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The claimed $\tau = +15$~d (grey dashed line) shows $r_\text {raw} = 0.079$ vs.\ $r_\text {partial} = 0.029$, a 63\% reduction once the shared solar-cycle component is regressed out.\relax }{figure.caption.21}{}} \@writefile{toc}{\contentsline {paragraph}{Mutual information.}{23}{section*.23}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {4.11}Missing-Data Sensitivity}{23}{subsection.4.11}\protected@file@percent } \newlabel{sec:res:missing}{{4.11}{23}{Missing-Data Sensitivity}{subsection.4.11}{}} \@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces \textbf {Left}: Magnitude-squared coherence between the CR index and seismic metric (blue), with the solar-cycle band shaded (orange, 0.08--0.115 cycles\nobreakspace {}yr$^{-1}$) and the 95\% significance level (red dashed). The mean coherence in the SC band is 0.840, confirming a strong shared solar-cycle component. \textbf {Right}: kNN mutual information ($k = 5$) at lag $\tau = 0$ (blue) and $\tau = +15$\nobreakspace {}d (orange) vs.\ their respective shuffle-null distributions. Both observed MI values are indistinguishable from zero; $p(+15\,\text {d}) = 1.000$.\relax }}{24}{figure.caption.24}\protected@file@percent } \newlabel{fig:coherence}{{11}{24}{\textbf {Left}: Magnitude-squared coherence between the CR index and seismic metric (blue), with the solar-cycle band shaded (orange, 0.08--0.115 cycles~yr$^{-1}$) and the 95\% significance level (red dashed). The mean coherence in the SC band is 0.840, confirming a strong shared solar-cycle component. \textbf {Right}: kNN mutual information ($k = 5$) at lag $\tau = 0$ (blue) and $\tau = +15$~d (orange) vs.\ their respective shuffle-null distributions. Both observed MI values are indistinguishable from zero; $p(+15\,\text {d}) = 1.000$.\relax }{figure.caption.24}{}} \@writefile{lot}{\contentsline {table}{\numberline {5}{\ignorespaces Missing-data sensitivity: global CR index and correlation at $\tau = +15$\nobreakspace {}days for three station-threshold values.\relax }}{24}{table.caption.25}\protected@file@percent } \newlabel{tab:missing}{{5}{24}{Missing-data sensitivity: global CR index and correlation at $\tau = +15$~days for three station-threshold values.\relax }{table.caption.25}{}} \citation{GardnerKnopoff1974} \@writefile{toc}{\contentsline {subsection}{\numberline {4.12}Bin-Size Sensitivity}{25}{subsection.4.12}\protected@file@percent } \newlabel{sec:res:binsize}{{4.12}{25}{Bin-Size Sensitivity}{subsection.4.12}{}} \@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Cross-correlation $r(\tau )$ for three bin sizes: 1-day (left), 5-day (centre), 27-day (right). The dominant peak (red dotted) consistently falls near $\tau \approx -520$\nobreakspace {}days across all bin sizes. The correlation at the claimed $\tau = +15$\nobreakspace {}days (grey dashed) increases from 0.036 to 0.123 as bin size increases, consistent with increasing solar-cycle leakage rather than a physical short-lag signal.\relax }}{25}{figure.caption.26}\protected@file@percent } \newlabel{fig:binsize}{{12}{25}{Cross-correlation $r(\tau )$ for three bin sizes: 1-day (left), 5-day (centre), 27-day (right). The dominant peak (red dotted) consistently falls near $\tau \approx -520$~days across all bin sizes. The correlation at the claimed $\tau = +15$~days (grey dashed) increases from 0.036 to 0.123 as bin size increases, consistent with increasing solar-cycle leakage rather than a physical short-lag signal.