= Solution
<General relativity> is not required for the ideal <twin paradox> in <Minkowski spacetime>. The relevant observable is the difference in <proper times> recorded by clocks that meet at departure and reunion. For a <world line> $x(t)$ in one <inertial frame>, the <clock hypothesis> gives
$$
\tau=\int_0^T\sqrt{1-\frac{\dot x(t)^2}{c^2}}\,dt.
$$
The home clock with $x=0$ records $T$. A traveler coasting outward at $v$ for $T/2$ and inward at $-v$ for $T/2$ records $T/\gamma$, in the ideal short-turnaround limit. For $T=10$ years and $v=0.6c$, these readings are ten and eight years. The complete paths, rather than conflicting applications of reciprocal <time dilation> to one pair of <inertial frames>, determine the invariant difference.
An exactly instantaneous reversal is an idealization, not an essential premise. Replace it by a smooth timelike turnaround. The <proper time> accumulated in a reversal interval of home duration $\delta t$ lies between zero and $\delta t$, so its contribution vanishes as the interval shrinks. The finite clock difference persists. Repeatedly lengthening the coasting legs while keeping the same reversal maneuver also changes the clock difference; the difference is not a universal function only of the peak <proper acceleration>.
The usual apparent symmetry fails because no single traveler <inertial frame> covers both legs. In the instantaneous rest frame at a traveler event $(t,x(t))$, the home event assigned as simultaneous has time
$$
t_H=t-\frac{v(t)x(t)}{c^2}.
$$
Hence a finite turnaround changes the home simultaneity assignment continuously. In the sharp-turnaround limit at $x=vT/2$, changing $v$ to $-v$ changes that assigned home time by $v^2T/c^2$. This is a change in a distant <relativity of simultaneity> assignment, not a sudden physical jump in the home clock's reading. The full <twin paradox simultaneity change> reconciles the two inertial coasting descriptions.
An accelerated-coordinate calculation is also available within <special relativity>. Nonzero connection coefficients in that chart do not establish nonzero <Riemann curvature tensor>. Thus neither using accelerated coordinates nor making the traveler accelerate requires the <Einstein field equations>. The <clock hypothesis> is a physical assumption about a sufficiently ideal clock, not a guarantee that every real apparatus survives arbitrary acceleration without disturbances. Experiments such as the <muon storage-ring time-dilation experiments> test clock behavior in specified regimes.
Real flights around <Earth> also compare different <gravitational potentials> and require gravitational corrections, as in the <twin paradox clock experiments>. Those refinements involve <general relativity>. They do not make the flat-spacetime reunion calculation incomplete on its stated assumptions. Even two mirrored, accelerating travelers can record equal <proper times>; the decisive quantity is the <proper time> of each entire path between the common events.
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