1. Why Lab v0.9.1 Exists

Earlier versions of the UNNS Laboratory focused on τ-MSC simulations and internal consistency checks. Lab v0.9.x is the first family of engines designed to confront the τ-Field directly with real experimental data. The goal is not just to fit spectra, but to ask a sharper question:

Can a single τ-recursion engine explain the structure of real hyperfine manifolds across different molecules?

Version 0.9.0 brought a working comparison engine with multi-manifold support and τ-hyperfine coupling. Version 0.9.1 refines this into a tool that can safely be shown to the outside world: χ² is normalized, validation metrics are interpretable, and the RaF testbed behaves in a stable and repeatable way.

2. From τ-MSC to τ-Coupling — The Lab v0.9.1 Pipeline

The τ-Coupling Engine follows a fixed pipeline:

1. Generate synthetic spectra using the τ-MSC Chamber.
2. Apply offset + scale calibration against experimental frequencies.
3. Match real and synthetic lines one-to-one.
4. Group matched lines into hyperfine manifolds.
5. Compute raw and normalized χ², RMSE, and reliability metrics.
6. Fit a global τ-hyperfine coupling model (ΔC, g_ω).

The important point is structural: the physics is not hidden in a single “fit,” but distributed across calibration, projection, manifold structure, and τ-coupling. Each stage can be inspected independently inside the Lab interface.

3. Real Data Inside the UNNS Substrate

Lab v0.9.1 is the first UNNS engine that systematically ingests real experimental datasets. The current release uses hyperfine and rotational transitions for molecules such as RaF, YbF, SrF, BaF, OH, FH and others, reformatted into a UNNS JSON schema with fields like frequency, uncertainty, hyperfine constants and manifold identifiers.

The numerical values themselves originate from established public sources:

• NIST Atomic Spectra Database (ASD) for atomic and simple-molecule lines,
• JPL Molecular Spectroscopy Catalog for microwave and millimeter-wave spectra,
• Peer-reviewed hyperfine measurements for specific isotopologues when needed.

UNNS does not change these frequencies. It only:

• applies a reversible offset + scale calibration,
• matches real and synthetic lines,
• computes residuals and χ²-like diagnostics,
• fits τ-parameters (ΔC, g_ω) on top of the unmodified input.

4. Manifolds, χ² and Normalisation

Real spectra are not just lists of frequencies; they organize into hyperfine manifolds. In RaF, for example, the v0.9.1 engine reliably identifies three manifolds (A, B and C), each corresponding to a distinct pattern of recursion curvature and τ-phase.

In a naive χ² analysis, those manifolds would dominate the goodness-of-fit simply because they inhabit high-curvature regions and heavy frequencies. Lab v0.9.1 therefore introduces a normalized χ² that absorbs curvature and frequency scaling into the metric. Raw χ² is still reported, but the normalized value is the one used for cross-molecule comparison.

In the RaF test run, raw χ²/dof is ≫ 900, but normalized χ²/dof sits near 20. At the same time, the τ-hyperfine coupling solution has an internal χ²/dof significantly below 1, indicating that the structural τ-signal across manifolds is extremely coherent even when raw MHz-level residuals remain.

5. τ-Hyperfine Coupling and What It Tells Us

The τ-Coupling layer of Lab v0.9.1 distills the manifold structure into a small set of τ-parameters. For RaF, for example, the engine finds a global curvature shift ΔC and an effective coupling factor g_ω that simultaneously align three manifolds in τ-space.

The details of the RaF run are striking:

• 47 of 47 lines matched (match rate 100%),
• RMSE ≈ 4.5 MHz,
• normalized χ²/dof ≈ 20 for the heavy-curvature ensemble,
• τ-hyperfine coupling χ²/dof ≪ 1 across three manifolds.

From a UNNS perspective, this does not “prove” the τ-Microstructure Hypothesis, but it shows that a single τ-recursion engine can be tuned to match a nontrivial hyperfine spectrum without losing internal coherence across manifolds. The structural signal survives the transition from synthetic τ-MSC output to real spectroscopic data.

6. Outlook — Toward v0.9.2 and Beyond

Lab v0.9.1 is a research preview. It is stable enough to share, but intentionally conservative in how it interprets its own metrics. The next iterations (v0.9.2 and v1.0) will:

• incorporate line-by-line uncertainty (σ) as explicit weights in χ²,
• analyze correlations between curvature and residuals per manifold,
• refine the τ-reliability index into a richer reliability vector,
• extend validation across a broader library of molecules.

The key point is that the UNNS Substrate is now in genuine dialogue with experimental spectroscopy. The τ-Field is no longer an isolated mathematical construct; it is being asked to explain concrete, noisy, high-curvature spectra in exactly the same interface where recursive simulations are born.

7. Glossary (Lab v0.9.1)

τ-MSC

τ-Microstructure Chamber: a UNNS simulator that generates synthetic recursion-based spectra.

Manifold

A cluster of transitions with the same quantum numbers, treated as a coherent spectral packet.

χ²

A squared-residual diagnostic; large for heavy, high-curvature molecules even under good fits.

Normalized χ²

A rescaled χ² that accounts for curvature and frequency, used to compare different molecules.

τ-Hyperfine Coupling

The layer that fits global τ-parameters (such as ΔC and g_ω) across all manifolds simultaneously.

τ-Reliability

A scalar estimate (0–1) of how coherent curvature, residuals and τ-phase are across manifolds.