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

tests/exp_data/test_livetime.py

@@ -0,0 +1,142 @@
+"""Unit tests for the LivetimeDetermination class."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from exp_data.spectrum import ExpSpectrum
+from exp_data.livetime import LivetimeDetermination, LivetimeResult
+
+
+class TestLivetimeResult:
+    def test_basic(self):
+        result = LivetimeResult(
+            live_time_fraction=0.95,
+            real_time_sec=3600.0,
+            pulser_frequency_hz=100.0,
+            observed_pulser_rate=95.0,
+            pulser_peak_center_keV=10.0,
+            pulser_peak_sigma_keV=0.5,
+            pulser_peak_chi2=1.2,
+        )
+        assert result.live_time_fraction == 0.95
+        assert result.metadata == {}
+
+    def test_metadata_populated(self):
+        result = LivetimeResult(
+            live_time_fraction=0.95,
+            real_time_sec=3600.0,
+            pulser_frequency_hz=100.0,
+            observed_pulser_rate=95.0,
+            pulser_peak_center_keV=10.0,
+            pulser_peak_sigma_keV=0.5,
+            pulser_peak_chi2=1.2,
+            metadata={"pulser_peak_channel": 100, "pulser_fit_success": True},
+        )
+        assert result.metadata["pulser_peak_channel"] == 100
+
+
+class TestLivetimeDetermination:
+    def test_from_file_requires_positive_frequency(self):
+        """Test that zero frequency raises ValueError."""
+        n_channels = 4096
+        energies = np.arange(n_channels, dtype=np.float64)
+        counts = np.ones(n_channels) * 10
+        spectrum = ExpSpectrum(energies=energies, counts=counts)
+
+        determiner = LivetimeDetermination(
+            spectrum,
+            pulser_frequency_hz=0.0,
+            real_time_sec=3600.0,
+        )
+        with pytest.raises(ValueError, match="positive"):
+            determiner.run()
+
+    def test_live_time_clamped_to_1(self):
+        """Test that live-time fraction > 1.0 is clamped to 1.0."""
+        n_channels = 4096
+        energies = np.arange(n_channels, dtype=np.float64)
+        counts = np.exp(-energies / 500) * 10  # background
+        # Add prominent pulser peak at channel 100
+        pulser_channel = 100
+        pulser_peak = 500 * np.exp(-0.5 * ((energies - pulser_channel) / 2.0) ** 2)
+        counts += pulser_peak.astype(float)
+        spectrum = ExpSpectrum(energies=energies, counts=counts)
+
+        determiner = LivetimeDetermination(
+            spectrum,
+            pulser_frequency_hz=10.0,  # low frequency -> observed rate > frequency
+            real_time_sec=0.01,  # very short time -> high observed rate
+        )
+        result = determiner.run()
+        assert result.live_time_fraction == 1.0
+
+    def test_live_time_clamped_to_0(self):
+        """Test that live-time fraction < 0 is clamped to 0."""
+        n_channels = 4096
+        energies = np.arange(n_channels, dtype=np.float64)
+        counts = np.exp(-energies / 500) * 10  # background only, no pulser peak
+        spectrum = ExpSpectrum(energies=energies, counts=counts)
+
+        determiner = LivetimeDetermination(
+            spectrum,
+            pulser_frequency_hz=100.0,
+            real_time_sec=3600.0,
+        )
+        result = determiner.run()
+        # With no pulser peak, the fitter may find a tiny spurious peak
+        # but the observed rate will be negligible -> live_time ~ 0
+        assert result.live_time_fraction >= 0.0
+        assert result.live_time_fraction <= 0.01
+
+    def test_pulser_peak_detection(self):
+        """Test that LivetimeDetermination correctly identifies a pulser peak."""
+        n_channels = 4096
+        energies = np.arange(n_channels, dtype=np.float64)
+        counts = np.exp(-energies / 500) * 10  # background
+        # Add pulser peak at channel 100 (10 keV)
+        pulser_channel = 100
+        pulser_peak = 500 * np.exp(-0.5 * ((energies - pulser_channel) / 2.0) ** 2)
+        counts += pulser_peak.astype(float)
+
+        spectrum = ExpSpectrum(
+            energies=energies,
+            counts=counts,
+            source="pulser",
+        )
+
+        determiner = LivetimeDetermination(
+            spectrum,
+            pulser_frequency_hz=100.0,
+            real_time_sec=3600.0,
+        )
+        result = determiner.run()
+
+        assert result.live_time_fraction > 0
+        assert result.live_time_fraction <= 1.0
+        assert result.pulser_peak_center_keV == pytest.approx(pulser_channel, abs=5.0)
+
+    def test_result_contains_pulser_info(self):
+        """Test that result contains pulser peak info."""
+        n_channels = 4096
+        energies = np.arange(n_channels, dtype=np.float64)
+        counts = np.exp(-energies / 500) * 10
+        pulser_channel = 100
+        pulser_peak = 500 * np.exp(-0.5 * ((energies - pulser_channel) / 2.0) ** 2)
+        counts += pulser_peak.astype(float)
+
+        spectrum = ExpSpectrum(energies=energies, counts=counts, source="pulser")
+
+        determiner = LivetimeDetermination(
+            spectrum,
+            pulser_frequency_hz=100.0,
+            real_time_sec=3600.0,
+        )
+        result = determiner.run()
+
+        assert result.pulser_peak_center_keV > 0
+        assert result.pulser_peak_sigma_keV > 0
+        assert result.pulser_peak_chi2 > 0
+        assert result.pulser_frequency_hz == 100.0
+        assert result.real_time_sec == 3600.0