diff --git a/Sources/SpectroEDX/Fit/SumEscapeFit.swift b/Sources/SpectroEDX/Fit/SumEscapeFit.swift
index c02f6e0..87adc58 100644
--- a/Sources/SpectroEDX/Fit/SumEscapeFit.swift
+++ b/Sources/SpectroEDX/Fit/SumEscapeFit.swift
@@ -111,6 +111,12 @@ public nonisolated struct SumEscapeResult: Sendable {
     public var escapeFraction: Double?
     public var escapeFractionSigma: Double?
     public var escapePeaks: [EscapeComponent]
+    /// The fitted sum and escape peaks together, counts per channel of `fit.channels` (c S(A) + f E(A) at the reported areas): what
+    /// the model explains beyond the line and continuum columns. The element proposer takes it as a fixed part of its model, so a
+    /// peak this model covers is not proposed as an element. All zeros when the model is off. It is the exact sum term at the
+    /// reported areas; `fit.model` holds its linearisation at the previous iterate, which differs by c times the squared area step
+    /// (nothing at convergence; the warnings say when the alternation did not converge).
+    public var componentCounts: [Double]
     public var iterations: Int
     public var converged: Bool
     /// The parameters of the model as run, one sentence each.
@@ -136,7 +142,8 @@ public nonisolated enum EDSSumEscapeFit {
         if model.isOff {
             return SumEscapeResult(fit: baseline, baseline: baseline, sumCoefficient: nil, sumCoefficientSigma: nil,
                                    sumCoefficientAtBound: false, sumPeaks: [], escapeFraction: nil, escapeFractionSigma: nil,
-                                   escapePeaks: [], iterations: 0, converged: true,
+                                   escapePeaks: [], componentCounts: [Double](repeating: 0, count: baseline.channels.count),
+                                   iterations: 0, converged: true,
                                    parameters: ["sum and escape model: off (the default fit)"], validation: validation)
         }
 
@@ -285,6 +292,9 @@ public nonisolated enum EDSSumEscapeFit {
         }
         var escComponents: [EscapeComponent] = []
         for gi in 0..<g where escColumns[gi] != nil { escComponents.append(EscapeComponent(group: groups[gi].id, area: f * area[gi])) }
+        var componentCounts = [Double](repeating: 0, count: n)
+        if c != 0 { let q = sumShape(area); for k in 0..<n { componentCounts[k] += c * q[k] } }
+        if f != 0 { let q = escShape(area); for k in 0..<n { componentCounts[k] += f * q[k] } }
 
         // Sigma of c and f: the term's shape with the fit's other columns projected out.
         func sigmaOf(_ q: [Double]) -> Double? {
@@ -331,7 +341,7 @@ public nonisolated enum EDSSumEscapeFit {
         return SumEscapeResult(fit: fit, baseline: baseline, sumCoefficient: model.sumPeaks ? c : nil, sumCoefficientSigma: cSigma,
                                sumCoefficientAtBound: cAtBound, sumPeaks: sumComponents,
                                escapeFraction: model.commonEscapeFraction ? f : nil, escapeFractionSigma: fSigma,
-                               escapePeaks: escComponents, iterations: iterations, converged: converged,
+                               escapePeaks: escComponents, componentCounts: componentCounts, iterations: iterations, converged: converged,
                                parameters: params, validation: validation)
     }
 }
diff --git a/Sources/SpectroEDX/Proposer/ElementProposer.swift b/Sources/SpectroEDX/Proposer/ElementProposer.swift
index 38b29a4..7cd72b0 100644
--- a/Sources/SpectroEDX/Proposer/ElementProposer.swift
+++ b/Sources/SpectroEDX/Proposer/ElementProposer.swift
@@ -236,12 +236,15 @@ public nonisolated struct ElementProposer: Sendable {
     /// strong line's shape error dragged the continuum beside it (data over model 3.1 in 1 to 2.5 keV beside a planted Al 6 eV narrower than the
     /// model) and the hump it left became an element (Os M). The pass's `result` is returned in counts (its model and residual unscaled).
     private static func fitPass(groups: [FitLineGroup], data: [Double], settings s: FitSettings, axis: EnergyAxis,
-                                channels: Range<Int>, dropped: [String], relative: Double, widths: [Int], weighted: Bool = true) throws -> Pass {
+                                channels: Range<Int>, dropped: [String], relative: Double, widths: [Int], weighted: Bool = true,
+                                explained: [Double]? = nil) throws -> Pass {
         let model = EDSLineModel(groups: groups, resolutionMnKaEV: s.resolutionMnKaEV, beamEnergy: s.beamEnergy,
                                  escapePeaks: s.escapePeaks, droppedLines: dropped, lineTail: s.lineTail)
         try EDSFit.validate(s.referenceShapes, axis: axis, model: model)
         var design = LinearDesign.build(model: model, axis: axis, channels: channels, background: s.background,
                                         shapes: s.referenceShapes, counts: data)
+        // Counts the caller's model already explains (the sum and escape peaks of a sum/escape fit): a fixed part of the model.
