⚛️ UNNS LABORATORY — v0.9.2 (Research Preview)

Real Data Assimilation Layer — σ-Weighted Quality Analysis
v0.9.2 • σ-Weighted + Reliability Scoring
🔬 τ-MSC Simulator
📁 Real Data Loader
🔍 Comparison Engine
📖 Laboratory Guide
Synthetic Spectrum Generator (τ-MSC)
Visualization
τ-Field Evolution
Curvature (∇²τ)
Generated Lines (τ-Microstructure)
Lines Detected
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Freq Range (MHz)
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Avg Curvature
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Status
Ready
# Frequency (MHz) Curvature τ-Phase Product (C×τ)
Dataset Selection
📦 Preset Datasets Available
Select from 10+ curated molecular hyperfine datasets, or upload your own JSON/CSV files.

Or Upload Custom Data

📂
Drag & drop JSON/CSV file here, or click to browse
Loaded Dataset
Molecule
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Lines Loaded
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Freq Range (MHz)
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Uncertainty
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# Frequency (MHz) Uncertainty (MHz) Intensity Assignment
Comparison Configuration
(pending)
(groups lines by manifold_id)
(requires manifold mode)
Nonlinear τ-Projection: (not yet computed)
Validation Metrics (C_RDA)
Match Rate
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RMSE (MHz)
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Correlation (R²)
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χ²/dof
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Mean Error (MHz)
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Max Error (MHz)
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Manifolds Matched
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χ²/dof (Normalized)
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χ²/dof (σ-Weighted)
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Fit Quality (v0.9.2 σ-Weighted + Reliability)
τ-Reliability (v2): —
Outliers (|Δf| > 20 MHz): —
Expected Outliers (ΣP): —
Weighted χ²/dof: —
Matched Pairs
# Real Freq (MHz) Synth Freq (MHz) Residual (MHz) Curvature τ-Phase
Laboratory Guide — UNNS Lab v0.9.2

v0.9.2 Architecture Overview

UNNS Laboratory v0.9.2 — Real Data Assimilation Pipeline τ-MSA Simulator Curvature Field τ-Phase Hotspot Detection Real Data Loader Spectral Lines Uncertainties (σ) Manifold IDs Nonlinear τ-Projection Engine (v0.9.1) f_real ≈ a₀ + a₁·f_syn + a₂·C + a₃·|C·τ| + a₄·τ + a₅·f_syn² 3-Pass: Normalization → Calibration → Projection → Matched Pairs (frequency aligned) Hyperfine Manifold Engine (v0.9) Groups by manifold_id → Per-manifold statistics χ² Normalization Layer (v0.9.1): curv_scale × freq_scale 🆕 Quality Metrics Layer (v0.9.2) σ-Weighted χ² w_i = 1/(σ_i²+ε) Adaptive weights Coherence κ |Corr(|C|, |Δf|)| Fit diagnostic Reliability R, τ_R R = exp(-κ·χ²/20) Manifold quality Output: Triple χ² + κ + R + Expected Outliers Per-manifold: {χ²_norm, χ²_weighted, κ, R} Output Metrics C_RDA Validation: ✓ Match Rate ≥ 60% ✓ RMSE < 10 MHz ✓ R² ≥ 0.85 ✓ χ²/dof < 1.5 χ² Metrics (Triple Display): • χ²/dof (Raw) — unscaled • χ²/dof (Norm) — τ-field scaled • χ²/dof (σ-W) — uncertainty weighted v0.9.2 Quality Metrics: • κ (Coherence): 0-1 scale • R (Per-manifold): 0-1 reliability • τ_R (Unified): mean(R_manifold) • ΣP: Expected outlier count τ-Hyperfine Coupling: • ΔC (MHz) — curvature offset • g_ω — τ-spin coupling Export: JSON bundle v0.9.2-R2

🎯 Overview

The UNNS Laboratory v0.9.2 provides a complete pipeline for validating the τ-Microstructure Hypothesis using real molecular spectral data. The system integrates: nonlinear τ-projection (v0.9.1), multi-manifold hyperfine analysis (v0.9), and the new v0.9.2 Quality Metrics Layer featuring σ-weighted χ², curvature–residual coherence, and τ-Reliability v2.

