Bin-Stable Log-Periodic Structure in Public NIST Atomic Line List

Bin-Stable Log-Periodic Structure in Public NIST Atomic Line Lists
Authors/Creators
Reyes, Richard J. (Researcher)

Description
Bin-Stable Log-Periodic Structure in Public NIST Atomic Line Lists
Richard J. Reyes - Original Release: May 28, 2026

GitHub: https://github.com/rickyjreyes/NIST

Description
This record presents an independent reproducible line-density analysis of public NIST Atomic Spectra Database line-list exports. The study tests whether atomic transition line lists contain stable log-periodic structure when represented in logarithmic wavenumber coordinates. The analysis is not a flux-spectrum measurement and is not endorsed or certified by NIST; NIST is used only as the public data source.

The tested coordinate is:

$$\ell =\ln (\sigma )$$

where:

• $\sigma$ - wavenumber in cm⁻¹
• $\ell$ - logarithmic wavenumber coordinate

For each line list, wavenumbers are cleaned, optionally filtered by ionization stage, transformed into $\ell$, binned, and compared against a Gaussian-smoothed baseline using a one-mode Poisson log-linear harmonic model.

The tested residual form is:

$$\Delta (\ell )\sim A\cos (k\ell +\varphi )$$

where:

• $A$ - bounded residual amplitude
• $k$ - log-frequency
• $\varphi$ - phase offset
• $\ell$ - logarithmic wavenumber coordinate

The primary canonical result is reported for Fe II. After cleaning and duplicate removal, the canonical Fe II run contains:

NFeII=9447N_{\mathrm{FeII}} = 9447NFeII=9447

unique usable lines.

Across histogram bin counts:

$$B\in \{120,160,200\}$$

Fe II yields the same best log-frequency:

k⋆=31.3265306122449k_\star = 31.3265306122449k⋆=31.3265306122449

with active-domain winding:

n⋆≈10.7n_\star \approx 10.7n⋆≈10.7

and zero null exceedances in 5000 parametric bootstrap draws for each bin setting.

A companion neighbor-ion batch analysis is included for Ni II, Co II, Cr II, Mn II, and Ti II. Among these neighboring ions, Co II is the only species that qualitatively reproduces the Fe II signature, showing bin-stable structure near:

k⋆≈30.24k_\star \approx 30.24k⋆≈30.24

with winding:

n⋆≈10.95–10.98n_\star \approx 10.95\text{–}10.98n⋆≈10.95–10.98

and zero null exceedances across the displayed bin counts.

Ni II is statistically marginal because of its smaller line count. Cr II, Mn II, and Ti II do not maintain bin-stable k⋆k_\stark⋆ at the displayed precision.

The result supports a reproducible log-periodic regularity in logarithmic atomic line-density space, especially in Fe II and secondarily in Co II. The claim is intentionally narrow: this is a bin-stability observation in public atomic line-list data, not a proof of a physical mechanism. The record separates the promoted Fe II verdict-bearing result from exploratory neighboring-ion scans and identifies baseline-sensitivity audits as a remaining validation step.

Input Data

Input data are public CSV exports from the NIST Atomic Spectra Database line-list interface.

Primary source:

NIST ASD Lines Form
https://physics.nist.gov/PhysRefData/ASD/lines_form.html

The analysis uses exported atomic transition line lists, including Fe II and neighboring transition-metal ions. Wavenumbers are parsed from the NIST exports; if direct wavenumber values are absent, wavelength values in nm may be converted by:

σi=107λi\sigma_i = \frac{10^7}{\lambda_i}σi=λi107

with λi\lambda_iλi in nm and σi\sigma_iσi in cm⁻¹.

Keywords
NIST Atomic Spectra Database; atomic spectra; atomic line lists; Fe II; Co II; transition metals; wavenumber; logarithmic wavenumber; log-periodic residuals; log-periodicity; discrete scale invariance; line-density analysis; Poisson likelihood; Poisson log-linear model; parametric bootstrap; bin stability; active-domain winding; spectral residuals; Gaussian-smoothed baseline; Wave Confinement Theory; WCT; reproducible data analysis; public scientific data

Author & Contact
Author: Richard J. Reyes
ORCID iD: 0009-0005-5975-8718
Email: reyes.ricky30@gmail.com