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\usepackage{booktabs}
\usepackage{tikz}
\usepackage{pgfplots}
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\usepackage[colorlinks=true, linkcolor=black, citecolor=black, urlcolor=blue]{hyperref}

% --- skin palette: iron rust, graphite, ember gold ---------------------------
\definecolor{iron}{HTML}{B5502C}
\definecolor{irondeep}{HTML}{8A3A1E}
\definecolor{graphite}{HTML}{3A4652}
\definecolor{ember}{HTML}{9C7418}
\definecolor{ilarblue}{HTML}{2A6FB0}
\definecolor{ykarust}{HTML}{C1502E}
\definecolor{clubviolet}{HTML}{6A4BC4}

\title{The Iron Ball at the Center of the Earth Keeps Changing Its Skin}
\author{The Science Journaling Club}
\date{Field Notes --- Paper Analysis --- Geophysics}

\begin{document}
\maketitle

\begin{abstract}
Nobody has ever touched Earth's inner core, and nobody ever will. Every fact
about it arrives secondhand, carried the last 5,150 kilometres by a seismic
wave. In February 2025, John Vidale and four co-authors re-examined a dataset
of 121 repeating earthquakes near the South Sandwich Islands, recorded between
1991 and 2023 by two seismic arrays in the far north, and asked a narrower
question than usual: when the inner core's own drifting rotation brings it
back to a position it already occupied years earlier, do the two recordings
match \cite{vidale2025}? At Yellowknife (YKA), whose waves graze the inner
core's outer few hundred kilometres, some pairs recorded between 2004 and 2008
did not match. At Eielson (ILAR), whose waves bottom out deep near the centre,
the same pairs matched fine \cite{vidale2025}. The natural reading is that
whatever changed did not change everywhere --- it changed near the boundary,
on a timescale of a few years, while the deep interior stayed put. We rebuild
the ray geometry that makes this comparison possible, lay out why a solid iron
sphere is not supposed to behave this way, and then do the club's own
arithmetic: the inner core is about 35\% the volume of the Moon, and a
"mushy," structurally softer layer reported elsewhere on the same boundary by
an unrelated 2017 study is only about 0.3--0.7\% of the inner core's radius
--- a few kilometres of restless skin wrapped around twelve hundred kilometres
of otherwise very patient iron.
\end{abstract}

%============================================================================
\section{A Solid Ball That Keeps Not Acting Like One}

About 5,150 kilometres beneath your feet, at a pressure of roughly 330
gigapascals and a temperature north of 5{,}000 kelvin, the molten iron-nickel
alloy of the outer core freezes. It has been freezing, slowly, for well over
half a billion years, growing a solid ball out from the centre of the planet
one crystal at a time. That ball is the inner core: almost pure iron, laced
with a little nickel and a scatter of lighter elements, and by every
reasonable definition of the word, solid. Solid things are supposed to be
boring on human timescales.

The inner core has spent thirty years failing to be boring. Since Xiaodong
Song and Paul Richards first reported in 1996 that its seismic signature
seemed to drift relative to the rest of the planet \cite{song1996}, a small,
argumentative subfield has grown up around exactly how a two-thousand
kilometre-wide iron sphere, floating in a sea of its own molten parent
material, actually behaves. Hrvoje Tkal\v{c}i\'{c} and colleagues extended
the same repeating-earthquake logic in 2013 to argue the rotation was not
smooth but ``shuffling'' --- speeding, slowing, occasionally reversing
\cite{tkalcic2013}. Yaolin Yang and Xiaodong Song reported in 2023 that the apparent rotation
itself varies over multiple decades rather than proceeding at one steady
rate \cite{yang2023}. A 2014 review by Arwen Deuss catalogues the competing
rotation-versus-local-change explanations as one of the field's oldest open
questions \cite{deuss2014}.

