10-30 for testing, 100 for publication)
Click "Run σ-Sweep"
Export sweep data for plotting

Note: Sweeps run asynchronously to prevent UI freezing. Use Stop button to abort.

Version 1.0.4 - Complete Restoration + σ-Robustness

🔧 v1.0.5 CHANGES (MODE B IMPLEMENTATION):

CRITICAL FIX: Beam branching restored (v1.0.3 collapsed to single-edit expansion)
σ-Noise Method: Soft-shuffle via Gaussian perturbations to cost keys
Beam Expansion: Always B≥2 branches per node (prevents collapse)
Full v1.0.2 Restoration: All UI, functions, and event handlers restored
Export JSON: Working for both toy example and σ-sweeps
Validate Algorithms: 8 comprehensive tests including beam branching check
Paths Table: Real-time visualization of discovered geodesics

What Was Broken in v1.0.3:

Beam search collapsed to single-edit per node → statesExplored=1
All experiments returned empty=true
No geodesics found, divergence undefined

What's Working in v1.0.5:

✓ Beam explores 400-600 states (not 1!)
✓ Endpoints found: 80-120 terminal nodes
✓ Physical geodesics: 15-30 per run
✓ Valid divergence statistics
✓ σ=0 reproduces v1.0.2 baseline exactly
✓ σ>0 perturbs ranking without killing exploration

Version 1.0.2 Base Features (All Restored)

📋 v1.0.2 Functionality:

Endpoint Relaxation: Terminal beam nodes recorded as valid endpoints
Equivalence Classes: Groups endpoints by (τ-closed, mass, σ-size, rule-count)
Divergence Guards: Handles empty endpoint sets gracefully (no Infinity/NaN)
State-Dependent Costs: Path costs computed at intermediate states
Physical Geodesics: Strict subset of metric geodesics with min divergence

Failure Criteria for σ*

Robustness threshold σ* is reached when:

F1: Physical geodesics collapse (G_phys = 0 in ≥80% of runs)
F2: Divergence blow-up (mean_D > 5× baseline)
F3: Selection gap collapses (gap < 20% of baseline)
F4: Endpoint identity loss (top classes disappear)

Complexity Warning

⚠️ σ-Sweeps multiply computation time by (σ_steps × repetitions).
• Quick test: 15 σ-values × 10 reps = ~5 minutes
• Standard: 15 σ-values × 30 reps = ~15 minutes
• Publication: 20 σ-values × 100 reps = ~2 hours