+        if let explained { for (k, ch) in channels.enumerated() { design.offset[k] += explained[ch] } }
         let y = channels.map { data[$0] }
         var prefix = [Double](repeating: 0, count: y.count + 1)
         for i in y.indices { prefix[i + 1] = prefix[i] + y[i] }
@@ -273,13 +276,14 @@ public nonisolated struct ElementProposer: Sendable {
 
     /// `fitPass` for every job, concurrently; the results are in job order.
     private static func fitPasses(jobs: [[FitLineGroup]], data: [Double], settings s: FitSettings, axis: EnergyAxis,
-                                  channels: Range<Int>, dropped: [String], relative: Double, widths: [Int]) -> [Result<Pass, Error>] {
+                                  channels: Range<Int>, dropped: [String], relative: Double, widths: [Int],
+                                  explained: [Double]?) -> [Result<Pass, Error>] {
         var out = [Result<Pass, Error>?](repeating: nil, count: jobs.count)
         out.withUnsafeMutableBufferPointer { buf in
             let box = ResultBox(buffer: buf)
             DispatchQueue.concurrentPerform(iterations: jobs.count) { i in
                 box.buffer[i] = Result { try fitPass(groups: jobs[i], data: data, settings: s, axis: axis, channels: channels,
-                                                     dropped: dropped, relative: relative, widths: widths) }
+                                                     dropped: dropped, relative: relative, widths: widths, explained: explained) }
             }
         }
         return out.map { $0! }
@@ -319,11 +323,16 @@ public nonisolated struct ElementProposer: Sendable {
     ///     its own `ProposerError.cancelled`; nothing partial is returned.
     ///   - progress: monotone in 0...1, ends at 1. The number of fits is not known in advance, so it is fits done over fits done plus the
     ///     fits the current step still has planned, clamped never to fall.
+    ///   - explained: counts per channel of `axis` that the caller's model already explains beyond line and continuum columns (the sum
+    ///     and escape peaks of `EDSSumEscapeFit`, `SumEscapeResult.componentCounts`). They are a fixed part of every fit here, so a peak
+    ///     they cover leaves no residual and is never proposed as an element. nil (the default) runs the proposer as before, bit for bit.
     public func propose(counts: [Double], axis: EnergyAxis, settings: FitSettings,
                          holeCounts: [Double]? = nil,
+                         explained: [Double]? = nil,
                          cancelled: @Sendable () -> Bool = SpectroCancellation.task,
                          progress: (@Sendable (Double) -> Void)? = nil) throws -> ProposalResult {
-        guard counts.count == axis.size, holeCounts.map({ $0.count == axis.size }) ?? true else { throw ProposerError.lengthMismatch }
+        guard counts.count == axis.size, holeCounts.map({ $0.count == axis.size }) ?? true,
+              explained.map({ $0.count == axis.size }) ?? true else { throw ProposerError.lengthMismatch }
         var s = settings
         s.method = .leastSquares
         let channels = axis.fitChannels(from: s.fitFrom, to: s.fitTo)
@@ -379,7 +388,8 @@ public nonisolated struct ElementProposer: Sendable {
         func runAll(_ jobs: [[FitLineGroup]], on data: [Double]) throws -> [Result<Pass, Error>] {
             if cancelled() { throw ProposerError.cancelled }
             fitsPlanned = max(fitsPlanned, jobs.count)
-            let out = Self.fitPasses(jobs: jobs, data: data, settings: s, axis: axis, channels: channels, dropped: dropped, relative: t.relativeModelTerm, widths: widths)
+            let out = Self.fitPasses(jobs: jobs, data: data, settings: s, axis: axis, channels: channels, dropped: dropped, relative: t.relativeModelTerm, widths: widths,
+                                     explained: explained)
             fitsDone += jobs.count; tick()
             return out
         }
@@ -600,7 +610,7 @@ public nonisolated struct ElementProposer: Sendable {
         // shape is off, and the statistic's weights spare that misfit). σ₀ and L_D are that fit's own null variance. Pruned, rejected and withheld
         // candidates keep the numbers of the fit that decided them (they are not in the final model).
         let report = try Self.fitPass(groups: model, data: counts, settings: s, axis: axis, channels: channels, dropped: dropped,
-                                      relative: t.relativeModelTerm, widths: widths, weighted: false)
+                                      relative: t.relativeModelTerm, widths: widths, weighted: false, explained: explained)
         fitsDone += 1
         // Candidates: the found elements from the final fit, then the pruned, then the rest that were tested.
         let finalParents = parents(report)
diff --git a/Sources/SpectroEDX/Quant/FitRange.swift b/Sources/SpectroEDX/Quant/FitRange.swift
index edf8b3f..55f878c 100644
--- a/Sources/SpectroEDX/Quant/FitRange.swift
+++ b/Sources/SpectroEDX/Quant/FitRange.swift
@@ -169,6 +169,7 @@ public nonisolated enum FitRangeSensitivityCheck {
         var refit = input
         refit.method.fitToKeV = to
         refit.refinement = q.refinement
+        refit.sumEscape = PooledQuantifier.sameSumEscape(as: q)   // the reported fit's sum-peak decision, not a new one
         let after: PooledQuantification
         do { after = try PooledQuantifier.run(refit, tables: nil, cancelled: cancelled, progress: progress.map { p in { @Sendable f in p(f * 0.95) } }) }
         catch let c as SpectroCancelled { throw c }
diff --git a/Sources/SpectroEDX/Quant/PooledQuantification.swift b/Sources/SpectroEDX/Quant/PooledQuantification.swift
index b743bbc..e99cf35 100644
--- a/Sources/SpectroEDX/Quant/PooledQuantification.swift
+++ b/Sources/SpectroEDX/Quant/PooledQuantification.swift
@@ -14,6 +14,10 @@
 //      is then computed WITHOUT the correction and the result says so; it never pretends.
 //
 //  DEVIATIONS (named):
+//    * Sum peaks (`FitPolicy.sumPeaks`, default `.whenSignificant`): exSpy fits one Gaussian per line and no sum peaks. The fit
+//      tests the strongest line's self pair and, when its pile-up coefficient is 3 sigma above 0, keeps the sum peaks of the four
+//      strongest lines (`EDSSumEscapeFit`, unvalidated); otherwise it is the exSpy-equivalent fit bit for bit. `.off` always is.
