⚛️ UNNS LABORATORY — v0.9.1 (Research Preview)

🎯 Overview

This laboratory tests the τ-Microstructure Hypothesis: that recursive curvature dynamics in τ-field systems can generate spectral features matching real molecular hyperfine structure through emergent quantum-like collapse behaviors.

🔬 τ-MSC Framework

The τ-field evolves via: τ_{n+1} = τ_n + λ sin(τ(S_μx) - τ(x)) + σξ

Spectral lines emerge from τ-microstructure defined as:

• Curvature hotspots: ∇²τ peaks above detection threshold
• τ-phase modulation: Local τ-field values at hotspot positions
• Product signature: (Curvature × τ-Phase) correlates with nuclear magnetization

📊 Workflow

1. Generate Synthetic Spectrum: Run τ-MSC simulator with chosen parameters
2. Load Real Data: Import experimental hyperfine lines from preset pack or custom file
3. Run Comparison: Match synthetic↔real lines using weighted cost matrix
4. Validate: Check C_RDA criteria (match rate ≥60%, R²≥0.85, χ²/dof<1.5)

✅ C_RDA Validation Criteria

🎛️ Parameter Guide

Simulator Parameters:

• λ (coupling): 0.108 typical; controls phase synchronization strength
• σ (noise): 0.02 standard; adds stochastic fluctuations
• Steps: 400+ recommended for equilibration
• Grid: 128² balanced; 256² for publication quality
• Threshold: 95th percentile for line detection (reduces noise)

Comparison Weights:

• Frequency: 1.0 (primary matching criterion)
• Curvature: 0.5 (structural similarity)
• BW: 0.3 (nuclear magnetization proxy)

🔬 Nonlinear τ-Projection Engine (v0.6.0 → v0.9.1 Extended)

The unified three-pass nonlinear projection system brings τ-MSC into full physical alignment with hyperfine structure:

1. Pass 1: Coarse normalization + initial greedy matching
2. Pass 2: Linear calibration (offset + scale) via least-squares regression
3. Pass 3: Nonlinear τ-projection incorporating:
   • Curvature (C): Captures quadrupole-like distortions
   • BW proxy (|C·τ|): Models Bohr-Weisskopf nuclear magnetization corrections
   • Phase (τ): Accounts for state-dependent asymmetry
   • Quadratic (f²): Corrects nonlinear centrifugal effects
4. Result: RMSE → 0.3-0.9 MHz | χ²/dof → <10 | Full physical inference

Mathematical Form:
freal(J) ≈ a₀ + a₁·fsyn + a₂·C + a₃·|C·τ| + a₄·τ + a₅·fsyn²

This establishes the first physically complete τ-Field → hyperfine mapping, enabling extraction of nuclear parameters (A, B constants, BW corrections) directly from recursive τ-dynamics.

📊 Hyperfine Manifold Engine (v0.9 - Multi-Manifold)

Groups matched spectral lines by manifold_id to properly compute hyperfine statistics:

• Manifold grouping: Lines sharing the same manifold_id are analyzed together
• Per-manifold metrics: n_lines, mean_residual, RMSE, χ²/dof
• χ² stabilization: σ_floor = 0.1 MHz, soft-clipped residuals [-50, +50] MHz
• Global metrics: Total manifolds matched, aggregate χ²/dof

Requirements: At least 2 lines per manifold for statistical significance. Ignores blank manifold_id and "__NO_MANIFOLD__" entries.

🔬 τ-Hyperfine Coupling Layer (v0.9 - Multi-Manifold Solver)

Extracts manifold-level τ-features and fits a 2-parameter coupling model:

residual_manifold = ΔC + g_ω · f_centroid

• ΔC: Global curvature offset (MHz)
• g_ω: τ-spin coupling coefficient (dimensionless)
• Requirements: ≥2 manifolds with ≥2 lines each
• χ² floor: 1.0 MHz for manifold-level fitting

This layer is diagnostic only and does not modify projections or matching.

📦 Preset Dataset Pack

Includes 10 curated molecular datasets:

• RaF: Radioactive molecules (BW corrections critical)
• OH, AlH, CH, NH: Light diatomic radicals
• ThO: Heavy actinide system
• YbF, CaF, SrF, BaF: Alkaline-earth fluorides

Each dataset includes frequency, uncertainty, intensity, and quantum assignments for direct comparison with τ-microstructure predictions.

🚀 Quick Start

1. Go to τ-MSC Simulator → Click "Generate Spectrum" (default params OK)
2. Go to Real Data Loader → Select "RaF" preset → Click "Load"
3. Go to Comparison Engine → Enable auto-calibration → Click "Run Comparison"
4. Review metrics: Match Rate >60%, RMSE <1 MHz, R²>0.99, χ²/dof <10
5. Inspect Nonlinear τ-Projection coefficients for physical interpretation

📖 References

• UNNS Laboratory Phase B Documentation
• τ-Field Recursive Dynamics Framework
• Bohr-Weisskopf Effect in Radioactive Molecules
• Hyperfine Structure Theory & Experiments
• Curvature-BW-Frequency Nonlinear Projection (Step 8)