Re-evaluation and discussion of possible correlation between

Solar Proton Density and Seismic Activity with help from

my AI friends, Gemini (Google AI) and Grok 3.0 (by xAi)

Author: Gordon Wayne Watts, A.S. United Electronics Institute, Valedictorian

B.S. The Florida State University, Biological & Chemical Sciences, Double major with honours

Cite: https://GordonWatts.com/education/ or https://GordonWayneWatts.com/education/

First published: Monday, 19 May 2025 (The Register) https://GordonWatts.com / https://GordonWayneWatts.com

National Director, CONTRACT WITH AMERICA: PART II® https://ContractWithAmerica2.com

Link 1: https://GordonWatts.com/ProtonDensity-vs-SeismicActiviy.pdf (Pub.05-19-2025)

Link 2: https://GordonWayneWatts.com/ProtonDensity-vs-SeismicActiviy.pdf (Version 1.0)

Abstract: There has been much discussion in the scientific literature about potential correlation between solar weather and seismic activity, most especially the seminal paper by Marchitelli et al., 2020 (e.g., Marchitelli, V., Harabaglia, P., Troise, C. et al. On the correlation between solar activity and large earthquakes worldwide. Sci Rep 10, 11495 (2020). https://doi.org/10.1038/s41598-020-67860-3). Although the USGS, and the scientific community at large, have not supported the theory of such a correlation, research and discussion is ongoing on this controversial topic. While X-class flares have been mentioned in connection with a possible effect on seismic activity, anecdotal mention of solar proton density appears – at least to this undersigned researcher – to show a stronger promise of possible correlation to seismic activity than solar flares: this researcher recalls recent discussion of that, and the Marchitelli paper focuses on “20 years of proton density and velocity data, as recorded by the SOHO satellite” (brief quote from abstract), so, in beginning our analysis, this researcher decided to pull raw data for solar photon density and USGS earthquake datasets and do a more comprehensive and robust statistical analysis de novo – afresh and anew. The results – in short – show that, while individual analyses seem to usually find no statistically-significant correlation, except in rare cases where I suspect Gemini got suspiciously low p-Values due to math errors – nonetheless, the meta-analysis of individual – mostly independent – analyses seems to find a weak, but persistent, pattern of >= 1.0 Odds ratios and positive R-values – which is very unlikely by chance. Thus, while there are certainly much greater factors elsewhere (inferred from very low R-values) and not much effect on the seismic activity – if at all (inferred from the close-to-one Odds Ratios), nonetheless, there may be a super weak – but statistically-significant – correlation that lies “just under the surface” of an individual analysis – implying the need for “further research.” Whatever effects solar proton density may (or may not) have on telluric seismic activity, the effect (if any) is very small, and generally not of scientific significance. However, the meta-analysis method employed here may prove useful for other researchers who are seeking to find a pattern that lies “just beneath” traditional statistical analysis inquiry. In this context, several theories have been bandied about as to a possible cause-and-effect relationship, chiefly the reverse piezoelectric effect where Maxwell currents induced by photons – either directly in telluric ground near fault lines, or indirectly, via disturbance of the geomagnetic field which would could, in turn, induce currents as it fluctuates. Also, the Schumann Resonance effect from inductive and capacities properties of telluric material, has been discussed in this context. But these details are beyond the limited scope of this paper, and such matters, as to a possible mechanism of “cause and effect,” are left for other researchers to study – again – implying the need for “further research” on these controversial and unsettled areas of space weather, earth science, and meta-analysis of individual analyses.

Summary and Introduction: Can solar weather (solar super storms, solar flares, coronal mass ejections, and solar particles – like photons, protons, electrons, Magnetic field, Solar Plasma, and EMF pulses) influence earthquake activity? The effect –if it exists– is quite small, so looking at large datasets over time from several different angles might provide clues. “Correlation” between 2 events doesn't necessarily mean “causation.” For example, umbrella use has been correlated with rain, so can we assume that “umbrellas cause rain?” (Hint: consider perhaps rain causes umbrella use to sharply increase!) Or: High rainfall in north Tampa has been correlated with high rainfall in south Tampa, so can we assume one causes another? (Hint: there may be a 'common cause' – namely clouds!) It's well known that seismic activity can be caused by many factors: movement of tectonic plates near fault lines, drilling for oil, injection of fluids near fault lines, volcanic activity, land mine explosions, landslides, nuclear testing, even collapse of underground structures. But can solar weather be a factor? Solar proton density can result from X-class flares, but CME's can also play a role. So, if there's any correlation between proton density and seismic activity, then any possible affect that X-flares might theoretically have would, necessarily, be attenuated because the relationship between solar flares and proton density is not a “direct 1-for-1” relationship. While some of the research claims to have applied statistical analyses, other papers mention only several incidents, which are anecdotal, and not a solid foundation for any sort of statistical analyses. This task is, necessarily, computationally intensive, thus AI was employed to do the heavy lifting. This researcher recalls asking META AI to run basic statistical tests, which found a strong correlation between flares & earthquakes, but upon attempts to rerun the analyses, META AI stated that he (it) was unable to scrape the necessary websites (USGA, NOAA, etc.) for the raw data. ChatGPT and ClaudeAI also both looked promising, but they had file upload limits on their free versions, as did Grok 3.0, (by xAi). Gemini (Google AI) gave very promising preliminary results, but these looked “too good to be true,” so this researcher paid a small fee and upgraded to “Premium” in X (Twitter), and was able to access stronger query, upload, and analysis capability of Grok 3.0 (by xAi) to get a “doctor's 2ND opinion” of GEMINI (Google AI), which proved very useful in sussing out analysis errors—made, in fact, by both AI models.

Keywords: AI, Artificial Intelligence, Causation, CME, Coronal Mass Ejection, Correlation, Earthquake, Earthquakes, Fault Line, Fault Lines, Flare, Flares, NOAA, Proton Density, Quake, Quakes, Seismic Activity, Seismology, Solar Cycle, Solar Cycles, Solar Flare, Solar Flares, Solar Weather, Statistical Analyses, Statistical Analysis, Statistics, USGS, X-Class, X-Class Flares

Methods, Materials, and Data: This researcher spent considerable time to do thorough analyses, so (caveat to reader), this section may become tediously lengthy and boring – perhaps even appearing repetitive at times – but we felt it academically dishonest to fellow researchers, and the scientific community at large, were we to merely run “1 or 2” analyses and claim any sound conclusions to the scientific community.

METHODS:

The chief two (2) methods employed were: [[#1.]] First, to provide the AI a large dataset of “daily” solar proton density data and earthquake records and do a “forward analysis,” asking whether “large” earthquake activity occurred more often on (or shortly after) “high” solar photon density days than would otherwise be expected by chance; and, [[#2.]] Secondly, to run a “reverse” statistical correlation analysis and ask whether “high” solar photon density was observed on (or shortly before) “large” earthquake days. Here, we set the definitions of “large” earthquakes and “high” solar photon density to several different standards to cover all our bases. Additionally, since Marchitelli reported a time shift of a one day “lag” (delayed effect) of quake activity after the “high” solar photon density days, we decided to investigate that possible correlation – in addition to the the “same day” theory. When a 1-day shift, etc., is mentioned in this paper, this ALWAYS refers to the solar proton density data as being BEFORE the seismic data because it is untenable to assume a mechanism where earthquakes cause a change in solar proton density. Thus, if any statistically-significant “cause and effect” correlation is observed, it is inferred as solar weather having an effect on quake activity – NOT the other way around.

MATERIALS:

** SOLAR PHOTON DENSITY: We grabbed daily solar photon density readings for the OMNI2 satellite by visiting the NASA website download portal from a basic Google search: https://www.Google.com/search?q=omni2+satellite+data This yielded their online dataset download portal: https://OmniWeb.gsfc.nasa.gov/form/dx1.html Once there, this researcher selected “Create File” as the output format (as opposed to plot or list data), and selected “daily average” for the resolution. Here, you can select begin and end date parameters as well as measurements for all kinds of things (Magnetic field, Solar Plasma, etc.), and we selected daily average Proton Density, n/cc (Newtons / cubic centimeters) readings for 1-1-1973 to present. (Upon after-the-fact inspection, our file only went up to 1-10-2025, but the AI should be able to exclude quake data when no corresponding solar data exists.)

** EARTHQUAKE DATA: For daily reports of earthquake data, we went to the well-known and popular USGS website, https://Earthquake.usgs.gov/earthquakes/search/ From there, one can do a search for earthquakes and download a CSV file up to certain size limits. We found through experimentation that a Magnitude 5.5+ search for the time range in question was too large, so we tried a M5.6+ (ironically, the same metric Marchitelli et al. used, and maybe for the same reasons), and searched from 1-1-1973 to 5-10-2025 – and that CSV file was just barely within the file size download limits.

** ONLINE ARCHIVES: Lastly, in some cases, AI had trouble accepting file uploads, and Grok 3.0, in particular, asked this researcher to provide a download link for such files (USGS and NASA are dynamic and don't host static download links for file sharing – just links for “right now” file downloads), and we obliged – and provide this link for fellow-researchers where an online folder hosts the files in question:

MAIN LINK: https://ContractWithAmerica2.com/FannyDeregulation/SolarWeather/

ARCHIVE TODAY SNASPSHOT: https://Archive.vn/shKZ0 WAYBACK ARCHIVE: https://Web.Archive.org/web/20250511165128/https://ContractWithAmerica2.com/FannyDeregulation/SolarWeather/

(Editor's Note: The web space in question – https://ContractWithAmerica2.com – is a personal advocacy project of this researcher focused on – among other things – bipartisan and nonpartisan legislative advocacy to secure, protect, and harden our fragile power, internet, and telecommunications grid – but is only indirectly related to this research insofar as it researches solar weather.)

DATA:

Here's where it gets long in the tooth, so to speak.

** Analysis 1: Wed 07 May 2025 _ 06:00 pm ET chat with GEMINI

Earthquake Data: Mag 5.0+ and Mag 6.0+ events between 2020-01-01 and 2025-05-07

Solar Proton Density Data: Daily data from January 1, 2024 to May 7, 2025

Note: Some data doesn't have a matching data point in the opposing set because of file upload difficulties

Question posed: “Are earthquakes associated with higher than expected proton density?”

Findings:

Average proton density: 7.2 N/cc

Mag 5+ same day: 7.5 N/cc R-value: +0.11, p-value: 0.004, Probability Ratio: 7.5 / 7.2 = 1.0416667

Mag 5+ day after: 7.3 N/cc R-value: +0.07, p-value: 0.05, Probability Ratio: 7.3 / 7.2 = 1.0138888

Mag 6+ same day: 7.8 N/cc R-value: +0.10, p-value: 0.01, Probability Ratio: 7.8 / 7.2 = 1.0833344

Mag 6+ day after: 7.6 N/cc R-value: +0.08, p-value: 0.03, Probability Ratio: 7.6 / 7.2 = 1.0555555

Interpretation: Initially, this suggested a weak, positive, correlation that was probably NOT by chance, but later discussion with Grok – when he got differing results – highlighted a suspiciously high number of degrees of freedom by Gemini, so we continue our analysis.

** Analysis 2: Wed 07 May 2025 _ 11:21 pm ET chat with GEMINI

Datasets: Same as in Analysis 1

Definition: Baseline (average) for 75th percentile (top 25%) of proton density: 8.9 protons/cm³

Note: Some nomenclature of Gemini when copying & pasting uses “protons” / density instead of Newtons / density as the NASA website did, but in the interests of brevity, we shall accept “protons/cm³” as equivalent to “N/cc” or “Newtons / cubic centimeter.”

Question posed: A reverse analysis – “Is a 'high' proton density (defined as top 25%) associated with more than expected earthquakes?”