+//      The axis refinement runs without them. The footer names the decision with its number.
 //    * Absorption is iterated to 1e-7 % (eXSpy stops at 0.5 %): the sigma terms are finite differences of
 //      the composition, and a loop that stops at 0.5 % would put steps into them.
 //    * The absorption "model spread" is |at%(geometric-mean transmission) - at%(weighted-mean transmission)|. The
@@ -86,8 +90,9 @@ public nonisolated struct PooledQuantificationInput: Sendable {
     /// The choices the library made about the fit and the step to composition (`QuantificationPolicy.default` is what it has always
     /// done). A non-default policy is named in the result's footer. It is not part of `method`, whose hash it leaves alone.
     public var policy: QuantificationPolicy
-    /// The optional sum-peak and common-escape-fraction components of the fit (0.10.0; nil, the default, runs the fit as it always ran).
-    /// Unvalidated (no Python reference); named in the footer when on.
+    /// The sum-peak and common-escape-fraction components of the fit, chosen by the caller (0.10.0). nil, the default, leaves the
+    /// choice to `policy.fit.sumPeaks` (sum peaks kept when the data support them); a model runs as given, and `SumEscapeModel()`
+    /// (both off) is the default fit as it ran before sum peaks were the default. Unvalidated (no Python reference); named in the footer.
     public var sumEscape: SumEscapeModel? = nil
 
     public init(counts: [UInt64], axis: EnergyAxis, method: QuantificationMethod, metadata: SpectrumImageMetadata,
@@ -162,6 +167,9 @@ public nonisolated struct PooledQuantification: Sendable {
     public var footerLines: [String]
     /// The settings the reported fit ran with (axis, width, range, continuum, estimator): the unlisted-line check proposes on them.
     package var fitSettings: FitSettings
+    /// The sum and escape peaks the reported fit modelled (`SumEscapeResult.componentCounts` on the full axis, 0 outside the fitted
+    /// channels); nil when the sum/escape model is off. The unlisted-line check hands it to the proposer as explained counts.
+    package var sumEscapeCounts: [Double]? = nil
     /// The fitted range as run and where its upper end came from (WP3c; the footer's "fit range" line).
     package var fitRange: FitRangeChoice
     /// WP3c: what one extra fit to the axis end does to each quantified net, when the axis runs past the default range;
@@ -174,6 +182,9 @@ public nonisolated struct PooledQuantification: Sendable {
     /// A2: a caveat on the at% rows ("assumes the listed elements only; unlisted: Cu (net 139 411) ..."), set by the unlisted-line
     /// check; "unlisted-line check running" while it runs; nil when the check found nothing. Never blanks a number.
     public var abundanceCaveat: String? = nil
+    /// The sum-peak (and escape) model the reported fit ran with; nil for the fit without sum peaks (one Gaussian per line).
+    /// Set by the caller's `PooledQuantificationInput.sumEscape`, or by `FitPolicy.sumPeaks` when the caller passes none.
+    public var appliedSumEscape: SumEscapeModel? = nil
     /// The detector Si dead layer of the continuum as run (typed or fitted), micrometres; nil when the term is off
     /// (`FitPolicy.continuumDeadLayer`). validation: "none".
     public var continuumDeadLayerMicrons: Double? = nil
@@ -309,19 +320,85 @@ public nonisolated enum PooledQuantifier {
         try SpectroCancellation.check(cancelled)
         progress?(0.85)
         var sumEscapeLines: [String] = []
+        var applied: SumEscapeModel?
+        var keptSumEscape: SumEscapeResult?
         do {
-            if let model = input.sumEscape, !model.isOff {
-                let r = try EDSSumEscapeFit.run(counts: counts, axis: axis, settings: fitSettings, model: model,
+            if let model = input.sumEscape {
+                // The caller chose the model: it runs as asked (an `isOff` model is the default fit).
+                if !model.isOff {
+                    let r = try EDSSumEscapeFit.run(counts: counts, axis: axis, settings: fitSettings, model: model,
                                                     escapeRatioWarning: policy.fit.escapeRatioWarning)
-                fit = r.fit; sumEscapeLines = r.parameters
+                    fit = r.fit; sumEscapeLines = r.parameters; applied = model; keptSumEscape = r
+                } else {
+                    fit = try EDSFit.run(counts: counts, axis: axis, settings: fitSettings, escapeRatioWarning: policy.fit.escapeRatioWarning)
+                }
             } else {
-                fit = try EDSFit.run(counts: counts, axis: axis, settings: fitSettings, escapeRatioWarning: policy.fit.escapeRatioWarning)
+                switch policy.fit.sumPeaks {
+                case .off:
+                    fit = try EDSFit.run(counts: counts, axis: axis, settings: fitSettings, escapeRatioWarning: policy.fit.escapeRatioWarning)
+                case .always:
+                    let model = SumEscapeModel(sumPeaks: true)
+                    let r = try EDSSumEscapeFit.run(counts: counts, axis: axis, settings: fitSettings, model: model,
+                                                    escapeRatioWarning: policy.fit.escapeRatioWarning)
+                    fit = r.fit; applied = model; sumEscapeLines = r.parameters; keptSumEscape = r
+                case .whenSignificant:
+                    // The test: the self pair of the strongest line alone (Al K-alpha + Al K-alpha in an Al alloy), the largest sum
+                    // peak and the one least likely to sit on an unlisted line. The full model's cross pairs can absorb the misfit of an
+                    // unlisted line at E_i + E_j (Ni K-alpha + O K-alpha on Cu K-alpha, measured on a synthetic spectrum with no pile-up),
+                    // so they are not the test.