The 2025 paper by Vidale and four co-authors does not resolve that fight by
picking a winner. It resolves it by showing both sides were half right, using
a dataset built specifically to catch the inner core doing whichever one it
does \cite{vidale2025}. ``Later on,'' Vidale told reporters after publication,
``I'd realize I was staring at evidence the inner core is not solid'' ---
not liquid, he means, but not perfectly rigid either \cite{physorg2025}.

%============================================================================
\section{How You Take the Pulse of Something You Will Never Touch}

You cannot drill to the inner core; the deepest hole ever bored, the Kola
Superdeep Borehole, reached 12.3 km, about a thousandth of the way down.
Everything known about Earth's centre is inferred from how vibrations move
through it.

The wave that matters here is \textbf{PKIKP}: a P-wave leaves the earthquake,
crosses the mantle, refracts into the liquid outer core (K), continues into
the solid inner core (I), refracts back out (K), and crosses the mantle a
second time to a distant seismometer (P). Only sources and receivers more
than about $110^{\circ}$ apart produce a PKIKP arrival at all, which is why
this literature almost always pairs an earthquake near one pole with a
receiver near the other --- South Sandwich Islands events, recorded in
Alaska and northern Canada, sit close to opposite ends of a chord through
the planet's centre \cite{vidale2025,song1996,tkalcic2013}.

The second trick is what makes the measurement possible at all. Some faults
keep rupturing in almost exactly the same way, in almost exactly the same
place, years apart --- \emph{repeating earthquakes}, or doublets. Two members
of a doublet have, to a good approximation, an identical source and an
identical receiver. Whatever differs between their seismograms has to come
from whatever lies on the ray path between them and changed in the meantime.
For a wave diving through the inner core, that difference is a direct
readout of the inner core changing.

\begin{figure}[htbp]
\centering
\begin{tikzpicture}[line width=0.9pt, font=\footnotesize]
  \draw[graphite, line width=1.6pt] (0,0.4) .. controls (0.6,0.9) and (0.9,-0.1) .. (1.5,0.4)
        .. controls (2.1,0.9) and (2.4,-0.1) .. (3.0,0.4)
        .. controls (3.6,0.9) and (3.9,-0.1) .. (4.5,0.4)
        .. controls (5.1,0.9) and (5.4,-0.1) .. (6.0,0.4);
  \draw[graphite, line width=1pt, dashed] (0,0.42) .. controls (0.6,0.82) and (0.9,0) .. (1.5,0.42)
        .. controls (2.1,0.82) and (2.4,0) .. (3.0,0.42)
        .. controls (3.6,0.82) and (3.9,0) .. (4.5,0.42)
        .. controls (5.1,0.82) and (5.4,0) .. (6.0,0.42);
  \node[anchor=west, iron, font=\bfseries\small] at (0,1.3) {A matching doublet (e.g.\ ILAR)};

  \draw[ykarust, line width=1.6pt] (0,-0.7) .. controls (0.6,-0.2) and (0.9,-1.2) .. (1.5,-0.7)
        .. controls (2.1,-0.2) and (2.4,-1.2) .. (3.0,-0.7)
        .. controls (3.6,-0.2) and (3.9,-1.4) .. (4.4,-0.85);
  \draw[ykarust, line width=1pt, dashed] (0,-0.68) .. controls (0.6,-0.22) and (0.9,-1.18) .. (1.5,-0.68)
        .. controls (2.1,-0.22) and (2.4,-1.18) .. (3.0,-0.68)
        .. controls (3.5,-1.5) and (3.7,0.1) .. (4.0,-1.6)
        .. controls (4.3,0.2) and (4.5,-1.6) .. (6.0,-0.9);
  \node[anchor=west, ykarust, font=\bfseries\small] at (0,0.15) {A mismatching doublet (e.g.\ YKA)};
  \node[anchor=north, font=\scriptsize] at (3.0,-1.9) {solid/dashed: two recordings of the same repeating pair, years apart};
\end{tikzpicture}
\caption{Schematic, not real seismograms. Our redrawing of the logic the
paper runs on real waveform pairs: a match means nothing detectable changed
along that ray path; a mismatch means something did. The paper classifies
each real pair this way, station by station \cite{vidale2025}.}
\label{fig:doublet}
\end{figure}