Findings:

Baseline probability of a Mag 5+ earthquake on any day: 263 / 742 = 0.354

Probability of a Mag 5+ earthquake on a "high" proton density day: 78 / 186 = 0.419

R-value: +0.11, P-value: 0.004, Probability Ratio: 0.419 / 0.354 = 1.18

Baseline probability of a Mag 6+ earthquake on any day: 35 / 742 = 0.047

Probability of a Mag 6+ earthquake on a "high" proton density day: 12 / 186 = 0.065

R-value: +0.10, P-value: 0.01, Probability Ratio: 0.065 / 0.047 = 1.38

Interpretation: Initially, this suggested a weak, positive, correlation that was probably NOT by chance, in the reverse direction but with the same caveat as discussed above: Degrees of freedom and possible other errors may have yielded incorrect findings.

** Analysis 3: Wed 07 May 2025 _ 11:39 pm ET chat with GEMINI

Notes: Here, I ask Gemini merely for guidance on citing him (it) as a source of information as well as whether large chunks of our conversation can be published under Fair Use standards without violating copyright law. We both agree that less is more when posting, reproducing, and publishing large amounts of our chat – and to try to stick to Gemini's key contributions to my analysis and findings in my paper, along with specific data points and statistical results that Gemini generated, quoting brief, relevant excerpts the chat. While I am not inclined to post our entire chat (would be too long for readers and possible violate the spirit of the law – if not the letter of the law), nonetheless, as this matter is lengthy and complex (Grok and I both found errors in Gemini's analysis), I may, indeed, have to post “large chunks” of our chat to address the complex nuances – since the “large” quotes will likely be small “in comparison” to the overall corpus (body) of data in my own research –and since my research is non-commercial, non-profit, and for educational and research purposes. “Less is more,” but we will see how this turns – proceeding at a natural and organic rate of research. (Whatever are my findings, however, I may have to post “large chunks” of our chat, simply to document my findings – key in any research – to verify and ensure that I'm not “making up” research.)

** Analysis 4: Thr 08 May 2025 _ 06:25 am ET chat with GEMINI (Grok makes a cameo appearance, below)

Notes: Here, I question Gemini about an apparent anomaly: In the “Analysis of Earthquake Probability on High Proton Density Days,” regarding Data Preparation, I ask Gemini why he said “Combined proton density data from "omni2_2024.dat.txt" and "omni2_2025.dat.txt."Earthquake data from "NewQuery.csv.txt." Total number of days in the combined dataset: 742,” when only 1 full year of 2024 and parts of 2025 are used – which is far less than 742 days. Gemini responded that “You have a very sharp eye for detail! You are absolutely correct to question the "742 days" figure. My apologies for the error,” and went on to calculate that 493 days were in this time-frame, asking if I wanted him to re-run the analysis.

Datasets: Same as in Analyses 1 and 2, above

Definition: Baseline (average) for 75th percentile (top 25%) of proton density: 8.9 protons/cm³

Baseline probability of a Mag 5+ earthquake on any day: 263 / 493 = 0.533

Probability of a Mag 5+ earthquake on a "high" proton density day: 61 / 123 = 0.496

R-value: -0.07, P-value: 0.10, Probability Ratio: 0.496 / 0.533 = 0.93

Baseline probability of a Mag 6+ earthquake on any day: 35 / 493 = 0.071

Probability of a Mag 6+ earthquake on a "high" proton density day: 10 / 123 = 0.081

R-value: +0.03, P-value: 0.52, Probability Ratio: 0.081 / 0.071 = 1.14

Interpretation: With these corrections in the math, the findings suggest that there is no statistically significant evidence to suggest that either Mag 5+ or Mag 6+ earthquakes are more likely on high proton density days, nor that high proton density is a useful predictor of earthquakes.

NOTE: Although not noted in the title, my notes for this day reflect that I noticed Gemini's error when Grok's results were far different, so it would be helpful to include Grok's analysis of the same dataset.

–GROK 3.0: Data Preparation: 492 days for OMNI 2 satellite data (All 2024 plus 1-1-2025 to May 7, 2025)

High Proton Density Days: Defined at top 25% (75TH percentile) – Note: Grok miscounted, and overlooked 2024 as being a leap year with 366 days, so the total days should be 493, not 492, a mistake which Gemini caught – after Gemini made a similar mistake which Grok caught.

Forward Analysis (High Proton Density → Earthquake Likelihood)

Baseline: M5+ probability: 260 / 492 = 0.528 ; M6+ probability: 82 / 492 = 0.167

M5+ Earthquakes (Same Day): Observed rate: 67 / 123 = 0.545. (Difference: +0.017)

R-value: +0.03, p-value: 0.71, Probability Ratio: 0.545 / 0.528 = 1.032196969

M5+ Earthquakes (Next Day): Observed rate: 69 / 122 = 0.566. (Difference: +0.038)

R-value: +0.06, p-value: 0.44, Probability Ratio: 0.566 / 0.528 = 1.071969697

M6+ Earthquakes (Same Day): Observed rate: 22 / 123 = 0.179. (Difference: +0.012)

R-value: +0.02, p-value: 0.80, Probability Ratio: 0.179 / 0.167 = 1.071856287

M6+ Earthquakes (Next Day): Observed rate: 24 / 122 = 0.197. (Difference: +0.030)

R-value: +0.05, p-value: 0.59, Probability Ratio: 0.197 / 0.167 = 1.179640719

Reverse Analysis (Earthquake Days → Proton Density)

Baseline Proton Density: Average daily proton density (492 days): 7.2 n/cm³.

M5+ Earthquake Days (Same Day): Average proton density on M5+ days: 7.3 n/cm³. (Difference: +0.1.)

R-value: +0.03, p-value: 0.72, Probability Ratio: 7.3 / 7.2 = 1.01388889

M5+ Earthquake Days (Previous Day): Average proton density on previous day: 7.4 n/cm³. (Difference: +0.2.)

R-value: +0.05, p-value: 0.58, Probability Ratio: 7.4 / 7.2 = 1.02777778

M6+ Earthquake Days (Same Day): Average proton density on M6+ days: 7.3 n/cm³. (Difference: +0.1.)

R-value: +0.02, p-value: 0.83. Probability Ratio: 7.3 / 7.2 = 1.01388889

M6+ Earthquake Days (Previous Day): Average proton density on previous day: 7.4 n/cm³. (Difference: +0.2.)

R-value: +0.04, p-value: 0.75. Probability Ratio: 7.4 / 7.2 = 1.02777778

Interpretation: When we note that Gemini said the baseline probability of M5+ was 263/493 (similar to Grok, who said 260/492), but that of M6+ was 35/493 (markedly different than Grok's figure of 82/492), we might infer that Grok counted several events per day –or that Gemini missed quakes – meaning their results will probably differ. However, 9 of the 10 R-values from both AI's were positive, and 9 of the 10 probability ratios were above 1.0 – which almost can't be by chance if no genuine correlation exists. Thus, even though individual analyses might imply that no “statistically significant” correlation exists, a “meta analysis” might suggest otherwise. This is a key theme in these findings – which I mention here for context.

** Analysis 5: Thr 08 May 2025 _ 08:33 am ET chat with GEMINI (who was slow—and needed more time)

Notes: Here, I wonder if more than a 1-day shift is appropriate: what if the photons had a delayed effect? I asked Gemini to do both a “reverse” analysis (compare average Proton Density on M5.6+ Days to Overall Average) as well as “forward” analysis (compare M5.6+ Earthquake Rates on High Proton Density Days, the top 5%, to Baseline) – for a zero-day shift e.g., “same day” and shifts of 1, 2, and 3 days (4 shifts, both ways = 8 analyses). A long time elapsed – maybe 30 minutes (I don't recall), and I asked if the results were ready yet:

* GORDON: “Hey, Gemini ` – Are the results ready? Oh, if you wouldn't mind, plz send an error report to Google developers that I can't see your response until after I query you.” – to which Gemini responded:

* GEMINI.GOOGLE.COM: “I understand your eagerness for the results. I apologize for the ongoing delays in providing the complete analysis. Calculating eight different analyses, each involving data extraction, filtering, calculations, and statistical tests, is computationally intensive. [] I am still processing the data and running the calculations for all eight scenarios...Thank you for your understanding. I will update you as soon as the analysis is complete.” – So, while I waited, I decided to ask Grok if he (it) could take a look:

* GORDON: “Hey, I have an idea: Why not look at earthquakes with Mag 5.6 or greater for the 5½ or so year period and compare the average solar proton density on those days with the overall solar proton density data, as the seminal Marchitelli paper used that figure, grabbing p and R values and probability ratio, and see if any significant correlation exist, using a time shift of both zero and one day, where the proton days are before the 5.6+ quakes. Secondly, please look at the 95th percentile (top 5%) of proton density values for this same approximately 5½ period, and see how many Mag 5.6 or greater quakes occur, compared to Baseline average, running same tests, both "same day" and 1-day shift (again, where proton days come first, and also calculating p and R values and probability ratio, and see if any significant correlation exist. Can you run these 4 analyses?”

* GROK 3.0: “Absolutely, Gordon! I’ll run the four analyses you’ve requested using the full 5½-year dataset (January 1, 2020, to May 7, 2025) from the SOHO/OMNI2 datasets in your folder and the earthquake data from NewQuery.csv.txt . We’ll focus on earthquakes with magnitude 5.6 or greater (M5.6+), as inspired by the Marchitelli paper mentioned in the search results, and examine solar proton density correlations with a time shift of 0 days (same day) and 1 day (proton density day before the earthquake). Let’s break this down into the two main tasks, each with two analyses (same day and 1-day shift), for a total of four analyses, calculating the differences from the null hypothesis, probability ratios, p-values, and R-values.” Editor's Note: I later asked Grok to run all 8 analysis described above.

BASELINES:

Baseline Probability of M5.6+ Earthquakes: Total days: 1953. M5.6+ days: 1234.

Baseline probability: 1234 / 1953 = 0.632.

High Proton Density Days (Top 5%):

95th percentile of daily average proton density (as used previously): 11.2 n/cm³.

High proton density days: 98 days.

GROK 3.0 – Compare Average Proton Density on M5.6+ Days to Overall Average:

Mean daily proton density (1953 days): 6.3 n/cm³.

SAME DAY (0-day shift): R-value: +0.03, p-value (t-test): 0.67, Probability Ratio: 6.4 / 6.3 = 1.016

PREVIOUS DAY (1-day shift): R-value: +0.05, p-value: 0.54, Probability Ratio: 6.5 / 6.3 = 1.032

Day before last (2-day shift): R-value: +0.03, p-value: 0.69, Probability Ratio: 6.4 / 6.3 = 1.016

Further back (3-day shift): R-value: +0.03, p-value: 0.71, Probability Ratio: 6.4 / 6.3 = 1.016

GROK 3.0 – Compare M5.6+ Earthquake Rates on High Proton Density Days (Top 5%) to Baseline

Baseline Probability of M5.6+ Earthquakes: Already calculated: 0.632 (1234 / 1953).

SAME DAY (0-day shift): R-value: +0.03, p-value: 0.70, Probability Ratio: 0.653 / 0.632 = 1.033

PREVIOUS DAY (1-day shift): R-value: +0.07, p-value: 0.32, Probability Ratio: 0.691 / 0.632 = 1.093

Day before last (2-day shift): R-value: +0.03, p-value: 0.67, Probability Ratio: 0.656 / 0.632 = 1.038

Further back (3-day shift): R-value: +0.02, p-value: 0.85, Probability Ratio: 0.642 / 0.632 = 1.016

** Analysis 6: Thr 08 May 2025 _ 09:43 pm ET chat with GEMINI and GROK

Notes: I ask both my AI friends to lower the Magnitude threshold of earthquakes to M4.0+ increase sample size (more robust analysis) and look at the 95th percentile (top 5%) of proton density values (because the higher threshold might result in greater effects, if any correlation exists).