📝 Change Log (v0.9.2 Research Preview)

  • Added Quality Metrics Layer: σ-weighted χ², κ-coherence, R reliability, unified τR, expected-outlier stats.
  • Modernized τ-MSA Framework: replaced legacy τ-MSC terminology with invariant-based τ-field descriptors.
  • Updated Workflow: clarified projection → manifold → quality → coupling sequence.
  • Refined Projection Model: consolidated six-term nonlinear τ-projection.
  • Improved Hyperfine Integration: clarified ΔC & gω manifold centroid solver behavior.
  • Guide Reorganization: reordered sections to match real v0.9.2 architecture.
  • Research Preview Notice: marked v0.9.2 as provisional pending extended molecule validation.

🔬 τ-MSA Framework (Modernized)

The τ-Microstructure Spectral Analysis (τ-MSA) pipeline replaces the older τ-MSC simulator language. τ-MSA treats τ as a recursive geometric field with curvature, phase, and mixed invariants that project into spectroscopic structure.

  • Curvature (C): second-order τ-geometry; correlates with hyperfine splittings
  • τ-phase: local recursive phase defining manifold-level offsets
  • Curvature × Phase: mixed invariant mapping to BW-like magnetization effects

These invariants feed into the unified nonlinear projection model and form the basis of cross-manifold τ-coupling.

📊 Workflow (Updated)

  1. Load Real Data: Choose a preset molecule or upload a custom dataset.
  2. Run Projection: Apply v0.9.1 nonlinear τ-projection to align synthetic/real lines.
  3. Manifold Grouping: Cluster matched lines into hyperfine manifolds.
  4. Compute Quality Metrics: Raw χ², normalized χ², σ-weighted χ², κ, R, τR.
  5. Hyperfine Analysis: Solve ΔC and gω via the multi-manifold coupling layer.

✅ C_RDA Validation Criteria (Unchanged)

The classical C_RDA metrics are preserved for backward compatibility.

CriterionTargetMeaning
C_RDA1: Match Rate≥ 60%Overlap of real/synthetic structure
C_RDA2: RMSE< 10 MHzSpectral alignment accuracy
C_RDA3: R²≥ 0.85Global linear agreement
C_RDA4: χ²/dof< 1.5Classical statistical fit quality

🎛️ Parameter Guide (Modernized)

Projection Parameters:

  • Scale (a): Linear projection slope
  • Offset (b): Calibration intercept
  • τ-Invariants: C, τ, |C·τ|, f² contributions
  • Detection Threshold: Controls hotspot extraction

Comparison Weights (fixed):

  • Frequency: 1.0
  • Curvature: 0.5
  • BW proxy: 0.3

🔬 Nonlinear τ-Projection Engine (v0.9.1)

The projection engine aligns synthetic τ-field features with real hyperfine spectra using a six-term nonlinear model:

f_real ≈ a₀ + a₁ f_syn + a₂ C + a₃|C·τ| + a₄ τ + a₅ f_syn²

This is the foundation for manifold-level analysis and higher-order coupling.

📈 Quality Metrics Overview (v0.9.2)

v0.9.2 introduces a modern three-layer evaluation system: structural adequacy, experimental precision, and τ-geometry reliability. These metrics are independent and should never be mixed.

  • χ²/dof (Raw): unscaled mismatch
  • χ²/dof (Normalized): τ-field structural accuracy
  • χ²/dof (σ-Weighted): dataset uncertainty consistency
  • κ: curvature–residual coherence
  • R: manifold reliability
  • τR: unified τ-reliability
  • ΣP: expected outliers

Quality Metrics Overview (v0.9.2)

Structural Adequacy σ-Weighted Analysis τ-Reliability v2

The v0.9.2 Laboratory layer evaluates each comparison through three independent lenses:
(1) structural adequacy of the τ-field model,
(2) experimental precision of the dataset, and
(3) reliability and coherence of the τ-geometry across manifolds. Keeping these tiers separate is crucial: the substrate must be judged on its geometry, while the data are judged on their uncertainties.

1. Structural Adequacy Metrics

Structural metrics answer: “How well does the τ-field microstructure explain the real spectroscopic pattern?” They depend only on deterministic outputs of the τ-projection engine and never on per-line uncertainties σ.

Match Rate
Fraction of real lines with a matched synthetic partner within the configured threshold. High match rate is a necessary precondition for any meaningful analysis.
RMSE (MHz)
Root-mean-square error of residuals Δf = freal − fsynth. Global measure of projection accuracy in MHz.
Correlation (R²)
Coefficient of determination between real and synthetic frequencies after calibration. Values near 1.0 indicate that the non-linear τ-projection is tracking the overall frequency ladder correctly.
χ²/dof (Raw)
Direct chi-square value per degree of freedom. This magnitude is not bounded and is reported only for transparency; it is not used in reliability scoring.
χ²/dof (Normalized)
v0.9.1 normalization of chi-square. This is the core measure of model–microstructure mismatch, independent of σ. It is the χ² used inside the reliability formula.