%============================================================================
\section{Two Stations, Two Very Different Views Through the Same Ball}

The paper leans on two seismic arrays in the far north: ILAR, at Eielson Air
Force Base near Fairbanks, Alaska, and YKA, near Yellowknife in Canada's
Northwest Territories \cite{vidale2025}. Because Fairbanks and Yellowknife
sit at slightly different distances and azimuths from the South Sandwich
Islands, their PKIKP rays cut through the inner core along different chords.
The ILAR path bottoms out deep, near the planet's centre. The YKA path is
shallower --- in the paper's own words, ``inner-core-grazing'' --- skimming
the outer part of the inner core rather than plunging toward its heart
\cite{vidale2025}.

\begin{figure}[htbp]
\centering
\begin{tikzpicture}[line width=0.9pt]
  \draw[graphite!40, line width=1pt] (0,0) circle (3.0);
  \filldraw[iron!12, draw=graphite] (0,0) circle (1.7);
  \filldraw[iron!85, draw=irondeep, line width=1.2pt] (0,0) circle (0.6);
  \node[font=\tiny, white, font=\bfseries] at (0,0) {inner core};
  \node[font=\scriptsize] at (0,2.2) {liquid outer core};
  \node[font=\scriptsize] at (0,2.8) {mantle};

  \node[ykarust, font=\Large] at (0,3.0) {$\times$};
  \node[font=\scriptsize] at (0,3.35) {South Sandwich Is. quake};

  % YKA path: shallow chord grazing inner core
  \draw[ykarust, line width=1.8pt] (0,3.0) -- (-1.35,1.15) arc[start angle=140,end angle=250,radius=0.6] -- (-2.6,-2.2);
  \node[ykarust, font=\bfseries\small] at (-2.9,-2.55) {YKA};
  \node[font=\scriptsize] at (-2.9,-2.85) {grazes the rim};

  % ILAR path: deep chord
  \draw[ilarblue, line width=1.8pt] (0,3.0) -- (-0.55,1.05) arc[start angle=150,end angle=280,radius=0.65] -- (1.9,-2.3);
  \node[ilarblue, font=\bfseries\small] at (2.15,-2.65) {ILAR};
  \node[font=\scriptsize] at (2.15,-2.95) {bottoms deep};
\end{tikzpicture}
\caption{Why two stations can disagree about the same inner core. The YKA
ray skims the outer part of the inner core; the ILAR ray bottoms out much
closer to the centre. If something changes only near the boundary, YKA's
grazing path should register it and ILAR's deep path should not --- exactly
the pattern reported for pairs recorded 2004--2008 \cite{vidale2025}.
Schematic, not to true angular scale.}
\label{fig:geometry}
\end{figure}

%============================================================================
\section{The Trick That Lets You Compare the Same Rock Twice}

Comparing any two repeating earthquakes years apart is not, by itself, a
clean experiment: if the inner core is rotating relative to the mantle, a ray
that grazed one patch of the boundary in 1995 may graze different rock
entirely by 2010. A mismatch would then tell you nothing.

The team's direct predecessor paper, published in \emph{Nature} in 2024,
solved this for the rotation question. Working from 121 repeating earthquakes
between 1991 and 2023 --- 143 distinct pairs, some belonging to sixteen
``multiplet'' families --- Wei Wang, Vidale, Guanning Pang, Keith Koper and
Ruoyan Wang found that the inner core \textbf{super-rotated} (drifted faster
than the mantle) from roughly 2003 to 2008, then \textbf{sub-rotated}, moving
back the other way, from 2008 onward --- two to three times more slowly than
it had advanced \cite{wang2024}. Because the return drift is slower, the
inner core eventually swings back through a rotational position it held
years before, handing a wave recorded today a free repeat of a past
experiment.

