fix(spectrum): lone branch defines endpoint in single-branch mode

When config.branches carries exactly one branch (e.g. after
--intensity-cutoff filtering), the branch endpoint/transition define
the spectrum, energy grid, analyzer unified branch view and CSV
header. The stale top-level endpoint inherited from the parent decay
no longer leaks into physics (proven wrong on Cs137: spectrum
extended to 1176 keV while the lone survivor ends at 514 keV).

tests/physics/test_core_spectrum.py

@@ -438,6 +438,90 @@ class TestVisualizerBuiltFromCSV:
         assert (tmp_path / "analysis.png").exists()
 
 
+def make_single_survivor_config(**over: Any) -> SpectrumConfig:
+    """A config whose top-level endpoint exceeds a lone branch's endpoint.
+
+    This mirrors the intensity_cutoff / decay_info_to_config path where the
+    parent endpoint_MeV keeps the strongest-decay value while the only
+    surviving branch sits far below it.
+    """
+    over.setdefault("endpoint_MeV", 1.176)
+    over.setdefault("transition_type", "F2")
+    over.setdefault(
+        "branches",
+        [BranchConfig(endpoint_MeV=0.514341, transition_type="A", intensity=1.0)],
+    )
+    return SpectrumConfig(
+        Z_parent=55,
+        Z_daughter=56,
+        A_number=137,
+        e_step_MeV=0.001,
+        **over,
+    )
+
+
+class TestSurvivingBranchEndpointFollows:
+    """When config.branches has exactly 1 entry, single-mode spectrum,
+    energy grid and analyzer must follow the branch endpoint/transition,
+    not the top-level endpoint fields."""
+
+    def test_single_mode_builds_from_branch_endpoint(self) -> None:
+        config = make_single_survivor_config()
+        spectrum = BetaSpectrum.from_config(config)
+        assert not spectrum._is_multi
+        W, E = spectrum.get_energy_grid(config)
+        # The energy grid must be capped at the lone branch endpoint
+        # (~514 keV), not the stale top-level endpoint (1176 keV), and
+        # stay non-negative everywhere it covers.
+        assert float(E.max()) < 0.514341 + 1e-12
+        values = spectrum(W)
+        assert np.all(np.isfinite(values))
+        assert np.all(values >= 0.0)
+
+    def test_single_mode_matches_reference_bare_config(self) -> None:
+        """Branch-driven single mode == a bare config set to the branch endpoint."""
+        branch_ep = 0.514341
+        cfg_branch = make_single_survivor_config()
+        cfg_ref = SpectrumConfig(
+            Z_parent=55,
+            Z_daughter=56,
+            A_number=137,
+            endpoint_MeV=branch_ep,
+            transition_type="A",
+            e_step_MeV=0.001,
+        )
+        spec_b = BetaSpectrum.from_config(cfg_branch)
+        spec_ref = BetaSpectrum.from_config(cfg_ref)
+        Wb, Eb = spec_b.get_energy_grid(cfg_branch)
+        Wr, Er = spec_ref.get_energy_grid(cfg_ref)
+        vb = spec_b(Wb)
+        vr = spec_ref(Wr)
+        # The branch-driven grid and values must be identical to a bare
+        # config built directly at the branch endpoint/transition.
+        assert len(Eb) == len(Er)
+        assert np.allclose(Eb, Er, rtol=0, atol=1e-12)
+        assert np.allclose(vb, vr, rtol=1e-10)
+
+    def test_analyzer_unified_view_follows_branch(self) -> None:
+        config = make_single_survivor_config()
+        spectrum = BetaSpectrum.from_config(config)
+        analyzer = BetaSpectrumAnalyzer(spectrum, config)
+        ub = analyzer._unified_branches[0]
+        assert ub.endpoint_MeV == pytest.approx(0.514341)
+        assert ub.transition_type == "A"
+
+    def test_csv_header_reports_branch_endpoint(self, tmp_path: Any) -> None:
+        config = make_single_survivor_config()
+        spectrum = BetaSpectrum.from_config(config)
+        analyzer = BetaSpectrumAnalyzer(spectrum, config)
+        path, _ = export_and_read(analyzer, tmp_path)
+        header = header_lines_of(path)
+        # The lone surviving branch must be reported at its own endpoint,
+        # not the 1176 keV top-level endpoint.
+        assert any("514.3 keV" in h for h in header)
+        assert not any("1176.0 keV" in h for h in header)
+
+
 class TestAnalyzerUniversalFactor:
     """analyzer.universal_factor() = product of components shared by all."""