2. Experimental Precision Metrics

Experimental metrics answer: “How well does the dataset agree with its own stated uncertainties?” They are σ-aware and intentionally decoupled from structural reliability.

χ²/dof (σ-Weighted)
Uses per-line uncertainties σ to weight each residual. Lines with small σ carry more influence. Large values typically indicate that uncertainties are very tight or underestimated; they do not automatically imply a bad τ-field model.
Expected Outliers (ΣP)
Probabilistic outlier count derived from Pi = 1 − exp(−(|Δfi| / 20)²). The sum over all lines gives the expected number of statistical outliers and can be compared with the actual outlier count as a consistency check.

3. Reliability Metrics (τ-Geometry Coherence)

Reliability metrics answer: “Is the τ-field solution structurally coherent across manifolds?” They are designed to be insensitive to σ and focus solely on τ-geometry.

Curvature–Residual Coherence (κ)
For each manifold, κ is the correlation between |curvature| and |Δf|. Values near 1 indicate that high curvature systematically produces larger residuals, signalling underfitting in that region of the τ-field.
Manifold Reliability R
Each manifold receives a reliability score R = exp(−κ · (χ²norm / 20)). High κ and large normalized χ² jointly suppress R. This 0–1 scale measures the structural stability of the τ-geometry in that manifold, independent of uncertainties σ.
Unified τ-Reliability (v2)
The global reliability τR is the mean of manifold reliabilities. It summarizes how coherent the τ-field solution is across all manifolds. High τR indicates a structurally stable τ-geometry; low τR flags tension between manifolds.

4. Separation of Roles: χ²_norm vs χ² (σ-Weighted)

Key principle.
Reliability uses χ²norm, not σ-weighted χ². χ²norm measures how well the τ-field geometry fits the microstructure. σ-weighted χ² measures how strongly the dataset punishes deviations relative to its declared uncertainties. Mixing them would make reliability depend on instrument sensitivity rather than τ-geometry.

5. Metric Summary

Metric Primary Role Uses σ? Feeds Reliability?
Match Rate Matching performance No No
RMSE Global frequency error No No
χ²/dof (Raw) Unscaled mismatch No No
χ²/dof (Normalized) Structural adequacy of τ-field No Yes
χ²/dof (σ-Weighted) Dataset precision and σ-consistency Yes No
κ Curvature–residual coupling No Yes
R Per-manifold τ-geometry reliability No Yes
τR (Unified Reliability) Global τ-field coherence No Yes
Expected Outliers (ΣP) Statistical consistency check Yes No

📊 Hyperfine Manifold Engine (v0.9)

Groups matched lines by manifold_id and computes statistics per manifold, including normalized χ², curvature correlation, and manifold-level residual patterns.

🔬 τ-Hyperfine Coupling Layer (v0.9.2)

Applies a two-parameter linear fit to manifold centroids:

residual_manifold = ΔC + g_ω · f_centroid

Outputs ΔC (curvature offset) and gω (τ-spin coupling coefficient).

📦 Preset Dataset Pack

Includes curated fluoride systems (CaF, SrF, BaF, YbF) and heavy molecules used for τ-field validation.

🚀 Quick Start

  1. Load a dataset (e.g., BaF)
  2. Run nonlinear projection
  3. Review manifold metrics
  4. Check τ-Reliability
  5. Interpret ΔC and g_ω

📖 References

  • UNNS Recursive Field Framework
  • τ-Microstructure Analysis Protocol
  • Hyperfine Structure Theory

✅ Version 0.9.2-R2 Status

Production Ready • σ-Weighted quality analysis active • Triple χ² display (Raw/Normalized/σ-Weighted) • Curvature-residual coherence (κ) • Manifold reliability scoring (R) • Unified τ-Reliability v2 • Outlier probability estimation • Per-manifold advanced metrics • Full backward compatibility with v0.9.1 • Export includes all quality metrics • Ready for publication-grade spectroscopic analysis

Real Data Notice: Frequency tables used in this UNNS Laboratory run originate from established public spectroscopy sources (e.g. NIST Atomic Spectra Database, JPL Spectral Catalog and peer-reviewed hyperfine measurements). Values are reformatted into the UNNS JSON standard but are not altered beyond the calibration and χ²/τ-projection procedures described in the Laboratory Guide.