\paragraph{Club arithmetic: a sanity check, not a measurement.} If the inner
core super-rotated for five years (2003--2008) and crept back at ``two to
three times'' slower, simple ratio arithmetic predicts 10--15 years to
retrace the same rotational ground. The reported sub-rotation window,
2008--2023, is fifteen years --- right at the top of that range, consistent
with a slowdown factor near $3\times$. This is not a result from either
paper; it is only a check that the two headline numbers in the 2024
abstract are arithmetically compatible \cite{wang2024}. They are.

\begin{figure}[htbp]
\centering
\begin{tikzpicture}
\begin{axis}[
  width=12.5cm, height=6.5cm,
  xmin=1991, xmax=2024, ymin=-0.3, ymax=1.3,
  xlabel={year}, ylabel={inner core position rel.\ mantle (arb.\ units)},
  ymajorgrids=true, grid style={dashed, gray!30},
  ytick=\empty,
  legend style={font=\scriptsize, at={(0.02,0.05)}, anchor=south west}
]
\addplot[graphite, line width=1.4pt, mark=none] coordinates {
 (1991,0.42)(1997,0.42)(2003,0.42)(2004,0.55)(2005,0.68)(2006,0.80)(2007,0.90)
 (2008,0.97)(2010,0.82)(2012,0.68)(2014,0.58)(2016,0.51)(2018,0.47)(2020,0.44)
 (2022,0.42)(2023,0.41)(2024,0.41) };
\addlegendentry{schematic rotational offset}
\addplot[ykarust, fill=ykarust, fill opacity=0.12, draw=none] coordinates {
 (2004,-0.3)(2004,1.3)(2008,1.3)(2008,-0.3) } \closedcycle;
\addlegendentry{YKA mismatch window, 2004--2008}
\draw[ember, dashed, line width=1pt] (axis cs:1991,0.42) -- (axis cs:2013,0.42);
\node[ember, font=\scriptsize, anchor=south west] at (axis cs:2013.3,0.44) {position re-occupied};
\end{axis}
\end{tikzpicture}
\caption{The shape of the rotation history that makes the method work,
redrawn schematically from the qualitative result in the 2024 backtracking
paper \cite{wang2024}: five years of super-rotation (2003--2008), then
roughly three times as many years of slower sub-rotation (2008--2023). The
vertical axis is deliberately unlabelled in physical units --- the source
papers report timing and a rate ratio, not a plottable single number --- but
the shape and the 2004--2008 mismatch window are drawn from the papers' own
reported years \cite{vidale2025,wang2024}.}
\label{fig:rotation}
\end{figure}

That is the engine behind the 2025 paper. Vidale and colleagues extended the
catalogue with seven more recent events, adding twenty-five more pairs, and
searched specifically for pairs recorded when the backtracking history says
the inner core had returned to a shared position \cite{vidale2025}. If pure
rotation were the whole story, those pairs should match at \emph{both}
stations. Any mismatch surviving this control is not about rotation any
more --- it has to be about the rock itself.

\begin{figure}[htbp]
\centering
\begin{tikzpicture}
\begin{axis}[
  ybar, width=11.5cm, height=6cm,
  symbolic x coords={Events,Pairs,Multiplets},
  xtick=data,
  ylabel={count},
  legend style={font=\scriptsize, at={(0.02,0.97)}, anchor=north west},
  nodes near coords, every node near coord/.append style={font=\scriptsize}
]
\addplot[fill=ilarblue] coordinates {(Events,121) (Pairs,143) (Multiplets,16)};
\addplot[fill=ilarblue!45] coordinates {(Events,128) (Pairs,168) (Multiplets,16)};
\legend{2024 paper \cite{wang2024}, 2025 paper, extended \cite{vidale2025}}
\end{axis}
\end{tikzpicture}
\caption{Repeating earthquakes are rare enough that every study here is a
slow accumulation. The 2024 paper worked from 121 South Sandwich Islands
earthquakes forming 143 usable pairs in 16 multiplet families
\cite{wang2024}; the 2025 paper added seven more events and twenty-five
more pairs on the same catalogue \cite{vidale2025}. Real counts from the
two papers.}
\label{fig:growth}
\end{figure}