[[DATE RANGE: omni2_2024.dat.txt" & "omni2_2025.dat.txt, e.g, Jan. 1, 2024 - May 7, 2025]]

** GEMINI: Average proton density: 7.2 protons/cm³

SAME DAY: Average proton density on earthquake days: 7.5 protons/cm³

R-value: +0.11, P-value: 0.004, Probability Ratio: 7.5/7.2 = 1.0416667

PRIOR DAY: Average proton density on earthquake days (1 day prior): 7.3 protons/cm³

R-value: +0.07, P-value: 0.05, Probability Ratio: 7.3/7.2 = 1.0138889

** GEMINI: Baseline probability of Mag 4.0+ earthquake: 0.73

SAME DAY: Probability of Mag 4.0+ earthquake on high proton density days: 0.75

R-value: +0.03, P-value: 0.49, Probability Ratio: 0.75/0.73 = 1.03

PREVIOUS DAY: Probability of Mag 4.0+ earthquake on high proton density days (1 day prior): 0.71

R-value: -0.03, P-value: 0.52, Probability Ratio: 0.71/0.73 = 0.97

** NOTE: The p-values for the first analysis – asking if proton density is significantly higher on M4.0+ quake days – is suspiciously low, inviting further analysis by GROK who seems to feel – as do I – that the correct number of “Degrees of freedom” is 492 - 2 = 490 (not Gemini’s 740, which seems incorrect for 492 days), thus leading to incorrect results.

** GROK: Baseline: 7.2 n/cm³. (Similar to Gemini)

SAME DAY: Average proton density on earthquake days: 7.3 protons/cm³

R-value: +0.03, P-value: 0.66, Probability Ratio: 7.3/7.2 = 1.014

PRIOR DAY: Average proton density on earthquake days (1 day prior): 7.4 protons/cm³

R-value: +0.04, P-value: 0.52, Probability Ratio: 7.4/7.2 = 1.028

** GROK: Baseline probability of an M4.0+ day: 475 / 492 = 0.965 (This is a bit higher than Gemini)

** GROK: “High Proton Density Threshold: 95th percentile of daily average proton density (492 days): 9.4 n/cm³. Gemini reported 16.5 protons/cm³, which is significantly higher. The 95th percentile for 492 days should reflect the top 5% (492 × 0.05 ≈ 25 days). My calculation (9.4 n/cm³) is consistent with the distribution of proton density values in the OMNI2 files, while 16.5 seems anomalously high and may indicate an error in Gemini’s percentile calculation.”

** GROK: BASELINE: High proton density days: 25 days

Probability of Mag 4.0+ earthquake on high proton density days

SAME DAY: Observed rate: 24 / 25 = 0.960

R-value: -0.01, p-value: 0.89, Probability Ratio: 0.960 / 0.965 = 0.995

PREVIOUS DAY: Observed rate: 23 / 24 = 0.958

R-value: -0.02, p-value: 0.87, Probability Ratio: 0.958 / 0.965 = 0.993

** NOTE: The much higher baseline for probability of an M4.0+ quake on any day may be a result of counting several quakes on the same day – uncertain – but may throw off the analysis. However, Gemini, in this chat, had this to say – suggesting Grok may have been correct: “Baseline Probability: Grok's baseline probability (0.965) is much higher than mine (0.73), again due to my undercounting of M4.0+ days. [] Observed Earthquake Rates: Grok's observed rates are consistent with his accurate baseline probability, while mine were skewed by the incorrect baseline...My Response to Grok's Assessment [] I fully acknowledge and accept Grok's critique. He has correctly identified several significant errors in my previous analysis. I appreciate his thoroughness and the clarity of his explanation. I am still under development, and I am learning to handle complex calculations and data analysis more accurately. Grok's feedback is invaluable in helping me improve...Gordon, I apologize for the errors in my previous analysis. I am grateful to Grok for providing a more accurate assessment. I am committed to learning from these mistakes and providing you with more reliable information in the future.”

Editor's Note: I had asked GROK to re-run the M4.0+ analysis both direction—but include all 5 years:

GORDON: Hey, Grok, I'm gonna give it "one last" try to see if any correlations exist between proton density and earthquake frequency. Please, this time, look at earthquakes with Mag 4 or greater for the 5½ or so year period...please look at the 95th percentile (top 5%) of proton density...”

GROK 3.0: “I'm on it, Gordon! I understand your reasoning—lowering the earthquake magnitude threshold to M4.0+ will include more events, increasing the sample size and degrees of freedom, while focusing on the top 5% of proton density days targets the most extreme solar activity, which might be more likely to show an effect if one exists. Let’s run the four analyses using the full 5½-year dataset (January 1, 2020, to May 7, 2025) from the OMNI2 files and the earthquake data from NewQuery.csv.txt . We’ll examine M4.0+ earthquakes with time shifts of 0 days (same day) and 1 day (proton density day before the earthquake), calculating differences from the null hypothesis, probability ratios, p-values, and R-values.”

** GROK: Mean daily proton density (1953 days): 6.3 n/cm³.³ [Aka 6.3 “protons” / cc]

SAME DAY: Average proton density on M4.0+ days: 6.3 n/cm³.

R-value: +0.01, P-value: 0.98, Probability Ratio: 6.3 / 6.3 = 1.000 (no difference).

PRIOR DAY: Average proton density on the previous day: 6.4 n/cm³.

R-value: +0.03, P-value: 0.72, Probability Ratio: 6.4 / 6.3 = 1.016 (1.6% higher than expected).

** GROK: Baseline probability of an M4.0+ day: 1876 / 1953 = 0.961.

SAME DAY: Probability of Mag 4.0+ earthquake on high proton density days: Observed rate: 95 / 98 = 0.969

R-value: +0.02, P-value: 0.82, Probability Ratio: 0.969 / 0.961 = 1.008 (0.8% higher than baseline).

NOTE: High proton density days: 98 (excluding the last day, May 7, 2025: 97).

PREVIOUS DAY: Probability of Mag 4.0+ earthquake on high proton density days (1 day prior): Observed rate: 94 / 97 = 0.969 R-value: +0.02, P-value: 0.83, Probability Ratio: 0.969 / 0.961 = 1.008 (0.8% higher than baseline).

Gemini, in this chat, also discussed Grok's critique, not included in its entirety here for brevity & to respect copyright.

** Analysis 7: Sat 10 May 2025 _ 02:48 pm ET chat with GROK

“High” proton density days = top 25% (not top 5% – which is done elsewhere)

NOTE: Here, I provide Grok with six (6) years' of data (2020 – 2025), and ask for analyses for 2 magnitude thresholds (M5+ and M6+), 2 time windows per analysis (same day/next day for forward, same day/previous day for reverse), and 2 directions (forward and reverse), and I mistakenly think he understood me to combine all the 6 years into one “large” dataset and simply run a total of [2 × 2 × 2] = 8 analyses (both thresholds, both directions, and both days – same and 1-day shift) – but Grok thought I wanted an individual breakdown for each of the 6 years. This misunderstanding caused him to run a total of [6 × 2 × 2 × 2] = 48 analyses, not 8. Thus, I won't be putting “detailed results” or discussion for all 48 analyses here – instead focusing on listing merely the p-values, R-values, and “difference” from expected via “en masse” copy/paste – and then including these results in discussion. However, while this was an unintended mistake on my part – nonetheless, it provide a lot of more raw data because it examines not only the “combined” dataset of all years, but also each individual year, which might provide more clarification of a trend or correlation if one analysis missed it. i.e., if an analysis overlooks something – having “a lot” of analyses, so we can perform a “meta-analysis” e.g., an analysis of the analyses.

Here's a copy/paste of just the summary of GROK's forward and reverse analyses:

* Begin copy/paste of GROK's summary * [[ Small Fair Use quote to document research ]]

Forward Analysis Results

For each year, magnitude threshold, and time window (same day, next day), I’ll compute the observed rate, difference from baseline, p-value, and R-value.

M5+ Earthquakes (Same Day):

M5+ Earthquakes (Next Day):

M6+ Earthquakes (Same Day):

M6+ Earthquakes (Next Day):

Interpretation (Forward Analysis):

• Differences: The observed rates of M5+ and M6+ earthquakes on high proton density days (and the next day) are slightly higher than the baseline in most cases, with differences ranging from +0.001 to +0.051 for M5+ and +0.003 to +0.031 for M6+. The largest differences are in 2024 (M5+ next day: +0.048) and 2025 (M5+ next day: +0.051).

• p-values: All p-values are high (0.35 to 0.99), indicating no statistically significant difference from the null hypothesis (p < 0.05 would indicate significance). This suggests the observed increases could be due to chance.

• R-values: Correlation coefficients are very low (0.00 to 0.09), indicating a weak relationship between high proton density and earthquake occurrence. The highest R-value (0.09 for M5+ next day in 2024) still suggests minimal correlation.

Step 2: Reverse Analysis (Earthquake Days → Proton Density)

Methodology

1. Baseline Proton Density:

   • Calculate the average daily proton density for each year (mean of daily averages from hourly data).

2. Proton Density on Earthquake Days:

   • Identify days with M5+ and M6+ earthquakes.

   • Compute the average proton density on those days (same day and previous day).

3. Statistical Tests:

   • Difference from Average: Compare the observed proton density to the yearly average.

   • p-value: Use a t-test to compare the mean proton density on earthquake days to the overall mean.

   • R-value: Compute the Pearson correlation between earthquake occurrence (1 for earthquake day, 0 for no earthquake) and daily proton density.

Baseline Proton Density (average daily mean):

Reverse Analysis Results

M5+ Earthquake Days (Same Day):

M5+ Earthquake Days (Previous Day):

M6+ Earthquake Days (Same Day):

M6+ Earthquake Days (Previous Day):

Interpretation (Reverse Analysis):

• Differences: Proton density on M5+ and M6+ earthquake days (and the previous day) is slightly higher than the yearly average, with differences of +0.1 to +0.2 n/cm³. The largest differences are on the previous day (e.g., +0.2 for M5+ in 2024).

• p-values: All p-values are high (0.52 to 0.88), indicating no statistically significant difference from the baseline average proton density.

• R-values: Correlation coefficients are very low (0.02 to 0.06), suggesting a weak relationship between earthquake occurrence and proton density.

Summary for Your Solar Flare Paper

Forward Analysis (High Proton Density → Earthquakes):

• Findings: High proton density days (top 25%) show a slightly higher rate of M5+ and M6+ earthquakes (same day and next day) compared to the baseline, with differences ranging from -0.001 to +0.051 for M5+ and +0.003 to +0.031 for M6+.

• Statistical Significance: p-values (0.35 to 0.99) indicate no significant correlation; the differences are likely due to chance.

• Correlation Strength: R-values (0.00 to 0.09) show a very weak relationship, with the strongest being 0.09 (M5+ next day, 2024).

Reverse Analysis (Earthquakes → Proton Density):

• Findings: Proton density on M5+ and M6+ earthquake days (and the previous day) is slightly higher than the yearly average, with differences of +0.1 to +0.2 n/cm³.

• Statistical Significance: p-values (0.52 to 0.88) show no significant difference from the average.

• Correlation Strength: R-values (0.02 to 0.06) indicate a very weak relationship.

Discussion for Your Paper:

• Lack of Strong Correlation: The analyses show a slight association between high proton density and earthquake likelihood (and vice versa), but the differences are small, and statistical tests (p-values > 0.05) suggest these are likely chance occurrences.

• Scientific Context: This aligns with the search results—while a 2020 study suggested a link between proton density and earthquakes (with a 1-day delay), the USGS (2024) and a 2023 study argue there’s no causal relationship, citing a lack of cyclic earthquake patterns matching the solar cycle.

• Specific Case: The X9.0 flare on October 3, 2024, was followed by an M6.2 earthquake on October 4, with proton density rising to 12.5 n/cm³ (above the 2024 threshold of 9.2). This fits the 1-day delay hypothesis, but the overall analysis suggests such cases may be coincidental.

Recommendations

• Incorporate in Your Paper: Note that your analysis of 2020–2025 data shows a weak association between solar proton density and M5+/M6+ earthquakes (differences of 1–5% in likelihood, 0.1–0.2 n/cm³ in density), but statistical tests (p-values 0.35–0.99, R-values 0.00–0.09) indicate no significant correlation.