\relax }{figure.caption.26}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.13}Earthquake Declustering (Gardner--Knopoff)}{25}{subsection.4.13}\protected@file@percent } \newlabel{sec:res:decluster}{{4.13}{25}{Earthquake Declustering (Gardner--Knopoff)}{subsection.4.13}{}} \@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Cross-correlation for the full catalogue ($n = 232{,}043$ events, blue) and the Gardner--Knopoff declustered catalogue ($n = 166{,}169$ mainshocks, orange), in-sample 1976--2019. Removing 28.4\% of events as aftershocks changes $r(+15\,\text {d})$ by only $\Delta r = 0.014$, confirming the result is not driven by aftershock swarms.\relax }}{26}{figure.caption.27}\protected@file@percent } \newlabel{fig:decluster}{{13}{26}{Cross-correlation for the full catalogue ($n = 232{,}043$ events, blue) and the Gardner--Knopoff declustered catalogue ($n = 166{,}169$ mainshocks, orange), in-sample 1976--2019. Removing 28.4\% of events as aftershocks changes $r(+15\,\text {d})$ by only $\Delta r = 0.014$, confirming the result is not driven by aftershock swarms.\relax }{figure.caption.27}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.14}Sub-Period Analysis by Solar Cycle}{26}{subsection.4.14}\protected@file@percent } \newlabel{sec:res:subcycles}{{4.14}{26}{Sub-Period Analysis by Solar Cycle}{subsection.4.14}{}} \@writefile{lot}{\contentsline {table}{\numberline {6}{\ignorespaces Per-solar-cycle cross-correlation at $\tau = +15$\nobreakspace {}days and the within-cycle dominant peak.\relax }}{26}{table.caption.28}\protected@file@percent } \newlabel{tab:subcycles}{{6}{26}{Per-solar-cycle cross-correlation at $\tau = +15$~days and the within-cycle dominant peak.\relax }{table.caption.28}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.15}Geographic Localisation}{26}{subsection.4.15}\protected@file@percent } \newlabel{sec:res:geo}{{4.15}{26}{Geographic Localisation}{subsection.4.15}{}} \@writefile{lof}{\contentsline {figure}{\numberline {14}{\ignorespaces Cross-correlation $r(\tau )$ within each of the four complete solar cycles (21--24) of the in-sample period (1976--2019). The claimed lag $\tau = +15$\nobreakspace {}days (grey dashed) shows modest positive correlations (0.018--0.073), but the dominant peak lag (red dotted) is inconsistent across cycles ($-65$, $-125$, $+125$, $-125$\nobreakspace {}days), pointing to a drift in the relative solar-cycle phase rather than a physical mechanism.\relax }}{27}{figure.caption.29}\protected@file@percent } \newlabel{fig:subcycles}{{14}{27}{Cross-correlation $r(\tau )$ within each of the four complete solar cycles (21--24) of the in-sample period (1976--2019). The claimed lag $\tau = +15$~days (grey dashed) shows modest positive correlations (0.018--0.073), but the dominant peak lag (red dotted) is inconsistent across cycles ($-65$, $-125$, $+125$, $-125$~days), pointing to a drift in the relative solar-cycle phase rather than a physical mechanism.\relax }{figure.caption.29}{}} \@writefile{lof}{\contentsline {figure}{\numberline {15}{\ignorespaces Heatmap of BH-significant station--grid-cell pairs ($q = 0.05$). Each row is an NMDB station; each column is a $10° \times 10°$ seismic grid cell. Significant pairs (455/7{,}037) are scattered without obvious geographic clustering, inconsistent with a local coupling mechanism.\relax }}{28}{figure.caption.30}\protected@file@percent } \newlabel{fig:geoheatmap}{{15}{28}{Heatmap of BH-significant station--grid-cell pairs ($q = 0.05$). Each row is an NMDB station; each column is a $10° \times 10°$ seismic grid cell. Significant pairs (455/7{,}037) are scattered without obvious geographic clustering, inconsistent with a local coupling mechanism.