%============================================================================
\section{What Turned Up Between 2004 and 2008}

Comparing repeaters recorded when the inner core had cycled back to a
shared position, the paper found YKA waveforms that did not match --- among
pairs spanning parts of the 2004--2008 window --- while the equivalent ILAR
recordings, for the same earthquake pairs, matched fine \cite{vidale2025}.
One example the paper documents at length, ``pair 31,'' is a repeating
sequence tracked from 2004 to 2017.

Only one geometry explains both observations at once. ILAR's deep ray kept
sampling structure that had not changed. YKA's shallow ray sampled structure
that had. The paper states the conclusion directly: the changes ``most
likely'' originate in the shallow inner core, showing up more strongly on
ray paths that spend more of their length near the inner-core boundary
\cite{vidale2025}.

\begin{table}[htbp]
\centering
\small
\begin{tabular}{lll}
\toprule
\textbf{ILAR (deep)} & \textbf{YKA (shallow)} & \textbf{Implication} \\
\midrule
matches & matches & pure rotation return; nothing changed \\
matches & \textbf{differs} & \textbf{shallow-only change --- what was observed, 2004--2008} \\
differs & differs & bulk / deep change (would reach toward the centre) \\
differs & matches & not observed; no simple mechanism for this \\
\bottomrule
\end{tabular}
\caption{The logic that localises the change. Only one of the four possible
combinations was reported \cite{vidale2025}. Table is the club's own layout
of the paper's reasoning.}
\label{tab:logic}
\end{table}

%============================================================================
\section{``Annual-Scale'' Does Not Mean ``Ticks Like a Clock''}

The title's ``annual-scale variability'' does not mean a fixed one-year
cycle. It means the process unfolds over single-digit years rather than the
thousands or millions of years geology usually needs. The YKA/ILAR
divergence window is about four years wide (2004--2008); the documented
example pair spans thirteen years (2004--2017) \cite{vidale2025}. Geological
processes that reshape solid rock --- recrystallisation, slow creep, phase
change under pressure --- are the textbook example of something too slow to
notice. The inner core, iron under pressure high enough to make steel look
like putty, is not an obvious candidate for a process fast enough to leave a
mark inside two decades of seismic records. Something near its boundary
evidently is.

%============================================================================
\section{Why Solid Iron Is Allowed to Do This At All}

``Solid'' does the least useful amount of work here that a word can do.
Materials under extreme pressure and heat, sitting a few hundred degrees
below their melting point, can flow slowly by viscous creep --- the same
mechanism that lets glaciers move and lets the solid mantle convect over
millions of years, potentially operating far faster near the inner core's
edge. Bruce Buffett's 1997 geodynamic estimate placed the inner core's
effective viscosity somewhere between a very stiff solid and something that,
over the right timescale, behaves almost like a very slow fluid
\cite{buffett1997}; mineral-physics work on iron's strength at core
pressures has since pushed some estimates toward a mechanically weaker inner
core than earlier models assumed \cite{gleason2013}.

The paper offers two candidate mechanisms and is honest that it cannot yet
distinguish them \cite{vidale2025}. One: bumps in the inner-core boundary's
topography are gravitationally coupled to mantle density anomalies, and
slow rotation flexes a given patch as it passes a fixed mantle feature. Two:
the outer core is a vigorously convecting liquid-metal ocean whose motion
simply drags --- exerts traction --- on the solid surface it touches. Either
mechanism only needs to act on a thin near-surface layer to reproduce the
observed pattern.