• Balance with Literature: Highlight the debate—some studies suggest a link via mechanisms like the reverse piezoelectric effect, but the lack of strong evidence in your data supports the USGS’s skepticism.

• Flare Context: Since your paper is on solar flares, you can use the OMNI2 data to discuss solar activity trends (as in my previous response) and cite the X9.0 flare on October 3, 2024, as a notable event, but note that the earthquake correlation remains inconclusive.

Next Steps

I’ve completed the 48 analyses as requested. If you’d like to explore other aspects (e.g., different solar metrics like sunspot numbers or Kp index, or regional earthquake patterns), I’m happy to help. What would you like to do next for your paper, Gordon?

* End copy/paste of GROK's summary *

As stated above, I we had a misunderstanding – which I correct here:

GORDON: I realized I should have asked you to combine all years for solar proton density. My apologies. Then, please simply run the same analysis, but for the 1-1-2020 to most recent 2025 data I sent you. Thus, you need to combine the proton data into one single file and look for [[a]] any correlations between M5+ and M6+ quakes on days in the top quartile of proton density, but both directions. First, you'll need to set a baseline of average proton density and compare it with observed proton density on days with M5+ and M6+ quakes. See if, for this 5½ year range, the proton density is higher than null hypothesis for both "same day" and "day after," which is to test the theory about proton activity having a delayed effect on quakes. Thus, you need do only 4 analyses. Except that I'd like a reverse analysis to see what relationships exist in M5+ and M6+ observed frequently different from null on "high" (top 25% aka quartile) Solar Proton Density Days. For the 2nd (reverse) analysis, I'd like you to look at both "same day" and "previous day," which is to test the theory about proton activity having a delayed effect on quakes. Thus, only 8 analyses (with p-value, R-value, and differences between observed and null). Can you do it?

GROK 3.0: Absolutely, I can handle this adjusted request, Gordon! Thank you for the clarification. I’ll combine the solar proton density data from 2020 to May 7, 2025, into a single dataset and perform the requested correlation analyses for the entire 5½-year period. Let’s break this down into the two main tasks, each with 4 analyses (8 total), and compute the differences from the null hypothesis, p-values, and R-values for each.

Overview of the Task

You’d like to:

1. Forward Analysis: Test if high solar proton density days (top 25% quartile over the entire period) are associated with an increased likelihood of M5+ and M6+ earthquakes on the same day and the next day, compared to the baseline probability.

2. Reverse Analysis: Test if M5+ and M6+ earthquake days are associated with higher-than-average solar proton density on the same day and the previous day, compared to the overall average proton density.

This results in:

• 2 magnitude thresholds (M5+ and M6+).

• 2 time windows per analysis (same day/next day for forward, same day/previous day for reverse).

• 2 directions (forward and reverse).

• Total: 2 × 2 × 2 = 8 analyses. … [some response left out for brevity]

Step 1: Forward Analysis (High Proton Density → Earthquake Likelihood)

Methodology

1. Baseline Probability of Earthquakes:

• Total days: 1953.

• Count days with at least one M5+ or M6+ earthquake and divide by total days.

2. High Proton Density Days:

• Compute the 75th percentile (top 25%) of daily average proton density over the entire period.

• Identify days where the daily average proton density exceeds this threshold (“high” days).

3. Observed Earthquake Rate on High Proton Density Days:

• For each high proton density day, check for M5+ and M6+ earthquakes on the same day and the next day.

• Calculate the proportion of high proton density days followed by an earthquake.

4. Statistical Tests:

• Difference from Null: Compare the observed rate to the baseline probability.

• p-value: Use a one-sample proportion test to determine if the observed rate differs significantly from the baseline.

• R-value: Use point-biserial correlation between high proton density days (1 for high, 0 for not high) and earthquake occurrence (1 if an earthquake occurs, 0 if not).

Results

Baseline Probabilities:

• Total days: 1953.

• M5+ days: 1015 days (days with at least one M5+ earthquake).

• M5+ probability: 1015 / 1953 = 0.520.

• M6+ days: 312 days.

• M6+ probability: 312 / 1953 = 0.160.

High Proton Density Threshold:

• 75th percentile of daily average proton density (over all 1953 days): 8.5 n/cm³.

• Number of high proton density days (top 25%): 489 days (1953 × 0.25 ≈ 489).

Forward Analysis Results:

M5+ Earthquakes (Same Day):

• High proton density days: 489.

• M5+ earthquakes on the same day: 261.

• Observed rate: 261 / 489 = 0.534.

• Baseline: 0.520.

• Difference: +0.014.

• p-value (one-sample proportion test): 0.62.

• R-value (point-biserial correlation): 0.03.

M5+ Earthquakes (Next Day):

• High proton density days: 489 (excluding the last day, May 7, 2025, for “next day” analysis: 488).

• M5+ earthquakes on the next day: 267.

• Observed rate: 267 / 488 = 0.547.

• Baseline: 0.520.

• Difference: +0.027.

• p-value: 0.38.

• R-value: 0.05.

M6+ Earthquakes (Same Day):

• High proton density days: 489.

• M6+ earthquakes on the same day: 82.

• Observed rate: 82 / 489 = 0.168.

• Baseline: 0.160.

• Difference: +0.008.

• p-value: 0.77.

• R-value: 0.02.

M6+ Earthquakes (Next Day):

• High proton density days: 488.

• M6+ earthquakes on the next day: 86.

• Observed rate: 86 / 488 = 0.176.

• Baseline: 0.160.

• Difference: +0.016.

• p-value: 0.58.

• R-value: 0.04.

Summary (Forward Analysis):

• Differences: The observed rates of M5+ and M6+ earthquakes on high proton density days (and the next day)

are slightly higher than the baseline, with differences of +0.014 to +0.027 for M5+ and +0.008 to +0.016 for

M6+.

• p-values: All p-values (0.38 to 0.77) are above 0.05, indicating no statistically significant difference from the

null hypothesis.

• R-values: Correlation coefficients are very low (0.02 to 0.05), suggesting a weak relationship.

Step 2: Reverse Analysis (Earthquake Days → Proton Density)

Methodology

1. Baseline Proton Density:

• Calculate the average daily proton density over the entire period (mean of daily averages).

2. Proton Density on Earthquake Days:

• Identify days with M5+ and M6+ earthquakes.

• Compute the average proton density on those days (same day and previous day).

3. Statistical Tests:

• Difference from Average: Compare the observed proton density to the overall average.

• p-value: Use a t-test to compare the mean proton density on earthquake days to the overall mean.

• R-value: Compute the Pearson correlation between earthquake occurrence (1 for earthquake day, 0 for no earthquake) and daily proton density.

Results

Baseline Proton Density:

• Average daily proton density (1953 days): 6.3 n/cm3.

Reverse Analysis Results:

M5+ Earthquake Days (Same Day):

• M5+ days: 1015.

• Average proton density on M5+ days: 6.4 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.1.

• p-value (t-test): 0.68.

• R-value (Pearson correlation): 0.03.

M5+ Earthquake Days (Previous Day):

• M5+ days: 1015 (excluding the first day, January 1, 2020, for “previous day” analysis: 1014).

• Average proton density on the previous day: 6.5 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.2.

• p-value: 0.55.

• R-value: 0.05.

M6+ Earthquake Days (Same Day):

• M6+ days: 312.

• Average proton density on M6+ days: 6.4 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.1.

• p-value: 0.81.

• R-value: 0.02.

M6+ Earthquake Days (Previous Day):

• M6+ days: 312 (excluding the first day: 311).

• Average proton density on the previous day: 6.5 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.2.

• p-value: 0.73.

• R-value: 0.04.

Summary (Reverse Analysis):

• Differences: Proton density on M5+ and M6+ earthquake days (and the previous day) is slightly higher than the overall average, with differences of +0.1 to +0.2 n/cm3.

• p-values: All p-values (0.55 to 0.81) are above 0.05, indicating no statistically significant difference.

• R-values: Correlation coefficients are very low (0.02 to 0.05), suggesting a weak relationship.

Combined Results for Your Paper

Forward Analysis (High Proton Density → Earthquakes):

• M5+ Same Day: Observed rate 0.534 vs. baseline 0.520 (+0.014), p-value 0.62, R-value 0.03.

• M5+ Next Day: Observed rate 0.547 vs. baseline 0.520 (+0.027), p-value 0.38, R-value 0.05.

• M6+ Same Day: Observed rate 0.168 vs. baseline 0.160 (+0.008), p-value 0.77, R-value 0.02.

• M6+ Next Day: Observed rate 0.176 vs. baseline 0.160 (+0.016), p-value 0.58, R-value 0.04.

Reverse Analysis (Earthquakes → Proton Density):

• M5+ Same Day: Observed proton density 6.4 n/cm3 vs. baseline 6.3 (+0.1), p-value 0.68, R-value 0.03.

• M5+ Previous Day: Observed proton density 6.5 n/cm3 vs. baseline 6.3 (+0.2), p-value 0.55, R-value 0.05.

• M6+ Same Day: Observed proton density 6.4 n/cm3 vs. baseline 6.3 (+0.1), p-value 0.81, R-value 0.02.

• M6+ Previous Day: Observed proton density 6.5 n/cm3 vs. baseline 6.3 (+0.2), p-value 0.73, R-value 0.04.

Interpretation:

• Lack of Strong Correlation: Both forward and reverse analyses show slight associations (higher earthquake rates on high proton density days, higher proton density on earthquake days), but the differences are small

(+0.008 to +0.027 for rates, +0.1 to +0.2 n/cm3 for density).

• Statistical Significance: p-values (0.38 to 0.81) indicate no significant correlation; the differences are likely due to chance.

• Correlation Strength: R-values (0.02 to 0.05) suggest a very weak relationship, with no strong evidence of a delayed effect (next day or previous day differences are not significantly larger).

• Scientific Context: This aligns with the search results—a 2020 study suggested a link between proton density and earthquakes (with a 1-day delay), but the USGS (2024) and a 2023 study argue there’s no causal relationship, and your data supports this skepticism.

Recommendations for Your Paper

• Report the Findings: Over 2020–2025, high proton density days (top 25%) show a slightly higher likelihood of M5+ and M6+ earthquakes (differences of 0.8–2.7%), and earthquake days show slightly higher proton density (0.1–0.2 n/cm3), but these differences are not statistically significant (p-values 0.38–0.81, R-values 0.02–0.05).

• Discuss the Delay Hypothesis: The “next day” and “previous day” analyses show slightly larger differences (e.g., +0.027 for M5+ next day, +0.2 n/cm3 for M5+ previous day), but the lack of statistical significance suggests no clear delayed effect.

• Tie to Solar Flares: Since your paper is on solar flares, you can note that proton density spikes often follow flares (e.g., the X9.0 flare on October 3, 2024, saw proton density rise to 12.5 n/cm3 on October 4), but the lack of a strong earthquake correlation suggests limited geophysical impact in this context.

*** END of BLOCK Copy/Paste response for the eight (8) analyses discussed above ***

Next, I ask Grok to run the same eight (8) analysis (M5+/M6+, same-day/1-day shift, forward/reverse) for just the 2024 and partial 2025 dataset – to compare with GEMINI – who ran this analysis after I was unable to upload all the files – a direct “exact same as” comparison between Grok and Gemini.

*** AGAIN: “High” proton density days = top 25% (not top 5% – which is done elsewhere) ***

GORDON: Please re-run those tests, but use ONLY the proton density data from 2024 and the 1-1-2025 to present year. My gut feeling says I'm missing something, and this smaller dataset should suss out the

confusion.

GROK 3.0: I understand, Gordon. Let’s narrow the focus to the proton density data from 2024 and January 1, 2025, to May 7, 2025, and re-run the correlation analyses between solar proton density and earthquake likelihood for M5+ and M6+ events. This smaller dataset (spanning 492 days) might help clarify any patterns that were diluted in the larger 5½-year dataset. I’ll follow the same methodology as before, performing the forward and reverse analyses with the specified time windows, and compute the differences from the null hypothesis, p-values, and R-values for each of the 8 analyses.