+                    let probe = try EDSSumEscapeFit.run(counts: counts, axis: axis, settings: fitSettings,
+                                                        model: SumEscapeModel(sumPeaks: true, parentCount: 1),
+                                                        escapeRatioWarning: policy.fit.escapeRatioWarning)
+                    let misfit = method.estimator == .poissonMaximumLikelihood ? probe.fit.reducedDeviance : probe.fit.pearsonReducedChiSquared
+                    let z = SumPeakRule.significance(probe, misfit: misfit)
+                    let pair = probe.sumPeaks.first?.label ?? "no self pair in the fitted range"
+                    var kept = false
+                    if probe.converged && z >= policy.fit.sumPeakSignificance {
+                        let model = SumEscapeModel(sumPeaks: true)
+                        let r = try EDSSumEscapeFit.run(counts: counts, axis: axis, settings: fitSettings, model: model,
+                                                        escapeRatioWarning: policy.fit.escapeRatioWarning)
+                        if r.converged {
+                            fit = r.fit; applied = model; kept = true; keptSumEscape = r
+                            sumEscapeLines = [String(format: "sum peaks kept: %@ alone is c / \u{03C3}_c = %.1f \u{2265} %g above 0 (\u{03C3}_c scaled by \u{221A}max(misfit, 1))",
+                                                     pair, z, policy.fit.sumPeakSignificance)] + r.parameters
+                            // A real line under the self pair is read as pile-up and never named by the unlisted-line check: say which.
+                            if let e = probe.sumPeaks.first?.energyKeV {
+                                let near = SumPeakRule.coincidentLines(energy: e, resolutionMnKaEV: fitSettings.resolutionMnKaEV, listed: active)
+                                if !near.isEmpty {
+                                    let names = near.prefix(4).map { String(format: "%@ %.3f keV", $0.id, $0.energy) }.joined(separator: ", ")
+                                    let caveat = String(format: "the %@ sum peak (%.3f keV) lies within one FWHM of %@: a real line there is read as pile-up; list the element to test it",
+                                                        pair, e, names)
+                                    sumEscapeLines.insert(caveat, at: 1)
+                                    warnings.append(caveat)
+                                }
+                            }
+                        } else {
+                            fit = probe.baseline
+                            sumEscapeLines = ["sum peaks tested, not kept: the full sum-peak model did not converge; the default fit (one Gaussian per line, no sum peaks)"]
+                        }
+                    } else {
+                        fit = probe.baseline
+                    }
+                    if !kept && sumEscapeLines.isEmpty {
+                        // Not supported by the data: the default fit (the baseline of the same settings, bit for bit).
+                        sumEscapeLines = [String(format: "sum peaks tested, not kept: %@ alone is c / \u{03C3}_c = %@ (needs %g)%@; the default fit (one Gaussian per line, no sum peaks)",
+                                                 pair, z.isFinite ? String(format: "%.1f", z) : "n/a", policy.fit.sumPeakSignificance,
+                                                 probe.converged ? "" : ", the alternation did not converge")]
+                    }
+                }
             }
         }
         catch {
             let why = (error as? LocalizedError)?.errorDescription ?? "\(error)"
             throw QuantificationRefusal("The fit could not run: \(why).")
         }
+        // The sum and escape peaks the kept model explains, on the full axis (0 outside the fitted channels).
+        var sumEscapeCounts: [Double]?
+        if let r = keptSumEscape {
+            var full = [Double](repeating: 0, count: axis.size)
+            for (k, ch) in r.fit.channels.enumerated() where k < r.componentCounts.count { full[ch] = r.componentCounts[k] }
+            sumEscapeCounts = full
+        }
         // The fit appends the weak-line bias note to every continuum fit; it is a statement about a weak line beside Al K-alpha
         // (measured at Mg K-alpha on synthetic data), so it is kept only when that situation is in this result.
         warnings += fit.warnings.filter { $0 != ContinuumForm.weakLineBiasNote }
@@ -452,10 +529,18 @@ public nonisolated enum PooledQuantifier {
             plotModel: plotModel, plotBackground: plotBackground, kSet: kSet, abundanceRefusal: abundanceRefusal,
             absorption: absorption, warnings: warnings, qualityLabel: qualityLabel, quality: quality, footerLines: footer,
             fitSettings: fitSettings, fitRange: fitRange)
+        result.sumEscapeCounts = sumEscapeCounts
+        result.appliedSumEscape = applied
         result.continuumDeadLayerMicrons = deadLayerMicrons
         return result
     }
 
+    /// The model a refit of the same quantification must run with so that it repeats this result's sum-peak decision instead of
+    /// taking it again on other data (the unlisted-line and fit-range checks): the applied model, or an off model (the default fit).
+    package static func sameSumEscape(as q: PooledQuantification) -> SumEscapeModel {
+        q.appliedSumEscape ?? SumEscapeModel()
+    }
+
     /// What every shown sigma covers (WP3b F3 wording): the fit's counting statistics, not the choice of model.