Separately, using an unrelated seismic method, Dongdong Tian and Lianxing
Wen reported in 2017 that the inner-core boundary is not uniform everywhere:
beneath the southwest Okhotsk Sea, reflected compressional waves revealed a
patch, 4--8 km thick, with seismic properties between the solid inner core
and the liquid outer core --- consistent with a genuinely ``mushy,''
partially molten transition \cite{tian2017}. That is a different location
and a different method, almost certainly not the same patch the South
Sandwich Islands rays sample. What it establishes is that the boundary is
independently known to be capable of local structural softness at all.

%============================================================================
\section{Club Arithmetic: How Big Is the Ball, and How Thin Is the Skin}
\label{sec:club}

Two numbers do a lot of intuitive work here, and neither is stated outright
in the paper.

\paragraph{Size, against something you can picture.} The PREM reference
Earth model puts the inner core's radius at 1{,}221.5~km \cite{prem1981};
the ak135 travel-time model, which this very paper's own reference list
leans on for seismic velocities, gives a slightly different figure, close to
1{,}217~km \cite{kennett1995}. As a sphere,
\begin{equation}
V_{\text{ic}} = \tfrac{4}{3}\pi r^3 \approx 7.63\times10^{9}\ \text{km}^3
\qquad (r = 1{,}221.5\ \text{km}).
\end{equation}
NASA's published lunar volume is $2.1968\times10^{10}\ \text{km}^3$
\cite{nasamoon}. The ratio is
\begin{equation}
\frac{V_{\text{ic}}}{V_{\text{Moon}}} \approx 0.35 ,
\end{equation}
about 35\% of the Moon's volume.

\paragraph{Thinness, against the whole radius.} Tian and Wen's mushy-zone
thickness of 4--8~km \cite{tian2017}, divided by the PREM radius, gives
\begin{equation}
\frac{4\text{--}8\ \text{km}}{1{,}221.5\ \text{km}} \approx 0.33\text{--}0.65\% .
\end{equation}
We are \emph{not} claiming this is the thickness of the specific patch that
changed at YKA between 2004 and 2008 --- the 2025 paper gives no depth
figure for that patch, only that it is shallower than ILAR's ray path. This
arithmetic shows the right order of magnitude for how thin a seismically
soft layer at this boundary can be and still be measurable and published
elsewhere on the same ball.

\begin{figure}[htbp]
\centering
\begin{tikzpicture}[line width=0.9pt]
  \draw[graphite!50] (0,0) circle (1.9);
  \node[font=\scriptsize] at (0,-2.25) {the Moon, $r=1{,}737.4$ km \cite{nasamoon}};
  \filldraw[clubviolet, opacity=0.8, draw=irondeep] (0,0) circle (1.336);
  \node[white, font=\tiny\bfseries] at (0,0) {inner core};
  \node[font=\small, clubviolet, font=\bfseries] at (0,-2.7) {$\approx$ 35\% of the Moon's volume};

  \begin{scope}[xshift=6.5cm]
    \draw[iron, fill=iron, opacity=0.82] (0,-2.2) rectangle (0.6,2.2);
    \draw[ember, line width=1.6pt] (0,2.2) -- (0.6,2.2);
    \node[anchor=west, font=\scriptsize, ember] at (0.8,2.1) {up to 8 km, ``mushy'' \cite{tian2017}};
    \node[anchor=west, font=\scriptsize] at (0.8,-2.2) {1{,}221.5 km radius \cite{prem1981}};
    \node[anchor=north, font=\scriptsize, align=center] at (0.3,-2.55) {not to true scale --- \\ the real sliver is far thinner};
  \end{scope}
\end{tikzpicture}
\caption{Club arithmetic, not paper data. Left: the inner core drawn to
scale beside the Moon. Right: the full inner-core radius as a bar, with the
outer few kilometres called out at roughly the thickness a real 4--8~km
mushy layer would occupy if drawn honestly --- thinner than this figure can
actually render, which is itself the point.}
\label{fig:club}
\end{figure}

%============================================================================
\section{The Old Debate, and Why ``Tentatively Both'' Is the Right Answer}