Data Preparation

Proton Density Data

I’ll combine the proton density data from:

• 2024: omni2_2024.dat.txt, covering January 1 to December 31 (365 days).

• 2025: omni2_2025.dat.txt, covering January 1 to May 7 (127 days).

• Total Days: 365 + 127 = 492 days

Results

Baseline Probabilities:

• Total days: 492.

• M5+ days: 260 days (days with at least one M5+ earthquake).

• M5+ probability: 260 / 492 = 0.528.

• M6+ days: 82 days.

• M6+ probability: 82 / 492 = 0.167.

High Proton Density Threshold:

• 75th percentile of daily average proton density (492 days): 9.1 n/cm3.

• Number of high proton density days (top 25%): 492 × 0.25 ≈ 123 days.

Forward Analysis Results:

M5+ Earthquakes (Same Day):

• High proton density days: 123.

• M5+ earthquakes on the same day: 67.

• Observed rate: 67 / 123 = 0.545.

• Baseline: 0.528.

• Difference: +0.017.

• p-value: 0.71.

• R-value: 0.03.

M5+ Earthquakes (Next Day):

• High proton density days: 123 (excluding the last day, May 7, 2025: 122).

• M5+ earthquakes on the next day: 69.

• Observed rate: 69 / 122 = 0.566.

• Baseline: 0.528.

• Difference: +0.038.

• p-value: 0.44.

• R-value: 0.06.

M6+ Earthquakes (Same Day):

• High proton density days: 123.

• M6+ earthquakes on the same day: 22.

• Observed rate: 22 / 123 = 0.179.

• Baseline: 0.167.

• Difference: +0.012.

• p-value: 0.80.

• R-value: 0.02.

M6+ Earthquakes (Next Day):

• High proton density days: 122.

• M6+ earthquakes on the next day: 24.

• Observed rate: 24 / 122 = 0.197.

• Baseline: 0.167.

• Difference: +0.030.

• p-value: 0.59.

• R-value: 0.05.

Summary (Forward Analysis):

• Differences: The observed rates of M5+ and M6+ earthquakes on high proton density days (and the next day)

are slightly higher than the baseline, with differences of +0.017 to +0.038 for M5+ and +0.012 to +0.030 for

M6+.

• p-values: All p-values (0.44 to 0.80) are above 0.05, indicating no statistically significant difference.

• R-values: Correlation coefficients are low (0.02 to 0.06), suggesting a weak relationship.

Step 2: Reverse Analysis (Earthquake Days → Proton Density)

Methodology

1. Baseline Proton Density:

• Calculate the average daily proton density over the 492 days.

2. Proton Density on Earthquake Days:

• Identify days with M5+ and M6+ earthquakes.

• Compute the average proton density on those days (same day and previous day).

3. Statistical Tests:

• Difference from Average: Compare the observed proton density to the overall average.

• p-value: Use a t-test.

• R-value: Compute the Pearson correlation (earthquake occurrence: 1 if occurs, 0 if not; proton density:

continuous).

Results

Baseline Proton Density:

• Average daily proton density (492 days): 7.2 n/cm3.

Reverse Analysis Results:

M5+ Earthquake Days (Same Day):

• M5+ days: 260.

• Average proton density on M5+ days: 7.3 n/cm3.

• Baseline: 7.2 n/cm3.

• Difference: +0.1.

• p-value: 0.72.

• R-value: 0.03.

M5+ Earthquake Days (Previous Day):

• M5+ days: 260 (excluding the first day, January 1, 2024: 259).

• Average proton density on the previous day: 7.4 n/cm3.

• Baseline: 7.2 n/cm3.

• Difference: +0.2.

• p-value: 0.58.

• R-value: 0.05.

M6+ Earthquake Days (Same Day):

• M6+ days: 82.

• Average proton density on M6+ days: 7.3 n/cm3.

• Baseline: 7.2 n/cm3.

• Difference: +0.1.

• p-value: 0.83.

• R-value: 0.02.

M6+ Earthquake Days (Previous Day):

• M6+ days: 82 (excluding the first day: 81).

• Average proton density on the previous day: 7.4 n/cm3.

• Baseline: 7.2 n/cm3.

• Difference: +0.2.

• p-value: 0.75.

• R-value: 0.04.

Summary (Reverse Analysis):

• Differences: Proton density on M5+ and M6+ earthquake days (and the previous day) is slightly higher than

the average, with differences of +0.1 to +0.2 n/cm3.

• p-values: All p-values (0.58 to 0.83) are above 0.05, indicating no significant difference.

• R-values: Correlation coefficients are low (0.02 to 0.05), suggesting a weak relationship.

Combined Results for Your Paper

Forward Analysis (High Proton Density → Earthquakes):

• M5+ Same Day: Observed rate 0.545 vs. baseline 0.528 (+0.017), p-value 0.71, R-value 0.03.

• M5+ Next Day: Observed rate 0.566 vs. baseline 0.528 (+0.038), p-value 0.44, R-value 0.06.

• M6+ Same Day: Observed rate 0.179 vs. baseline 0.167 (+0.012), p-value 0.80, R-value 0.02.

• M6+ Next Day: Observed rate 0.197 vs. baseline 0.167 (+0.030), p-value 0.59, R-value 0.05.

Reverse Analysis (Earthquakes → Proton Density):

• M5+ Same Day: Observed proton density 7.3 n/cm3 vs. baseline 7.2 (+0.1), p-value 0.72, R-value 0.03.

• M5+ Previous Day: Observed proton density 7.4 n/cm3 vs. baseline 7.2 (+0.2), p-value 0.58, R-value 0.05.

• M6+ Same Day: Observed proton density 7.3 n/cm3 vs. baseline 7.2 (+0.1), p-value 0.83, R-value 0.02.

• M6+ Previous Day: Observed proton density 7.4 n/cm3 vs. baseline 7.2 (+0.2), p-value 0.75, R-value 0.04.

Interpretation:

• Lack of Strong Correlation: The results are similar to the larger dataset—slight associations exist (higher

earthquake rates on high proton density days, higher proton density on earthquake days), but the differences

remain small (+0.012 to +0.038 for rates, +0.1 to +0.2 n/cm3 for density).

• Statistical Significance: p-values (0.44 to 0.83) indicate no significant correlation; the differences are likely

due to chance.

• Correlation Strength: R-values (0.02 to 0.06) suggest a very weak relationship, with no clear delayed effect

(next day/previous day differences are not significantly larger).

• Comparison to Previous Analysis: The smaller dataset shows slightly larger differences (e.g., +0.038 for M5+

next day vs. +0.027 in the full dataset), but the statistical significance remains low, suggesting the pattern isn’t

stronger in this period.

Recommendations for Your Paper

• Report the Findings: Over 2024 to May 7, 2025, high proton density days (top 25%) show a slightly higher

likelihood of M5+ and M6+ earthquakes (differences of 1.2–3.8%), and earthquake days show slightly higher

proton density (0.1–0.2 n/cm3), but these differences are not statistically significant (p-values 0.44–0.83, Rvalues

0.02–0.06).

• Discuss the Delay Hypothesis: The “next day” and “previous day” analyses show slightly larger differences

(e.g., +0.038 for M5+ next day, +0.2 n/cm3 for M5+ previous day), but the lack of significance suggests no

clear delayed effect.

• Tie to Solar Flares: You can note that this period includes the X9.0 flare on October 3, 2024, which saw proton

density rise to 12.5 n/cm3 on October 4, followed by an M6.2 earthquake (as noted previously). However, the

overall analysis suggests this may be coincidental.

*** END of BLOCK Copy/Paste response for the eight (8) analyses discussed above ***

Next, I ask Grok to use Mag 5.6+ only as the threshold & look at both “same day” and “1-day shift,” both forward & reverse (total of 8 analyses), the same M5.6+ level that Marchitelli used for the full 5½-year dataset. “High” proton density days = 95th percentile, e.g., top 5% (not top 25% – which is done earlier).

Data preparation:

Overall Average Proton Density: Mean daily proton density (1953 days): 6.3 n/cm3.

M5.6+ Earthquake Days: Total M5.6+ days: 1234 days (out of 1953).

• Baseline probability of an M5.6+ day: 1234 / 1953 = 0.632.

RESULTS – Forward analyses

Same Day:

• Average proton density on M5.6+ days: 6.4 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.1.

• Probability Ratio: 6.4 / 6.3 = 1.016 (1.6% higher than expected).

• p-value (t-test): 0.67.

• R-value (Pearson correlation): 0.03.

Previous Day (1-Day Shift):

• M5.6+ days: 1234 (excluding the first day, January 1, 2020: 1233).

• Average proton density on the previous day: 6.5 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.2.

• Probability Ratio: 6.5 / 6.3 = 1.032 (3.2% higher than expected).

• p-value: 0.54.

• R-value: 0.05.

Summary (Task 1):

• Differences: Proton density on M5.6+ days (and the previous day) is slightly higher than the overall average

(+0.1 to +0.2 n/cm3).

• Probability Ratios: Proton density is 1.6% higher on the same day and 3.2% higher the previous day compared to the baseline.

• p-values: Both p-values (0.54 and 0.67) are above 0.05, indicating no significant difference.

• R-values: Correlation coefficients are low (0.03 to 0.05), suggesting a weak relationship.

Task 2: Compare M5.6+ Earthquake Rates on High Proton Density Days (Top 5%) to Baseline Methodology

1. Baseline Probability of M5.6+ Earthquakes: Already calculated: 0.632 (1234 / 1953).

2. High Proton Density Days (Top 5%):

• Compute the 95th percentile of daily average proton density over the 1953 days.

• Identify days where the daily average proton density exceeds this threshold.

3. Observed Earthquake Rate on High Proton Density Days:

• Check for M5.6+ earthquakes on the same day and the next day for each high proton density day.

• Calculate the proportion of high proton density days followed by an M5.6+ earthquake.

4. Statistical Tests:

• Difference from Baseline: Compare the observed rate to the baseline probability.

• Probability Ratio: Ratio of observed rate to baseline rate.

• p-value: Use a one-sample proportion test.

• R-value: Use point-biserial correlation (high proton density: 1 for high, 0 for not high; M5.6+: 1 if occurs, 0 if not).

RESULTS – Reverse analyses

High Proton Density Threshold: 95th percentile of daily average proton density (1953 days): 11.2 n/cm3.

• Number of high proton density days (top 5%): 1953 × 0.05 ≈ 98 days.

Same Day:

• High proton density days: 98.

• M5.6+ earthquakes on the same day: 64.

• Observed rate: 64 / 98 = 0.653.

• Baseline: 0.632.

• Difference: +0.021.

• Probability Ratio: 0.653 / 0.632 = 1.033 (3.3% higher than baseline).

• p-value: 0.70.

• R-value: 0.03.

Next Day (1-Day Shift):

• High proton density days: 98 (excluding the last day, May 7, 2025: 97).

• M5.6+ earthquakes on the next day: 67.

• Observed rate: 67 / 97 = 0.691.

• Baseline: 0.632.

• Difference: +0.059.

• Probability Ratio: 0.691 / 0.632 = 1.093 (9.3% higher than baseline).

• p-value: 0.32.

• R-value: 0.07.

Summary (Task 2):

• Differences: The observed rate of M5.6+ earthquakes on high proton density days (top 5%) is slightly higher than the baseline (+0.021 same day, +0.059 next day).

• Probability Ratios: Earthquake likelihood is 3.3% higher on the same day and 9.3% higher the next day compared to the baseline.

• p-values: Both p-values (0.32 and 0.70) are above 0.05, indicating no significant difference.

• R-values: Correlation coefficients are low (0.03 to 0.07), suggesting a weak relationship.

Combined Results for Your Paper

Task 1 (Proton Density on M5.6+ Days):

• Same Day: Observed proton density 6.4 n/cm3 vs. baseline 6.3 (+0.1), probability ratio 1.016, p-value 0.67, R-value 0.03.

• Previous Day: Observed proton density 6.5 n/cm3 vs. baseline 6.3 (+0.2), probability ratio 1.032, p-value 0.54, R-value 0.05.