     /// R7 (wp3e item 2): "\u{03C7}\u{00B2}\u{1D63} 54.8 (Pearson)" / "reduced deviance 1.02". Three significant figures at most; no
     /// threshold: the expectation of 1 is a property of the statistic, not a measured cliff.
diff --git a/Sources/SpectroEDX/Quant/ProposalAxisRefinement.swift b/Sources/SpectroEDX/Quant/ProposalAxisRefinement.swift
index ba76f12..1657b4b 100644
--- a/Sources/SpectroEDX/Quant/ProposalAxisRefinement.swift
+++ b/Sources/SpectroEDX/Quant/ProposalAxisRefinement.swift
@@ -73,7 +73,9 @@ extension ElementProposer {
             m.elements = (listed + anchors.filter { !listed.contains($0) }).map { QuantificationMethod.ElementState(symbol: $0, role: .quantify, isManual: false) }
             m.beamEnergyKeV = beamEnergy
             let input = PooledQuantificationInput(counts: spectrum, axis: fileAxis, method: m, metadata: metadata, regionName: regionName, pixelCount: 1,
-                                                  resolutionMnKaEV: resolutionMnKaEV)
+                                                  resolutionMnKaEV: resolutionMnKaEV,
+                                                  sumEscape: SumEscapeModel())   // only the refinement is read: no sum-peak fits
+                                                                                 // (the refinement itself runs without them)
             let fit: PooledQuantification
             do { fit = try PooledQuantifier.run(input, tables: tables, cancelled: cancelled) }
             catch let c as SpectroCancelled { throw c }
diff --git a/Sources/SpectroEDX/Quant/QuantificationPolicy.swift b/Sources/SpectroEDX/Quant/QuantificationPolicy.swift
index 8989e9f..2c7af23 100644
--- a/Sources/SpectroEDX/Quant/QuantificationPolicy.swift
+++ b/Sources/SpectroEDX/Quant/QuantificationPolicy.swift
@@ -94,20 +94,60 @@ public nonisolated struct FitPolicy: Sendable, Equatable, Codable {
     public var escapeRatioWarning: Double
     /// The energy-axis refinement on the pooled spectrum: which of offset, gain and width, the cap, the tolerance and the width bounds.
     public var axisRefinement: AxisRefinementSettings
+    /// Sum (pile-up) peaks of the four strongest alpha lines in the pooled fit (`EDSSumEscapeFit`), when the caller passes no
+    /// `PooledQuantificationInput.sumEscape`. Default `.whenSignificant`: kept when the strongest line's self pair is
+    /// `sumPeakSignificance` sigma above 0. `.off` is the fit before sum peaks were the default (one Gaussian per line, no sum peaks,
+    /// exSpy's model): its numbers are bit for bit the old ones; as a non-default policy it adds the footer line
+    /// `policy (non-default): fit.sumPeaks = off`.
+    public var sumPeaks: SumPeakRule
+    /// The c / sigma_c a pile-up coefficient needs under `.whenSignificant`, sigma_c scaled by the square root of the self-pair fit's
+    /// reduced chi2 (or deviance) when that is above 1. Default 3: a stated choice, not a measured false-keep rate (c is clipped at 0,
+    /// and the rate holds only for a model that fits; a real line under the self pair is read as pile-up whatever the level).
+    public var sumPeakSignificance: Double
 
     public init(fitFromKeV: Double = 0.2, defaultUpperLimitKeV: Double = 20, continuumOrders: [Int] = [9, 5],
                 continuumEdges: [Double] = [FitPolicy.alKEdgeKeV], continuumNonNegative: Bool = true,
                 continuumEfficiency: DetectorLayers? = nil, escapePeaks: Bool = true, maximumPolynomialOrder: Int = 8,
                 irls: IRLSSettings = IRLSSettings(), escapeRatioWarning: Double = 0.05,
                 axisRefinement: AxisRefinementSettings = AxisRefinementSettings(),
-                lineTail: LineTail? = nil, continuumDeadLayer: ContinuumDeadLayer? = nil) {
+                lineTail: LineTail? = nil, sumPeaks: SumPeakRule = .whenSignificant, sumPeakSignificance: Double = 3,
+                continuumDeadLayer: ContinuumDeadLayer? = nil) {
         self.continuumDeadLayer = continuumDeadLayer
         self.fitFromKeV = fitFromKeV; self.defaultUpperLimitKeV = defaultUpperLimitKeV
         self.continuumOrders = continuumOrders; self.continuumEdges = continuumEdges
         self.continuumNonNegative = continuumNonNegative; self.continuumEfficiency = continuumEfficiency
         self.escapePeaks = escapePeaks; self.maximumPolynomialOrder = maximumPolynomialOrder
         self.irls = irls; self.escapeRatioWarning = escapeRatioWarning; self.axisRefinement = axisRefinement
-        self.lineTail = lineTail
+        self.lineTail = lineTail; self.sumPeaks = sumPeaks; self.sumPeakSignificance = sumPeakSignificance
+    }
+
+    /// The fit before sum peaks were the default (one Gaussian per line, no sum peaks): exSpy's line model.
+    public static let exspyEquivalent = FitPolicy(sumPeaks: .off)
+
+    private enum CodingKeys: String, CodingKey {
+        case fitFromKeV, defaultUpperLimitKeV, continuumOrders, continuumEdges, continuumNonNegative, continuumEfficiency, escapePeaks,
+             lineTail, maximumPolynomialOrder, irls, escapeRatioWarning, axisRefinement, sumPeaks, sumPeakSignificance, continuumDeadLayer
+    }
+
+    /// A policy stored before sum peaks were the default has no `sumPeaks`: it reads `.off`, the fit it was stored with (and gets the
+    /// non-default footer line). Every other field is required, as before.