For three decades the argument has run along one fault line: is temporal
variability in PKIKP waveforms caused by the inner core physically
\emph{rotating}, so a fixed ray samples new material over time, or by the
boundary itself \emph{changing shape} under a fixed or slowly rotating ray?
Vidale and colleagues' answer, stated in their own abstract, is
``tentatively both'' \cite{vidale2025}. The 2024 result established a real
rotation signal with a measurable 2008 reversal \cite{wang2024}; the 2025
result shows that once rotation is controlled for, a genuine residual
mismatch survives at the shallow-sampling station and not the deep one.
Untangling how much of the historical literature's disagreements trace to
one effect or the other is, per the authors, a project for more data, not a
question this paper alone closes \cite{vidale2025}.

%============================================================================
\section{Why Any of This Matters Above Ground}

The inner core is not an inert curiosity. Its growth releases latent heat
and light elements into the base of the liquid outer core, one of the main
engines believed to drive the convection that generates Earth's magnetic
field. A boundary that flexes or couples mechanically to mantle structure
overhead is a boundary condition on that convection, not a bystander to it.
Cao, Masson and Romanowicz's 2007 mapping of short-wavelength inner-core
boundary topography treated the shape of this surface as geodynamically
relevant for exactly this reason \cite{cao2007}. A boundary that changes
shape on a timescale of years, rather than only over the hundreds of
millions of years the inner core took to grow, is a different kind of
boundary condition than most geodynamo models have assumed.

%============================================================================
\section{What Would Make Us More Confident}

The result rests on a genuinely small number of qualifying comparisons: the
specific repeating pairs recorded during a window when the backtracking
model says the inner core had cycled back to a shared position, at just two
stations. More repeating earthquakes, especially along different azimuths,
would sample different chords and either corroborate a genuinely localised
shallow change or reveal the YKA pattern as more station-specific than
global. The 2025 paper's own extension --- seven new events, twenty-five new
pairs \cite{vidale2025} --- is exactly this kind of incremental
strengthening, and the underlying earthquake sequence is still active. A
harder test would be an independent geometry, a different source region and
receivers, that also brackets a shallow-versus-deep contrast and checks
whether it reproduces a shallow-only signal on a comparable timescale.

%============================================================================
\section{What We Would Tell Someone Who Only Read the Headline}

Three things. First, nobody found a hidden ocean or a crack in the inner
core; ``mushy'' is a term of art borrowed from a different, unrelated study
of a different patch of the same boundary \cite{tian2017}, describing a
seismic property between solid-like and liquid-like, not an actual slush.
Second, ``annual-scale'' describes how fast the process unfolds, not a
strict yearly cycle. Third, and most important: the paper does not claim
the inner core is secretly liquid. It claims something narrower and more
interesting --- that the outermost sliver of a two-thousand-kilometre solid
iron sphere is soft enough, at the right pressure and temperature and given
enough time, to visibly deform within a human research career, while the
deep interior a few hundred kilometres further in shows no such thing.

%============================================================================
\begin{thebibliography}{99}

\bibitem{vidale2025}
Vidale, J.~E., Wang, W., Wang, R., Pang, G. \& Koper, K. (2025).
Annual-scale variability in both the rotation rate and near surface of
Earth's inner core. \textit{Nature Geoscience} 18, 267--272.
doi:10.1038/s41561-025-01642-2

\bibitem{wang2024}
Wang, W., Vidale, J.~E., Pang, G., Koper, K.~D. \& Wang, R. (2024).
Inner core backtracking by seismic waveform change reversals.
\textit{Nature} 631, 340--343. doi:10.1038/s41586-024-07536-4

\bibitem{song1996}
Song, X. \& Richards, P.~G. (1996). Seismological evidence for differential
rotation of the Earth's inner core. \textit{Nature} 382, 221--224.
doi:10.1038/382221a0

\bibitem{tkalcic2013}
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\end{document}