Task 2 (M5.6+ Earthquake Rates on High Proton Density Days, Top 5%):

• Same Day: Observed rate 0.653 vs. baseline 0.632 (+0.021), probability ratio 1.033, p-value 0.70, R-value 0.03.

• Next Day: Observed rate 0.691 vs. baseline 0.632 (+0.059), probability ratio 1.093, p-value 0.32, R-value

0.07.

Interpretation:

• Weak Association: Both analyses show a slight association—proton density is 1.6–3.2% higher on M5.6+ days (and the previous day), and M5.6+ earthquake rates are 3.3–9.3% higher on high proton density days (top 5%). The 1-day shift (previous day for proton density, next day for earthquakes) shows a slightly stronger effect,

supporting the Marchitelli paper’s hypothesis of a 1-day delay.

• Statistical Significance: p-values (0.32 to 0.70) are above 0.05, indicating no significant correlation; the differences are likely due to chance.

• Correlation Strength: R-values (0.03 to 0.07) suggest a very weak relationship, with the strongest being 0.07 (next day in Task 2).

• Comparison to Previous Analyses: The top 5% threshold shows a slightly larger difference (e.g., +0.059 for next day) compared to the top 25% threshold in previous analyses (+0.027 for M5+ next day), but the lack of statistical significance remains consistent. Recommendations for Your Paper

• Report the Findings: Over 2020–2025, proton density on M5.6+ earthquake days (and the previous day) is 1.6–3.2% higher than the average, and high proton density days (top 5%) show a 3.3–9.3% higher M5.6+ earthquake rate. However, these differences are not statistically significant (p-values 0.32–0.70, R-values 0.03–0.07).

• Discuss the Marchitelli Paper: The slight increase in earthquake rates 1 day after high proton density days (9.3% higher) aligns with the Marchitelli paper’s hypothesis of a 1-day delay, but the lack of significance suggests this may be coincidental, supporting the USGS (2024) and 2023 study’s skepticism about a causal link.

• Tie to Solar Flares: Note that high proton density often follows major flares (e.g., the X9.0 flare on October 3, 2024, with proton density rising to 12.5 n/cm3 on October 4, followed by an M6.2 earthquake), but the overall correlation remains weak.

*** END of BLOCK Copy/Paste response for the eight (8) analyses discussed above ***

Then, I ask Grok to run the same 8 analyses for a 2-day and 3-day shift – for variety:

“High” proton density days = 95th percentile, e.g., top 5%

Data Recap

• Proton Density Data: Combined from omni2_2020.dat.txt to omni2_2025.dat.txt, covering 1953 days (366 in 2020, 365 each for 2021–2024, 127 for 2025 up to May 7). Daily average proton density computed, excluding missing values.

• Earthquake Data: From NewQuery.csv.txt, filtered for M5.6+ earthquakes over the same period. Task 1: Forward Analysis (High Proton Density → M5.6+ Earthquake Likelihood) Methodology. This mirrors the previous forward analysis (Task 2 from your last request), but with 2-day and 3-day delays instead of

0-day and 1-day shifts:

1. Baseline Probability of M5.6+ Earthquakes:

• Total days: 1953.

• M5.6+ days: 1234.

• Baseline probability: 1234 / 1953 = 0.632.

2. High Proton Density Days (Top 5%):

• 95th percentile of daily average proton density (as used previously): 11.2 n/cm3.

• High proton density days: 98 days.

3. Observed Earthquake Rate:

• Check for M5.6+ earthquakes 2 days and 3 days after each high proton density day.

• Calculate the proportion of high proton density days followed by an M5.6+ earthquake.

4. Statistical Tests:

• Difference from Baseline: Compare the observed rate to the baseline.

• Probability Ratio: Observed rate / baseline rate.

• p-value: One-sample proportion test.

• R-value: Point-biserial correlation (high proton density: 1 for high, 0 for not high; M5.6+: 1 if occurs, 0

if not).

Results

2-Day Delay:

• High proton density days: 98 (excluding the last 2 days, May 6–7, 2025: 96).

• M5.6+ earthquakes 2 days later: 63.

• Observed rate: 63 / 96 = 0.656.

• Baseline: 0.632.

• Difference: +0.024.

• Probability Ratio: 0.656 / 0.632 = 1.038 (3.8% higher than baseline).

• p-value: 0.67.

• R-value: 0.03.

3-Day Delay:

• High proton density days: 98 (excluding the last 3 days, May 5–7, 2025: 95).

• M5.6+ earthquakes 3 days later: 61.

• Observed rate: 61 / 95 = 0.642.

• Baseline: 0.632.

• Difference: +0.010.

• Probability Ratio: 0.642 / 0.632 = 1.016 (1.6% higher than baseline).

• p-value: 0.85.

• R-value: 0.02.

Summary (Forward Analysis):

• Differences: The observed rate of M5.6+ earthquakes 2 days after high proton density days is +0.024 higher than the baseline, and +0.010 higher after 3 days.

• Probability Ratios: Earthquake likelihood is 3.8% higher after 2 days and 1.6% higher after 3 days.

• p-values: Both p-values (0.67 and 0.85) are above 0.05, indicating no significant difference.

• R-values: Correlation coefficients are low (0.02 to 0.03), suggesting a weak relationship.

Task 2: Reverse Analysis (M5.6+ Earthquake Days → Proton Density)

Methodology: This mirrors the previous reverse analysis (Task 1 from your last request), but with 2-day and 3-day delays:

1. Overall Average Proton Density:

• Mean daily proton density (1953 days): 6.3 n/cm3.

2. Proton Density Before M5.6+ Days:

• Identify M5.6+ earthquake days.

• Compute the average proton density 2 days and 3 days before those earthquake days.

3. Statistical Tests:

• Difference from Average: Compare the observed proton density to the overall average.

• Probability Ratio: Observed / expected proton density.

• p-value: t-test.

• R-value: Pearson correlation (M5.6+ occurrence: 1 if occurs, 0 if not; proton density: continuous).

Results

2 Days Before:

• M5.6+ days: 1234 (excluding the first 2 days, January 1–2, 2020: 1232).

• Average proton density 2 days before: 6.4 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.1.

• Probability Ratio: 6.4 / 6.3 = 1.016 (1.6% higher than expected).

• p-value: 0.69.

• R-value: 0.03.

3 Days Before:

• M5.6+ days: 1234 (excluding the first 3 days, January 1–3, 2020: 1231).

• Average proton density 3 days before: 6.4 n/cm3.

• Baseline: 6.3 n/cm3.

• Difference: +0.1.

• Probability Ratio: 6.4 / 6.3 = 1.016 (1.6% higher than expected).

• p-value: 0.71.

• R-value: 0.03.

Summary (Reverse Analysis):

• Differences: Proton density 2 days and 3 days before M5.6+ earthquake days is +0.1 higher than the overall average.

• Probability Ratios: Proton density is 1.6% higher for both time shifts.

• p-values: Both p-values (0.69 and 0.71) are above 0.05, indicating no significant difference.

• R-values: Correlation coefficients are low (0.03), suggesting a weak relationship.

Combined Results for Your Paper

Forward Analysis (High Proton Density → M5.6+ Earthquakes):

• 2-Day Delay: Observed rate 0.656 vs. baseline 0.632 (+0.024), probability ratio 1.038, p-value 0.67, R-value 0.03.

• 3-Day Delay: Observed rate 0.642 vs. baseline 0.632 (+0.010), probability ratio 1.016, p-value 0.85, R-value 0.02.

Reverse Analysis (M5.6+ Earthquake Days → Proton Density):

• 2 Days Before: Observed proton density 6.4 n/cm3 vs. baseline 6.3 (+0.1), probability ratio 1.016, p-value

0.69, R-value 0.03.

• 3 Days Before: Observed proton density 6.4 n/cm3 vs. baseline 6.3 (+0.1), probability ratio 1.016, p-value

0.71, R-value 0.03.

Interpretation:

• Weak Association: The results show a slight association—earthquake rates are 1.6–3.8% higher 2–3 days after

high proton density days (top 5%), and proton density is 1.6% higher 2–3 days before M5.6+ earthquakes. The 2-day delay shows a slightly stronger effect in the forward direction (+0.024 vs. +0.010 for 3 days).

• Statistical Significance: p-values (0.67 to 0.85) are above 0.05, indicating no significant correlation; the differences are likely due to chance.

• Correlation Strength: R-values (0.02 to 0.03) suggest a very weak relationship, with no clear trend as the delay increases from 2 to 3 days.

• Comparison to Previous Analyses: The 2-day delay (+0.024) is less pronounced than the 1-day delay (+0.059)

from the previous analysis, and the 3-day delay (+0.010) is even weaker. This suggests that slower CMEs (2–3 days) don’t show a stronger correlation in this dataset.

Recommendations for Your Paper

• Report the Findings: Over 2020–2025, high proton density days (top 5%) show a 1.6–3.8% higher M5.6+ earthquake rate 2–3 days later, and proton density is 1.6% higher 2–3 days before M5.6+ earthquakes. However, these differences are not statistically significant (p-values 0.67–0.85, R-values 0.02–0.03).

• Discuss Slower CMEs: While you hypothesized that slower CMEs (2–3 day delays) might show a stronger effect, the correlation weakens compared to the 1-day delay (+0.059 from the last analysis), suggesting that any delayed effect may peak closer to 1 day rather than 2–3 days.

• Tie to Solar Flares and CMEs: Note that proton density spikes often follow flares and CMEs (e.g., the X9.0 flare on October 3, 2024, with proton density rising to 12.5 n/cm3 on October 4, followed by an M6.2 earthquake on October 4). The weaker correlation at longer delays suggests that slower CMEs may have less geophysical impact in this context.

*** END of BLOCK Copy/Paste response for the eight (8) analyses discussed above ***

My notes for this day (** Analysis 7: Sat 10 May 2025 _ 02:48 pm ET chat with GROK) say as follows: “GORDON: “Hey, Grok, I'm gonna give it "one last" try to see if any correlations exist between proton density and earthquake frequency. Please, this time, look at earthquakes with Mag 4 or greater for the 5½ or so year period...please look at the 95th percentile (top 5%) of proton density,” however, these results were already reported above, (** Analysis 6: Thr 08 May 2025 _ 09:43 pm ET chat with GEMINI and GROK), where p-values of 0.98, 0.72, 0.82, and 0.83 were reported – so I shall omit them in this section, as they're reported elsewhere. I think that when making notes I accidentally duplicated these findings for redundancy – to ensure I'd have a copy of the results. We may safely ignore—and proceed with caution.

** To be very thorough, I then ask Grok to use Mag 4.0+ only as the threshold and look at both “same day” and “1-day shift” – and both forward and reverse (total of just 4 analyses) – including the same 1-day time shift that Marchitelli used – but for the 2024 and 2025 dataset alone (just 1½ years) – to see if smaller quakes are associated with solar weather.

** “High” proton density days = 95th percentile, e.g., top 5% which might be more likely to show an effect if one exists – and limit the number of data points to review.

Task 1: Compare Average Proton Density on M4.0+ Days to Overall (E.g., a 'reverse' analysis)

Methodology

1. Overall Average Proton Density:

• Compute the mean daily proton density across all 492 days.

2. Proton Density on M4.0+ Days:

• Identify days with at least one M4.0+ earthquake.

• Compute the average proton density on those days (same day) and the previous day (1-day shift).

3. Statistical Tests:

• Difference from Average: Observed minus overall average.

• Probability Ratio: Observed / expected proton density.

• p-value: t-test to compare means.

• R-value: Pearson correlation (M4.0+ occurrence: 1 if occurs, 0 if not; proton density: continuous).

Results

Overall Average (Mean) daily proton density (492 days): 7.2 n/cm3 (matches Gemini’s 7.2 protons/cm3).

M4.0+ Earthquake Days:

• Total M4.0+ days: 475 days (out of 492). This high frequency is expected for M4.0+ events.

• Baseline probability of an M4.0+ day: 475 / 492 = 0.965. (Editor's Note: Gemini thought this was high.)

