Five independent measurement series, one fractional deviation band
Measurements made in four laboratories by three independent groups, using four different detection techniques, over intervals from a single solar flare to fifteen years, report fractional deviations that fall in the same narrow band:
The series are unrelated to one another. They measure different isotopes, at different facilities, with different instruments, for different reasons. The shared quantity is the order of magnitude of the deviation, not its sign, its phase, or its period.
| Series | Facility | Interval | Fitted \(\alpha\) | Source |
|---|---|---|---|---|
| \(^{32}\mathrm{Si}\) seasonal | Brookhaven | 1982–1986, four years | \(7.9 \times 10^{-4}\) | Jenkins et al. 2008 |
| \(^{36}\mathrm{Cl}\) seasonal | Brookhaven | 1982–1986, four years | \(6.2 \times 10^{-4}\) | Jenkins et al. 2008 |
| \(^{226}\mathrm{Ra}\) seasonal | PTB, Germany | 1983–1998, fifteen years | \(8.3 \times 10^{-4}\) | Siegert et al. 1998 |
| \(^{54}\mathrm{Mn}\) solar flare transient | Purdue | 13 December 2006, hours | \(\alpha\,A_{\mathrm{flare}} = -2.5 \times 10^{-3}\) | Jenkins & Fischbach 2009 |
| \(^{32}\mathrm{Si}\)/\(^{36}\mathrm{Cl}\) amplitude | Brookhaven | 239 data points | \(7.9(3) \times 10^{-4}\) | Jenkins et al. 2008 |
Fitted coupling \(\alpha\) under the model of the time-gradient field, except where noted. The \(^{54}\mathrm{Mn}\) entry is not a bare \(\alpha\): the source reports the product \(\alpha\,A_{\mathrm{flare}}\), the coupling multiplied by the flare amplitude, and that product is negative. It is listed as published and is not a like-for-like value in the column. The Brookhaven series additionally reports an annual oscillation of \(7.9(3) \times 10^{-4}\) with a 35(2) day phase shift, a correlation of \(r = 0.52\) against \(1/R^2\), and a formal probability of random correlation \(p = 6 \times 10^{-18}\). The \(^{54}\mathrm{Mn}\) transient preceded electromagnetic arrival by 36–40 hours.
The three seasonal fitted couplings span \(6.2 \times 10^{-4}\) to \(8.3 \times 10^{-4}\), a ratio of \(1.34\) across three isotopes and two facilities. The table above lists four seasonal rows, but the fourth repeats the Brookhaven amplitude already given in the first row rather than adding a separate measurement, so there are three distinct seasonal series. The \(^{54}\mathrm{Mn}\) transient \(\alpha\,A_{\mathrm{flare}} = -2.5 \times 10^{-3}\) is a factor of about three larger in magnitude and is not a bare coupling. Across different isotopes, different facilities, and different physical circumstances, the couplings agree to within an order of magnitude.
No isotope-specific parameter was introduced to achieve this. The model form is fixed in advance:
with a single coupling \(\alpha\) per isotope and a field \(G(t)\) of order \(10^{-3}\). The agreement across the four series is therefore a constraint on the model form, not a consequence of fitting freedom in it.
Power-spectrum analysis of the Brookhaven data by Sturrock et al. (2010) reports the annual frequency, a prominent peak at \(11.18\,\text{yr}^{-1}\) (a period of \(32.7\) days, conventionally rounded to the \(33\)-day period) in the solar synodic rotation band, and a running-mean peak at \(11.93\,\text{yr}^{-1}\). The \(12.5\,\text{yr}^{-1}\) frequency cited elsewhere in this body of work is reported by Sturrock, Javorsek, Fischbach, Jenkins, and Lee (arXiv:1301.3754) as a periodicity common to the BNL decay data and Super-Kamiokande solar neutrino data, described there as indicative of the solar radiative zone. The r-mode association in that literature belongs to the Rieger periodicity near \(2.1\,\text{yr}^{-1}\), not to the \(12.5\,\text{yr}^{-1}\) line.
The same band appears in two non-nuclear series, reported in the same corpus:
| Series | Fractional deviation | Basis |
|---|---|---|
| Lunar Mascon residuals | \(10^{-4}\) to \(10^{-3}\) | Residual after standard spherical-harmonic modelling |
| Apollo navigation residuals | \(10^{-4}\) to \(10^{-3}\) | Velocity and guidance residuals on deep-space legs |
This page records an observation: that five independent measurement series report deviations of the same fractional magnitude. It does not claim a mechanism, and it does not present the field interpretation.
Every value above is quoted from published measurements or from the companion papers in this body of work, with the source named in each row. The interpretation of these deviations as a response to a scalar field is developed separately, in the time-gradient field model and its verification papers, and is not required to read this page.
[1] Jenkins, J.H. et al. "Evidence of Correlations between Nuclear Decay Rates and the Earth-Sun Distance." Nuclear Physics A, 807(1–2), 81–101, 2008.
[2] Siegert, H., Schrader, H., and Schötzig, U. "Half-Life Measurements of the Ra-226 Alpha Decay." Applied Radiation and Isotopes, 49(9–11), 1397–1401, 1998.
[3] Jenkins, J.H. and Fischbach, E. "Perturbation of nuclear decay rates during the solar flare of 2006 December 13." Astroparticle Physics, 31(6), 407–411, 2009.
[4] Sturrock, P.A., Buncher, J.B., Fischbach, E., Gruenwald, J.T., Javorsek, D. II, Jenkins, J.H., Lee, R.H., Mattes, J.J., and Newport, J.R. "Power Spectrum Analysis of BNL Decay-Rate Data." Astroparticle Physics, 34, 121–127, 2010.
[5] Sturrock, P.A., Javorsek, D., Fischbach, E., Jenkins, J.H., and Lee, R.H. "The Case for a Solar Influence on Certain Nuclear Decay Rates." arXiv:1301.3754, 2013.
Full derivations, fitted parameters, and verification: Time-Gradient Field Model and Mathematical Verification of the Time-Gradient Field Model.
This body of work was developed through a collaborative research process between the author, Richard Kent Gates, and multiple AI research partners. The author provides full transparency on this process.
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The AI tools functioned as research assistants — analogous to graduate students or technical collaborators who help formalize, compute, and organize ideas that originate from the principal investigator. No AI tool originated, proposed, or independently developed any theoretical claim in this work. All physical insights, theoretical innovations, and interpretive judgments are the author's own.