feat: experimental data calibration pipeline with ROOT I/O

- Fix chi2 calculation bug in calibration.py (remove incorrect
  coeffs[::-1] reversal in np.polyval)
- Fix broken beta_spectrum/cli.py (remove orphaned detector response
  add_argument calls and unused imports)
- Add ExpSpectrum.apply_calibration() and EnergyCalibrator.from_am241_spectrum()
- Add LivetimeDetermination class for pulser-based livetime
- Add SpectrumPipeline orchestration (read→subtract→calibrate→livetime→validate)
- Add ROOT I/O with PyROOT primary + uproot fallback
- Add bs_exp CLI with process, livetime, export subcommands
- Add exp_calibration notebook with pre-calibration visualization
- Add comprehensive tests (73 passing)
- Add bs_exp console script and [root] extra to pyproject.toml
- Remove obsolete detector_response module and unused notebooks

exp_data/spectrum.py

@@ -8,7 +8,10 @@ and calibration information.
 from __future__ import annotations
 
 from dataclasses import dataclass, field
-from typing import Optional
+from typing import TYPE_CHECKING, Optional
+
+if TYPE_CHECKING:
+    from exp_data.calibration import CalibrationResult
 
 import numpy as np
 
@@ -140,6 +143,44 @@ class ExpSpectrum:
             date=self.date,
         )
 
+    def apply_calibration(self, calibration: "CalibrationResult") -> ExpSpectrum:
+        """Return a new spectrum with energies recalibrated via the given CalibrationResult.
+
+        The calibration polynomial is applied to the current energy axis:
+        calibrated_energies = calibration(channel_indices).
+
+        Parameters
+        ----------
+        calibration : CalibrationResult
+            A CalibrationResult from EnergyCalibrator (e.g., from Am-241 peak detection).
+
+        Returns
+        -------
+        ExpSpectrum
+            New ExpSpectrum with recalibrated energies, all other fields preserved.
+        """
+
+        calibrated_energies = calibration(self.energies)
+        return ExpSpectrum(
+            energies=calibrated_energies,
+            counts=self.counts.copy(),
+            errors=self.errors.copy(),
+            metadata={
+                **self.metadata,
+                "calibration": {
+                    "type": "linear" if calibration.order == 1 else "quadratic",
+                    "coefficients": calibration.coefficients.tolist(),
+                    "chi2_per_dof": calibration.chi2_per_dof,
+                    "n_points": calibration.n_points,
+                },
+            },
+            dead_time=self.dead_time,
+            live_time=self.live_time,
+            source=self.source,
+            run_id=self.run_id,
+            date=self.date,
+        )
+
     def to_dict(self) -> dict:
         """Serialize to dictionary."""
         return {