+    public init(from decoder: any Decoder) throws {
+        let c = try decoder.container(keyedBy: CodingKeys.self)
+        self.init(fitFromKeV: try c.decode(Double.self, forKey: .fitFromKeV),
+                  defaultUpperLimitKeV: try c.decode(Double.self, forKey: .defaultUpperLimitKeV),
+                  continuumOrders: try c.decode([Int].self, forKey: .continuumOrders),
+                  continuumEdges: try c.decode([Double].self, forKey: .continuumEdges),
+                  continuumNonNegative: try c.decode(Bool.self, forKey: .continuumNonNegative),
+                  continuumEfficiency: try c.decodeIfPresent(DetectorLayers.self, forKey: .continuumEfficiency),
+                  escapePeaks: try c.decode(Bool.self, forKey: .escapePeaks),
+                  maximumPolynomialOrder: try c.decode(Int.self, forKey: .maximumPolynomialOrder),
+                  irls: try c.decode(IRLSSettings.self, forKey: .irls),
+                  escapeRatioWarning: try c.decode(Double.self, forKey: .escapeRatioWarning),
+                  axisRefinement: try c.decode(AxisRefinementSettings.self, forKey: .axisRefinement),
+                  lineTail: try c.decodeIfPresent(LineTail.self, forKey: .lineTail),
+                  sumPeaks: try c.decodeIfPresent(SumPeakRule.self, forKey: .sumPeaks) ?? .off,
+                  sumPeakSignificance: try c.decodeIfPresent(Double.self, forKey: .sumPeakSignificance) ?? 3,
+                  continuumDeadLayer: try c.decodeIfPresent(ContinuumDeadLayer.self, forKey: .continuumDeadLayer))
     }
 
     /// The Al K absorption edge, keV (X-ray Data Booklet, Table 1-1): the default continuum split.
@@ -132,6 +172,7 @@ public nonisolated struct FitPolicy: Sendable, Equatable, Codable {
         }
         if maximumPolynomialOrder < 0 { return "The largest polynomial order must be 0 or more." }
         if !(escapeRatioWarning.isFinite && escapeRatioWarning > 0) { return "The escape-ratio warning level must be positive." }
+        if !(sumPeakSignificance.isFinite && sumPeakSignificance >= 0) { return "The sum-peak significance level must be a number of 0 or more." }
         if irls.maxIterations < 1 || !(irls.tolerance > 0) || !(irls.muFloor > 0) { return "The Poisson iteration needs a cap of 1 or more, a positive tolerance and a positive floor." }
         if axisRefinement.maxIterations < 1 || !(axisRefinement.tolerance > 0)
             || !(axisRefinement.minimumResolutionEV < axisRefinement.maximumResolutionEV) {
@@ -182,6 +223,53 @@ public nonisolated struct AbundancePolicy: Sendable, Equatable, Codable {
     }
 }
 
+/// Whether the pooled fit models sum (pile-up) peaks (`FitPolicy.sumPeaks`).
+///
+/// Why it is the default: on the public synthetic AlMgSi demo (planted truth: the simulation recipe of `sim_edx.py` v2.0, not a
+/// measurement) the fit without sum peaks read noise-free Si K-alpha 15-18 % low on the Al-rich map and fixture pools (57 % on
+/// the highest-rate pool, 8 % on the precipitate pool) and held a planted Cu K-alpha at 0 at high rate, because the Al+Al sum peak
+/// (2.97 keV) and its neighbours pull the continuum above the Al K edge. With sum peaks the same pools read Si within 4 % (8 % at the
+/// highest rate) and recover the Cu (`DemoEDXPoolTests`). On the Poisson counts of every demo pool the self pair passes the test
+/// (`DemoEDXPoolTests.reducedChiSquareOnThePoissonCounts` pins it); on the one noise-free spectrum without pile-up tested
+/// (`eds-unlisted-sim.json`) the default keeps the fit without sum peaks bit for bit.
+/// What it cannot tell apart: a real line under the self pair (Ar K-alpha 2.957 or Ag L-alpha 2.984 keV under Al+Al 2.973 keV) is
+/// read as pile-up; the footer and the warnings name the alpha lines within one FWHM of it when the sum peaks are kept.
+/// The Al K-alpha tail is NOT part of this rule: fitted together with the sum peaks on the demo's Poisson pools (256 to 2 897
+/// pixels) it read 0 to a third of the planted fraction and left Mg K-alpha up to 25 % low on the map pools, so it is a detector
+/// calibration (`FitPolicy.lineTail`, measured once with `TailEstimate` on a high-count spectrum).
+public nonisolated enum SumPeakRule: String, Sendable, Codable, CaseIterable {
+    /// No sum peaks: one Gaussian per line, the fit as it ran before (exSpy's line model).
+    case off
+    /// Test the sum peak of the strongest line with itself (Al K-alpha + Al K-alpha in an Al alloy) alone; when its pile-up coefficient
+    /// is `FitPolicy.sumPeakSignificance` sigma above 0 (`significance(_:misfit:)`), fit and keep the sum peaks of the four strongest lines; otherwise the default
+    /// fit, bit for bit. Either way the footer says which, with the number. The self pair is the test because the cross pairs can
+    /// absorb an unlisted line at E_i + E_j: on a synthetic spectrum with no pile-up and Cu, Ga and Ge left out of the list, the
+    /// four-parent model kept c at 48 sigma (Ni K-alpha + O K-alpha on Cu K-alpha) while the Si self pair read 0.
+    case whenSignificant
+    /// Fit and keep the sum peaks whatever the data say.
+    case always
+
+    /// c / (sigma_c sqrt(max(misfit, 1))) of a sum-peak fit: NaN when no pair lies in the fitted range (nothing was tested) or there
+    /// is no sigma, 0 when c is held at 0. sigma_c is counting statistics (Var(data) = model); `misfit` (the fit's reduced chi2 or
+    /// deviance) scales it, so a misfit near E_i + E_j does not pass as pile-up on a fit that is far from chi2_red = 1.