\relax }{figure.caption.30}{}} \@writefile{lof}{\contentsline {figure}{\numberline {16}{\ignorespaces Optimal lag $\tau ^*(s,g)$ vs.\ great-circle distance $d(s,g)$ for all 7{,}037 station--cell pairs (grey) and BH-significant pairs (coloured by peak $|r|$). The OLS regression line (red) has slope $\beta = -0.45$\nobreakspace {}days/1000\,km ($p=0.21$), indistinguishable from zero. A local propagation or diffusion mechanism predicts a positive slope; the null result is inconsistent with such models but does not exclude globally instantaneous coupling.\relax }}{28}{figure.caption.31}\protected@file@percent } \newlabel{fig:geodistlag}{{16}{28}{Optimal lag $\tau ^*(s,g)$ vs.\ great-circle distance $d(s,g)$ for all 7{,}037 station--cell pairs (grey) and BH-significant pairs (coloured by peak $|r|$). The OLS regression line (red) has slope $\beta = -0.45$~days/1000\,km ($p=0.21$), indistinguishable from zero. A local propagation or diffusion mechanism predicts a positive slope; the null result is inconsistent with such models but does not exclude globally instantaneous coupling.\relax }{figure.caption.31}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.16}Pre-Registered Out-of-Sample Validation (2020--2025)}{29}{subsection.4.16}\protected@file@percent } \newlabel{sec:res:oos}{{4.16}{29}{Pre-Registered Out-of-Sample Validation (2020--2025)}{subsection.4.16}{}} \@writefile{lof}{\contentsline {figure}{\numberline {17}{\ignorespaces Out-of-sample cross-correlation function (2020--2025, $T=390$ bins, $10^5$ phase surrogates). The observed $r(\tau )$ (black) lies within the surrogate 95th-percentile envelope (grey shading). The claimed signal at $\tau = +15$\nobreakspace {}d (vertical line) is $r = 0.030$ --- below the surrogate 95th percentile of 0.101.\relax }}{29}{figure.caption.32}\protected@file@percent } \newlabel{fig:oosxcorr}{{17}{29}{Out-of-sample cross-correlation function (2020--2025, $T=390$ bins, $10^5$ phase surrogates). The observed $r(\tau )$ (black) lies within the surrogate 95th-percentile envelope (grey shading). The claimed signal at $\tau = +15$~d (vertical line) is $r = 0.030$ --- below the surrogate 95th percentile of 0.101.\relax }{figure.caption.32}{}} \@writefile{lot}{\contentsline {table}{\numberline {7}{\ignorespaces Pre-registered prediction scorecard for the out-of-sample window.\relax }}{29}{table.caption.33}\protected@file@percent } \newlabel{tab:prereg}{{7}{29}{Pre-registered prediction scorecard for the out-of-sample window.\relax }{table.caption.33}{}} \@writefile{lof}{\contentsline {figure}{\numberline {18}{\ignorespaces Rolling $r(+15\,\text {d})$ in 18-month overlapping windows across the out-of-sample period. Error bars are bootstrap 95\% confidence intervals. The grey horizontal band shows the surrogate 95th percentile. The signal shows no consistent sign or trend.\relax }}{30}{figure.caption.34}\protected@file@percent } \newlabel{fig:rolling}{{18}{30}{Rolling $r(+15\,\text {d})$ in 18-month overlapping windows across the out-of-sample period. Error bars are bootstrap 95\% confidence intervals. The grey horizontal band shows the surrogate 95th percentile. The signal shows no consistent sign or trend.