Same Day:

• Average proton density on M4.0+ days: 7.3 n/cm3. (Difference: +0.1)

• Probability Ratio: 7.3 / 7.2 = 1.014 (1.4% higher than expected).

• t-test: Degrees of freedom: 492 - 2 = 490 (approximated as in Gemini’s 740, which seems incorrect for 492

days; they may have used a different method).

• p-value: 0.66.

• R-value (Pearson correlation): 0.03.

Previous Day (1-Day Shift):

• M4.0+ days: 475 (excluding the first day, January 1, 2024: 474).

• Average proton density on the previous day: 7.4 n/cm3. (Difference: +0.2.)

• Probability Ratio: 7.4 / 7.2 = 1.028 (2.8% higher than expected).

• t-test: Degrees of freedom: 490.

• p-value: 0.52.

• R-value: 0.04.

Comparison to Gemini (Task 1):

• Same Day:

• My results: 7.3 n/cm3 vs. 7.2 (+0.1), p-value 0.66, R-value 0.03.

• Gemini: 7.5 n/cm3 vs. 7.2 (+0.3), p-value 0.004, R-value 0.11.

• Discrepancy: My proton density is lower (7.3 vs. 7.5), and I find no statistical significance (p-value

0.66 vs. 0.004). My R-value is much weaker (0.03 vs. 0.11).

• Previous Day:

• My results: 7.4 n/cm3 vs. 7.2 (+0.2), p-value 0.52, R-value 0.04.

• Gemini: 7.3 n/cm3 vs. 7.2 (+0.1), p-value 0.05, R-value 0.07.

• Discrepancy: My proton density is slightly higher (7.4 vs. 7.3), but again, I find no significance (pvalue

0.52 vs. 0.05), and my R-value is weaker (0.04 vs. 0.07).

Task 2: Compare M4.0+ Earthquake Rates on High Proton Density Days (Top 5%) to Baseline (E.g., a 'forward' analysis)

Methodology

1. Baseline Probability of M4.0+ Earthquakes:

• Already calculated: 0.965.

2. High Proton Density Days (Top 5%):

• Compute the 95th percentile of daily average proton density.

• Identify high proton density days.

3. Observed Earthquake Rate:

• Check for M4.0+ earthquakes on the same day and the next day.

• Calculate the proportion of high proton density days followed by an M4.0+ earthquake.

4. Statistical Tests:

• Difference from Baseline: Observed rate minus baseline.

• Probability Ratio: Observed / baseline.

• p-value: One-sample proportion test.

• R-value: Point-biserial correlation.

Results

High Proton Density Threshold:

• 95th percentile of daily average proton density (492 days): 9.4 n/cm3.

• Note: Gemini reported 16.5 protons/cm3, which is significantly higher. The 95th percentile for 492 days should

reflect the top 5% (492 × 0.05 ≈ 25 days). My calculation (9.4 n/cm3) is consistent with the distribution of

proton density values in the OMNI2 files, while 16.5 seems anomalously high and may indicate an error in

Gemini’s percentile calculation.

• High proton density days: 25 days.

Same Day:

• High proton density days: 25.

• M4.0+ earthquakes on the same day: 24.

• Observed rate: 24 / 25 = 0.960. (Difference: -0.005.)

• Probability Ratio: 0.960 / 0.965 = 0.995 (0.5% lower than baseline).

• p-value: 0.89.

• R-value: -0.01.

Next Day (1-Day Shift):

• High proton density days: 25 (excluding the last day, May 7, 2025: 24).

• M4.0+ earthquakes on the next day: 23.

• Observed rate: 23 / 24 = 0.958. (Difference: -0.007.)

• Probability Ratio: 0.958 / 0.965 = 0.993 (0.7% lower than baseline).

• p-value: 0.87.

• R-value: -0.02.

Comparison to Gemini (Task 2):

• Same Day:

• My results: Observed rate 0.960 vs. 0.965 (-0.005), probability ratio 0.995, p-value 0.89, R-value -0.01.

• Gemini: Observed rate 0.75 vs. 0.73 (+0.02), probability ratio 1.03, p-value 0.49, R-value 0.03.

• Discrepancy: My baseline (0.965) is much higher than Gemini’s (0.73), likely because I correctly counted M4.0+ days (475 / 492 = 0.965), while Gemini’s 0.73 suggests a miscalculation (possibly counting individual earthquakes, 1331, instead of days). My observed rate is slightly lower than the baseline, while Gemini’s is higher, but neither result is significant.

• Next Day:

• My results: Observed rate 0.958 vs. 0.965 (-0.007), probability ratio 0.993, p-value 0.87, R-value -0.02.

• Gemini: Observed rate 0.71 vs. 0.73 (-0.02), probability ratio 0.97, p-value 0.52, R-value -0.03.

• Discrepancy: Again, the baseline difference drives the mismatch. My results show a slight decrease in probability, consistent with the same-day findings, while Gemini’s show a decrease but with a much lower baseline.

*** END of BLOCK Copy/Paste response for the eight (8) analyses discussed above ***

** Analysis 8: Sat 10 May 2025 _ 06:22 pm ET chat with GROK

To be EXCEEDINGLY thorough, I ask Grok to analyze a fifty-two (52) year period – even longer than the period Marchitelli et al. reviewed (my analysis: 1-1-1973 to 5-10-2025) for M5.6+ and define “High Proton Density Days” as the top 5%, e.g., the 95th percentile of daily proton density, excluding missing values of “999.9,” which are important for accurate calculation.

GORDON: Good news: https://contractwithamerica2.com/FannyDeregulation/SolarWeather/Txt_FileFormat_Quakes_5.6-or-greater_1-1-1973_to_5-10-2025.csv.txt is a link to a text format dataset of 5.6+ Mag quakes from 1-1-1973 to today, Saturday, 10 May 2025, and https://contractwithamerica2.com/FannyDeregulation/SolarWeather/omni2_daily_1c8u4kNMil.lst.txt is a daily proton density reading from the OMNI 2 satellite in this format:

FORMAT OF THE SUBSETTED FILE

ITEMS FORMAT

1 YEAR I4

2 DOY I4

3 Hour I3

4 SW Proton Density, N/cm^3 F6.1

GROK 3.0: This is fantastic news, Gordon! You’ve successfully provided links to both the earthquake data and the OMNI2 solar proton density data, and I can access both files. The earthquake data appears to be a duplicate of the file you shared earlier, but the OMNI2 file is new and contains daily proton density readings, which is exactly what we need for the analysis. Let’s inspect both files, confirm their contents, and proceed with the correlation analysis.

Task 1: Compare Average Proton Density on M5.6+ Days to Overall Average

Results

BASELINES – Overall Average Proton Density:

Total days with valid data: 18,750 (out of 19,046; 296 days have missing values, mostly in 1973–1975).

Sum of proton densities (excluding missing values): 121,875 n/cm³.

Mean: 121,875 / 18,750 = 6.5 n/cm³.

Same Day:

M5.6+ days with valid proton density: 12,152 (out of 12,345; 193 days have missing proton density).

Average proton density on M5.6+ days: 6.6 n/cm³.

Baseline: 6.5 n/cm³.

Difference: +0.1.

Probability Ratio: 6.6 / 6.5 = 1.015 (1.5% higher than expected).

p-value (t-test): 0.68.

R-value (Pearson correlation): 0.02.

Previous Day (1-Day Shift):

M5.6+ days: 12,345 (excluding the first day, January 1, 1973: 12,344).

Days with valid proton density on the previous day: 12,150.

Average proton density on the previous day: 6.7 n/cm³.

Baseline: 6.5 n/cm³.

Difference: +0.2.

Probability Ratio: 6.7 / 6.5 = 1.031 (3.1% higher than expected).

p-value: 0.55.

R-value: 0.04.

Task 2: Compare M5.6+ Earthquake Rates on High Proton Density Days (Top 5%) to Baseline

Results

High Proton Density Threshold:

95th percentile of daily proton density (18,750 valid days): 12.8 n/cm³.

Number of high proton density days (top 5% of 18,750): 938 days.

Same Day:

High proton density days: 938.

M5.6+ earthquakes on the same day: 615.

Observed rate: 615 / 938 = 0.656.

Baseline: 0.648.

Difference: +0.008.

Probability Ratio: 0.656 / 0.648 = 1.012 (1.2% higher than baseline).

p-value: 0.76.

R-value: 0.02.

Next Day (1-Day Shift):

High proton density days: 938 (excluding the last day, May 10, 2025: 937).

M5.6+ earthquakes on the next day: 622.

Observed rate: 622 / 937 = 0.664.

Baseline: 0.648.

Difference: +0.016.

Probability Ratio: 0.664 / 0.648 = 1.025 (2.5% higher than baseline).

p-value: 0.61.

R-value: 0.03.

*** END of BLOCK Copy/Paste response for Grok's 52-year period analyses discussed above ***

** Analysis 9: Sun 11 May 2025 _ 04:26 pm ET chat with GEMINI

To be EXCEEDINGLY thorough, I, now, also ask Gemini to analyze a fifty-two (52) year period – even longer than the period Marchitelli et al. reviewed:

GEMINI.GOOGLE.COM: Yes, I have completed the statistical analysis and have the results ready to share. I've calculated the p-values, R-values, probability ratios, and the total numbers of events, including the "999" entries.

Here's a summary of my findings:

Data Overview

Date Range: 1-1-1973 to 5-10-2025

Total Days: 19,137

Total Solar Data Points: 19,137 (including "999.9" entries)

Number of "999.9" Solar Data Entries: 1,731

Number of Earthquakes (Mag 5.6+): 1,189

Analysis 1: Same Day - High Proton Density vs. Earthquake Frequency

High Proton Density Threshold (95th Percentile): 18.0 n/cm³

Number of High Proton Density Days: 957

Number of Earthquake Days: 1,061

Number of High Proton Density Days with Earthquakes: 54

Baseline Probability of Earthquake on Any Day: 1061 / 19137 = 0.055

Probability of Earthquake on High Proton Density Day: 54 / 957 = 0.056

Probability Ratio: 0.056 / 0.055 = 1.02

R-value: 0.003

p-value: 0.81

Analysis 2: One-Day Shift - High Proton Density vs. Earthquake Frequency

High Proton Density Threshold (95th Percentile): 18.0 n/cm³

Number of High Proton Density Days: 957

Number of Earthquake Days: 1,061

Number of High Proton Density Days preceding Earthquake Days: 52

Baseline Probability of Earthquake on Any Day: 0.055

Probability of Earthquake on Day after High Proton Density Day: 52 / 957 = 0.054

Probability Ratio: 0.054 / 0.055 = 0.98

R-value: -0.002

p-value: 0.86

Analysis 3: Same Day - Earthquake Frequency vs. Average Proton Density

Average Proton Density on All Days: 7.6 n/cm³

Average Proton Density on Earthquake Days: 7.7 n/cm³

Difference in Average Proton Density: 0.1 n/cm³

R-value: 0.003

p-value: 0.77

Note: I used a t-test to calculate the p-value here.

Analysis 4: One-Day Shift - Earthquake Frequency vs. Average Proton Density

Average Proton Density on All Days: 7.6 n/cm³

Average Proton Density on Days before Earthquake Days: 7.6 n/cm³

Difference in Average Proton Density: 0.0 n/cm³

R-value: -0.001

p-value: 0.92

Note: I used a t-test to calculate the p-value here.

Key Observations

Data Completeness: The total number of solar data points matches the expected number of

days, confirming the data's completeness.

High Proton Density Threshold: The 95th percentile for proton density is 18.0 n/cm³.

Probability Ratios: The probability ratios are very close to 1 in both the same-day and one-day shift analyses, indicating that high proton density days do not significantly alter the probability of earthquakes.

R-values: The R-values are extremely close to 0 in all four analyses, indicating no meaningful linear correlation between proton density and earthquake occurrence.

p-values: The p-values are all far greater than 0.05, indicating that the observed differences are not statistically significant.

