When calibrating Radiocarbon dates, we aren’t just looking up a value on a curve. We are multiplying two probability distributions.
The uncalibrated date is a Gaussian distribution:
$$ R(t) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2} \left( \frac{t - \mu}{\sigma} \right)^2} $$We convolute this with the calibration curve $C(t)$ to get the posterior density:
$$ P(t_{cal}|t_{raw}) \propto \int R(t_{raw}) \cdot C(t) \, dt $$This is why strict “intercept” methods fail for wiggles in the Hallstatt Plateau. We need the full area under the curve.