\relax }{figure.caption.34}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {4.17}Combined 1976--2025 Analysis: Sinusoidal Modulation}{30}{subsection.4.17}\protected@file@percent } \newlabel{sec:res:combined}{{4.17}{30}{Combined 1976--2025 Analysis: Sinusoidal Modulation}{subsection.4.17}{}} \@writefile{lof}{\contentsline {figure}{\numberline {19}{\ignorespaces Annual rolling $r(+15\,\text {d})$ across the full 1976--2025 period (grey points with 95\% bootstrap CI). The sinusoidal best-fit (red curve, $P = 13.0$\nobreakspace {}yr) and the constant-mean model (dashed) are nearly indistinguishable; BIC comparison slightly favours the constant model ($\text {BF} = 0.75$). The vertical dashed line marks the in-sample/out-of-sample split (2020).\relax }}{30}{figure.caption.35}\protected@file@percent } \newlabel{fig:combined}{{19}{30}{Annual rolling $r(+15\,\text {d})$ across the full 1976--2025 period (grey points with 95\% bootstrap CI). The sinusoidal best-fit (red curve, $P = 13.0$~yr) and the constant-mean model (dashed) are nearly indistinguishable; BIC comparison slightly favours the constant model ($\text {BF} = 0.75$). The vertical dashed line marks the in-sample/out-of-sample split (2020).\relax }{figure.caption.35}{}} \citation{KassRaftery1995} \citation{Homola2023} \citation{Odintsov2006} \@writefile{toc}{\contentsline {section}{\numberline {5}Discussion}{31}{section.5}\protected@file@percent } \newlabel{sec:discussion}{{5}{31}{Discussion}{section.5}{}} \@writefile{toc}{\contentsline {subsection}{\numberline {5.1}Why Does the Raw Correlation Appear So Strong?}{31}{subsection.5.1}\protected@file@percent } \citation{Aplin2005} \citation{Pulinets2004} \citation{Homola2023} \citation{Urata2018} \@writefile{toc}{\contentsline {subsection}{\numberline {5.2}Physical Plausibility of the Claimed Mechanism}{32}{subsection.5.2}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {5.3}Comparison with Prior Replication Attempts}{32}{subsection.5.3}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {5.4}Limitations}{32}{subsection.5.4}\protected@file@percent } \citation{Homola2023} \citation{Homola2023} \@writefile{toc}{\contentsline {section}{\numberline {6}Conclusions}{33}{section.6}\protected@file@percent } \newlabel{sec:conclusions}{{6}{33}{Conclusions}{section.6}{}} \bibstyle{plainnat} \bibdata{refs} \bibcite{Aplin2005}{{1}{2006}{{Aplin}}{{}}} \bibcite{Bartlett1946}{{2}{1946}{{Bartlett}}{{}}} \bibcite{Benjamini1995}{{3}{1995}{{Benjamini and Hochberg}}{{}}} \bibcite{Bretherton1999}{{4}{1999}{{Bretherton et~al.}}{{Bretherton, Widmann, Dymnikov, Wallace, and Blade}}} \bibcite{Cleveland1990}{{5}{1990}{{Cleveland et~al.}}{{Cleveland, Cleveland, McRae, and Terpenning}}} \bibcite{GardnerKnopoff1974}{{6}{1974}{{Gardner and Knopoff}}{{}}} \bibcite{HP1997}{{7}{1997}{{Hodrick and Prescott}}{{}}} \bibcite{Homola2023}{{8}{2022}{{Homola et~al.}}{{}}} \bibcite{Kanamori1977}{{9}{1977}{{Kanamori}}{{}}} \bibcite{KassRaftery1995}{{10}{1995}{{Kass and Raftery}}{{}}} \bibcite{Kraskov2004}{{11}{2004}{{Kraskov et~al.}}{{Kraskov, St{\"o}gbauer, and Grassberger}}} \bibcite{Odintsov2006}{{12}{2006}{{Odintsov et~al.}}{{Odintsov, Boyarchuk, Georgieva, Kirov, and Atanasov}}} \bibcite{Potgieter2013}{{13}{2013}{{Potgieter}}{{}}} \bibcite{Pulinets2004}{{14}{2004}{{Pulinets and Boyarchuk}}{{}}} \bibcite{RahnUhlig2002}{{15}{2002}{{Ravn and Uhlig}}{{}}} \bibcite{Schreiber2000}{{16}{2000}{{Schreiber and Schmitz}}{{}}} \bibcite{SIDC2024}{{17}{2024}{{SILSO World Data Center}}{{}}} \bibcite{Stoupel1990}{{18}{1990}{{Stoupel}}{{}}} \bibcite{Tavares2011}{{19}{2011}{{Tavares and Azevedo}}{{}}} \bibcite{Theiler1992}{{20}{1992}{{Theiler et~al.}}{{Theiler, Eubank, Longtin, Galdrikian, and Farmer}}} \bibcite{Urata2018}{{21}{2018}{{Urata and Tanimoto}}{{}}} \bibcite{USGS2024}{{22}{2024}{{USGS Earthquake Hazards Program}}{{}}} \gdef \@abspage@last{36}