Preliminary Conclusion

Based on my analysis, there is no statistically significant correlation between solar proton density and the occurrence of magnitude 5.6+ earthquakes in this dataset.

*** END of BLOCK Copy/Paste response for Gemini's 52-year period analyses discussed above ***

NOTE: Gemini and I compared his findings with Grok, and one mistake Gemini made – reading the “999.9” values as measurements (instead of missing data points” resulted in his 95TH percentile proton density being wrong initially, until I caught his mistake, and then he agreed with Grok's calculation:

BEGIN COPY/PASTE of selected Gemini response under Fair Use:

GEMINI: Here's an updated comparison table Gemini provided me, mostly accurate except for misquoting what I had told him that Grok said on one p-Value finding – see below for details.

Export to Sheets

Key Observations and Improvements

• 95th Percentile Alignment: My revised analysis now matches Grok's result for the 95th percentile (12.8 n/cm³). This is a significant improvement and suggests that excluding the "999.9" values was crucial.

• Probability Ratios: The probability ratios are now closer to 1, indicating a weaker relationship between high proton density and earthquake occurrence.

• R-values and p-values: The R-values remain very low, and the p-values remain high, reinforcing the conclusion of no significant correlation.

• Differences with Grok: There are still some differences between my results and Grok's, particularly in the total number of days, missing solar data entries, and the number of earthquakes.

I believe the revised analysis is much more accurate. Thank you again for pointing out the potential error in handling the "999.9" values.

*** END of BLOCK Copy/Paste response for Gemini's 52-year period comparison response ***

** Analysis 10: Tue 13 May 2025 _ 02:07 am ET chat with ClaudeAI. GEMINI, and Grok 3.0

First, I try out the free version of Claude AI, and here are the results:

GORDON: (uploaded 2 files)

ClaudeAI: Conversation is 5877% over the length limit. Try replacing the attached files with smaller excerpts.

GORDON: Hey, I get this error: "Conversation is 5875% over the length limit. Try replacing the attached files with smaller excerpts." I want help doing statistical analysis of 2 datasets. Should I provide a link instead?

ClaudeAI: (was unable to handle my files, as too large)

FINALLY – I ask both Gemini and Grok to look at M5.6+ quake activity versus solar proton density – with a “new” twist: calculate the threshold for the 99TH Percentile (e.g., the top 1%) of proton density days, and make sure it's a full 52-year period from 1-1-1973 until 1-10-2025, so only “strong” photon effects are considered over a large time period – to help maximize the chances of finding a correlation. I ask them both to run these 4 analyses, in both directions:

1) Chi-squared test for association;

2) T-test and Wilcoxon rank-sum tests to compare mean and median;

3) Correlation analyses, obtaining Pearson and Spearman correlation coefficients to examine the possibility of

a relationship both ways;

4) Logistic regression to model probability of each variable when knowing the other.

GEMINI: Defined “top 1%” proton density as than or equal to 29.8 n/cm^3

Direction 1: Influence of High Proton Density on Earthquakes

Chi-Squared Chi2 Statistic: 1.05

Chi-Squared p-value: 0.305

T-test t-statistic: 0.29

T-text p-value: 0.772

Wilcoxon Rank-Sum Test W-statistic: 9514781.0

Wilcoxon Rank-Sum Test: p-value: 0.730

Pearson Correlation Coefficient: R-value = 0.003

Spearman Correlation Coefficient: R-value = 0.002

Logistic Regression: Coefficient for is_high_proton_day : -0.17

Odds (Probably) Ratio: 0.84

Logistic Regression: p-value: 0.304

Probability Ratio (Observed quake probability on high density days / average quake probability): 0.96

Direction 2: Influence of Earthquakes on Proton Density

Chi-Squared Chi2 Statistic: 1.05

Chi-Squared p-value: 0.305

T-test t-statistic: 0.29

T-text p-value: 0.772

Wilcoxon Rank-Sum Test W-statistic: 147551.0

Wilcoxon Rank-Sum Test: p-value: 0.730

Pearson Correlation Coefficient: R-value = 0.003

Spearman Correlation Coefficient: R-value = 0.002

Logistic Regression: Coefficient for is_high_proton_day : -0.17

Odds (Probably) Ratio: 0.84

Logistic Regression: p-value: 0.304

Probability Ratio (Observed quake probability on high density days / average quake probability): 0.96

GROK: Defined “top 1” proton density as 16.5 n/cm³ or greater. (Note: Gemini was much higher, suggesting he misread the “999.9” data points.) High proton density days: 187 days with proton density ≥ 16.5 n/cm³.

USGS Earthquake Data (Date Range: January 1, 1973, to May 9, 2025, last event). Events: 26,162 for M5.6+ earthquakes. Unique Days: 12,345 days with at least one M5.6+ earthquake (out of 19,045 days). Thus: Baseline Probability: 12,345 / 19,045 = 0.648.

Statistical Analyses in Both Directions

Direction 1: Are There More M5.6+ Earthquakes on High Proton Density Days (Top 1%)?

Definition: High proton density days = top 1% (187 days, proton density ≥ 16.5 n/cm³).

Baseline Probability: 0.648 (12,345 / 19,045).

Observed:

High proton density days: 187.

M5.6+ earthquakes on those days: 123.

Observed rate: 123 / 187 = 0.658.

1. Chi-Squared Test for Association

Contingency Table:

High proton density & M5.6+: 123 days.

High proton density & No M5.6+: 64 days.

Not high proton density & M5.6+: 12,222 days.

Not high proton density & No M5.6+: 6,340 days.

Chi-Squared Statistic: 0.14.

p-value: 0.71.

Interpretation: No significant association (p > 0.05).

2. T-Test and Wilcoxon Rank-Sum Test

T-Test: Compare the proportion of M5.6+ days (0.658) to the baseline (0.648).

p-value: 0.78.

Wilcoxon Rank-Sum Test: Compare the binary occurrence (1 for M5.6+, 0 for no M5.6+) on high vs. non-high proton density days.

p-value: 0.75.

Interpretation: No significant difference in means or medians (p > 0.05).

3. Correlation Analysis

Pearson Correlation: Between binary variables (high proton density: 1 if top 1%, 0 otherwise; M5.6+: 1 if occurs, 0 otherwise).

R-value: 0.03.

p-value: 0.72.

Spearman Correlation: Same binary variables.

R-value: 0.03.

p-value: 0.72.

Interpretation: Very weak correlation, not significant (p > 0.05).

4. Logistic Regression

Model: Predict M5.6+ occurrence (1/0) based on high proton density (1/0).

Coefficient: 0.05 (log-odds).

p-value: 0.69.

Interpretation: High proton density is not a significant predictor of M5.6+ occurrence (p > 0.05).

Additional Metrics (Requested):

p-value: 0.71 (from chi-squared test).

R-value: 0.03 (from Pearson correlation).

Probability Ratio: 0.658 / 0.648 = 1.015 (1.5% higher than baseline).

Direction 2: Is Proton Density Higher on M5.6+ Earthquake Days?

Overall Average Proton Density: 6.5 n/cm³ (18,749 valid days).

M5.6+ Days:

Days with valid proton density: 12,152.

Average proton density: 6.6 n/cm³.

1. Chi-Squared Test for Association

Contingency Table: Same as above, reversed perspective.

Chi-Squared Statistic: 0.14.

p-value: 0.71 (same as Direction 1, as chi-squared is symmetric).

Interpretation: No significant association.

2. T-Test and Wilcoxon Rank-Sum Test

T-Test: Compare mean proton density on M5.6+ days (6.6) vs. non-M5.6+ days (6.4).

p-value: 0.62.

Wilcoxon Rank-Sum Test: Compare distributions of proton density.

p-value: 0.65.

Interpretation: No significant difference in means or medians (p > 0.05).

3. Correlation Analysis

Pearson Correlation: Between proton density (continuous) and M5.6+ occurrence (1/0).

R-value: 0.03.

p-value: 0.63.

Spearman Correlation: Same variables.

R-value: 0.03.

p-value: 0.64.

Interpretation: Very weak correlation, not significant.

4. Logistic Regression

Model: Predict high proton density (1/0) based on M5.6+ occurrence (1/0).

Coefficient: 0.04.

p-value: 0.70.

Interpretation: M5.6+ occurrence is not a significant predictor of high proton density (p > 0.05).

Additional Metrics (Requested):

p-value: 0.62 (from t-test).

R-value: 0.03 (from Pearson correlation).

Probability Ratio: 6.6 / 6.5 = 1.015 (1.5% higher than baseline).

Grok suggested I report these results: “Combined Results for Your Paper

Direction 1: M5.6+ Earthquake Rates on High Proton Density Days (Top 1%):

Chi-Squared Test: p-value 0.71.

T-Test: p-value 0.78.

Wilcoxon Test: p-value 0.75.

Pearson Correlation: R-value 0.03, p-value 0.72.

Spearman Correlation: R-value 0.03, p-value 0.72.

Logistic Regression: p-value 0.69.

Additional Metrics:

Observed rate: 0.658 vs. baseline 0.648 (+0.010).

Probability Ratio: 1.015 (1.5% higher).

p-value: 0.71, R-value: 0.03.

Direction 2: Proton Density on M5.6+ Earthquake Days:

Chi-Squared Test: p-value 0.71.

T-Test: p-value 0.62.

Wilcoxon Test: p-value 0.65.

Pearson Correlation: R-value 0.03, p-value 0.63.

Spearman Correlation: R-value 0.03, p-value 0.64.

Logistic Regression: p-value 0.70.

Additional Metrics:

Observed proton density: 6.6 n/cm³ vs. baseline 6.5 (+0.1).

Probability Ratio: 1.015 (1.5% higher).

p-value: 0.62, R-value: 0.03.”

******* END of Data Dump *******

Compiled data chart of statistical analyses by Gemini (Google AI) and Grok 3.0 (by xAi) using data from OMNI2 (by NASA) and Quakes (by USGS) to look for statistically significant correlation in both directions between solar proton density and seismic (quake) activity – Four charts (A, B, C, & D) for different time frames. NOTE: If shift is other than “zero days” (same day), then solar photon density is EARLIER and quake data LATER, as quakes don't cause solar proton density.

Key and definitions:

* “Forward” analysis asks: “Is a 'high' proton density associated with (perhaps a cause of) “higher than baseline” (e.g., 'more') earthquakes?”

* “Reverse” analysis asks: “Are earthquakes associated with (perhaps caused by) “higher than baseline” (e.g., 'more') proton density?”

* NOTE on ordering of time-shift: When a 1-day shift, etc., is mentioned, this ALWAYS refers to the solar proton density data as being BEFORE the seismic data because it is untenable to assume a mechanism where earthquakes cause a change in solar proton density. Thus, if any statistically-significant “cause and effect” correlation is observed, it is inferred as solar weather having an effect on quake activity – NOT the other way around.

* NOTE on definition: “High” proton density is defined differently in each analysis – such as top 25%, top 5%, or top 1%.

** Analysis 1: Wed 07 May 2025 _ 06:00 pm ET chat with GEMINI

** Analysis 2: Wed 07 May 2025 _ 11:21 pm ET chat with GEMINI

** Analysis 3: Wed 07 May 2025 _ 11:39 pm ET chat with GEMINI

** Analysis 4: Thr 08 May 2025 _ 06:25 am ET chat with GEMINI (Grok makes a cameo appearance)

** Analysis 5: Thr 08 May 2025 _ 08:33 am ET chat with GEMINI (slow-needed more time-so I asked Grok)

** Analysis 6: Thr 08 May 2025 _ 09:43 pm ET chat with GEMINI and GROK

** Analysis 7: Sat 10 May 2025 _ 02:48 pm ET chat with GROK

** Analysis 8: Sat 10 May 2025 _ 06:22 pm ET chat with GROK

** Analysis 9: Sun 11 May 2025 _ 04:26 pm ET chat with GEMINI

** Analysis 10: Tue 13 May 2025 _ 02:07 am ET chat with ClaudeAI. GEMINI, and Grok 3.0