+    package static func significance(_ r: SumEscapeResult, misfit: Double) -> Double {
+        guard let c = r.sumCoefficient, !r.sumPeaks.isEmpty else { return .nan }
+        if r.sumCoefficientAtBound || c == 0 { return 0 }
+        guard let s = r.sumCoefficientSigma, s > 0, s.isFinite else { return .nan }
+        let scale = misfit.isFinite ? max(misfit, 1).squareRoot() : 1
+        return c / (s * scale)
+    }
+
+    /// The alpha lines of elements not in `listed` that lie within one FWHM of `energy`: a real line there is read as the sum peak.
+    package static func coincidentLines(energy: Double, resolutionMnKaEV: Double, listed: [String]) -> [XRayLine] {
+        let w = XRayLines.fwhm(resolutionMnKaEV: resolutionMnKaEV, atEnergy: energy) ?? 0.13
+        return XRayLines.all.filter {
+            ["Ka", "La", "Ma"].contains($0.name) && !XRayLines.notRealLines.contains($0.element) && !listed.contains($0.element)
+                && abs($0.energy - energy) <= w
+        }.sorted { abs($0.energy - energy) < abs($1.energy - energy) }
+    }
+}
+
 /// Fewer than two lines above Cliff-Lorimer's intensity floor.
 public nonisolated enum SingleLineRule: String, Sendable, Codable {
     /// Refuse the at% (a 100 % for one element is a property of dose and the floor, not of the specimen).
diff --git a/Sources/SpectroEDX/Quant/UnlistedLineCheck.swift b/Sources/SpectroEDX/Quant/UnlistedLineCheck.swift
index 31bf367..1c5b413 100644
--- a/Sources/SpectroEDX/Quant/UnlistedLineCheck.swift
+++ b/Sources/SpectroEDX/Quant/UnlistedLineCheck.swift
@@ -171,7 +171,10 @@ public nonisolated enum UnlistedLineChecker {
                                 proposer: ElementProposer = ElementProposer(),
                                 cancelled: @Sendable () -> Bool = SpectroCancellation.task,
                                 progress: (@Sendable (Double) -> Void)? = nil) throws -> ProposalResult {
-        try proposer.propose(counts: counts, axis: q.usedAxis, settings: proposerSettings(q), cancelled: cancelled, progress: progress)
+        // The sum and escape peaks the reported fit modelled are explained counts for the proposer: a peak they cover is not an
+        // unlisted element (nil when the sum/escape model is off: the proposer runs as it always ran).
+        try proposer.propose(counts: counts, axis: q.usedAxis, settings: proposerSettings(q), explained: q.sumEscapeCounts,
+                             cancelled: cancelled, progress: progress)
     }
 
     /// "Al_Ka" -> "Al K\u{03B1}", "Lu_Ma" -> "Lu M\u{03B1}", "Cu_Lb1" -> "Cu L\u{03B2}1".
@@ -276,6 +279,7 @@ public nonisolated enum UnlistedLineChecker {
         refit.method.elements.removeAll { e in elements.contains { $0.element == e.symbol } }
         refit.method.elements += elements.map { .init(symbol: $0.element, role: .fitOnly, isManual: false) }
         refit.refinement = q.refinement
+        refit.sumEscape = PooledQuantifier.sameSumEscape(as: q)   // the reported fit's sum-peak decision, not a new one
         let after: PooledQuantification
         do { after = try PooledQuantifier.run(refit, tables: nil, cancelled: cancelled, progress: progress.map { p in { @Sendable f in p(f * 0.95) } }) }
         catch let c as SpectroCancelled { throw c }
diff --git a/Sources/SpectroEDX/SpectroEDX.docc/Quantifying-an-EDX-spectrum.md b/Sources/SpectroEDX/SpectroEDX.docc/Quantifying-an-EDX-spectrum.md
index bcc719f..ef8f615 100644
--- a/Sources/SpectroEDX/SpectroEDX.docc/Quantifying-an-EDX-spectrum.md
+++ b/Sources/SpectroEDX/SpectroEDX.docc/Quantifying-an-EDX-spectrum.md
@@ -90,6 +90,23 @@ func report(_ result: PooledQuantification) {
 - ``PooledQuantification/Row/net`` is the fitted area of the element's alpha line, in counts; `atBound` marks an upper limit.
 - ``PooledQuantification/Row/atomicPercent`` and ``PooledQuantification/Row/atomicSigma`` are present only when at% was computed.
 - ``PooledQuantification/absorption`` says whether the absorption correction applied or was refused, and why.
+- ``PooledQuantification/appliedSumEscape`` is the sum-peak model the fit kept, or nil for the fit without sum peaks.
+
+## Sum peaks and the line tail
+
+By default (``FitPolicy/sumPeaks`` `.whenSignificant`) the pooled fit tests the sum (pile-up) peak of the strongest line with
+itself, and when it lies 3 sigma or more above 0 it models the sum peaks of the four strongest lines (``EDSSumEscapeFit``). The
+footer says which, with the number. exSpy fits one Gaussian per line and no sum peaks; ``FitPolicy/exspyEquivalent`` (or
+``SumPeakRule/off``) gives that fit: its numbers are bit for bit the old ones, and the footer names the non-default policy. On
+the synthetic AlMgSi demo (planted truth: a simulation recipe, not a measurement) the fit without sum peaks read noise-free
+Si K-alpha 8-57 % low, depending on the pool and its count rate, and held a stray Cu K-alpha at 0; with them Si reads within 4 %
+(8 % at the highest count rate) and the Cu is recovered. A real line under the self pair (Ar K-alpha or Ag L-alpha under
+Al+Al) is read as pile-up: when the sum peaks are kept, the footer and the warnings name the lines within one FWHM of it.
+
+The low-energy tail of a strong line (``LineTail``) is a property of the detector, not of the sample, and is not on by default:
+fitted together with the sum peaks on the demo's Poisson pools (256 to 2 897 pixels) it read 0 to a third of the planted fraction
+and left Mg K-alpha beside Al K-alpha up to 25 % low. Measure it once with ``TailEstimate`` on a high-count spectrum of the same
+detector and set it as ``FitPolicy/lineTail``.
 
 ## What is and is not validated
 
diff --git a/Tests/SpectroCoreTests/Fixtures/spectro-golden/demo-edx-tiny-dm4.txt b/Tests/SpectroCoreTests/Fixtures/spectro-golden/demo-edx-tiny-dm4.txt
index 9c71be5..d42ac65 100644
--- a/Tests/SpectroCoreTests/Fixtures/spectro-golden/demo-edx-tiny-dm4.txt
+++ b/Tests/SpectroCoreTests/Fixtures/spectro-golden/demo-edx-tiny-dm4.txt
@@ -663,6 +663,7 @@ whole.quantification.fitSettings.escapePeaks = true
 whole.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 whole.quantification.fitSettings.method = .leastSquares
 whole.quantification.fitSettings.lineTail = nil
+whole.quantification.sumEscapeCounts = nil
 whole.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 whole.quantification.fitRange.toKeV = 40239d932f3bac54 9.8077635536521157
 whole.quantification.fitRange.source = .defaultReach
@@ -674,6 +675,7 @@ whole.quantification.rangeSensitivity = nil
 whole.quantification.unlistedCheck = nil
 whole.quantification.unlistedCheckPending = false
 whole.quantification.abundanceCaveat = nil
+whole.quantification.appliedSumEscape = nil
 whole.quantification.continuumDeadLayerMicrons = nil
 whole.csv-fnv = 37c2c8963acfc357
 whole.rangeSensitivity = nil
@@ -902,6 +904,7 @@ region-locked-axis.quantification.fitSettings.escapePeaks = true
 region-locked-axis.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 region-locked-axis.quantification.fitSettings.method = .leastSquares
 region-locked-axis.quantification.fitSettings.lineTail = nil
+region-locked-axis.quantification.sumEscapeCounts = nil
 region-locked-axis.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 region-locked-axis.quantification.fitRange.toKeV = 402380c28065dbf0 9.7514839290942916
 region-locked-axis.quantification.fitRange.source = .defaultReach
@@ -913,6 +916,7 @@ region-locked-axis.quantification.rangeSensitivity = nil
 region-locked-axis.quantification.unlistedCheck = nil
 region-locked-axis.quantification.unlistedCheckPending = false
 region-locked-axis.quantification.abundanceCaveat = nil
+region-locked-axis.quantification.appliedSumEscape = nil
 region-locked-axis.quantification.continuumDeadLayerMicrons = nil
 region-locked-axis.csv-fnv = 90f4608d5329d926
 region-locked-axis.rangeSensitivity = nil
diff --git a/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-realistic-l-sim.txt b/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-realistic-l-sim.txt
index db10077..8cdd09a 100644
--- a/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-realistic-l-sim.txt
+++ b/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-realistic-l-sim.txt
@@ -318,6 +318,7 @@ seed0.seven.quantification.fitSettings.escapePeaks = true
 seed0.seven.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 seed0.seven.quantification.fitSettings.method = .leastSquares
 seed0.seven.quantification.fitSettings.lineTail = nil
+seed0.seven.quantification.sumEscapeCounts = nil
 seed0.seven.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 seed0.seven.quantification.fitRange.toKeV = 4034000000000000 20
 seed0.seven.quantification.fitRange.source = .defaultLimit
@@ -329,6 +330,7 @@ seed0.seven.quantification.rangeSensitivity = nil
 seed0.seven.quantification.unlistedCheck = nil
 seed0.seven.quantification.unlistedCheckPending = false
 seed0.seven.quantification.abundanceCaveat = nil
+seed0.seven.quantification.appliedSumEscape = nil
 seed0.seven.quantification.continuumDeadLayerMicrons = nil
 seed0.seven.csv-fnv = 176c2eb938b3c80a
 seed0.seven.rangeSensitivity.alternativeToKeV = 4053fdf036df3a38 79.967786520000004
@@ -687,6 +689,7 @@ seed0.seven-60keV.quantification.fitSettings.escapePeaks = true
 seed0.seven-60keV.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 seed0.seven-60keV.quantification.fitSettings.method = .leastSquares
 seed0.seven-60keV.quantification.fitSettings.lineTail = nil
+seed0.seven-60keV.quantification.sumEscapeCounts = nil
 seed0.seven-60keV.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 seed0.seven-60keV.quantification.fitRange.toKeV = 404e000000000000 60
 seed0.seven-60keV.quantification.fitRange.source = .typed
@@ -698,6 +701,7 @@ seed0.seven-60keV.quantification.rangeSensitivity = nil
 seed0.seven-60keV.quantification.unlistedCheck = nil
 seed0.seven-60keV.quantification.unlistedCheckPending = false
 seed0.seven-60keV.quantification.abundanceCaveat = nil
+seed0.seven-60keV.quantification.appliedSumEscape = nil
 seed0.seven-60keV.quantification.continuumDeadLayerMicrons = nil
 seed0.seven-60keV.csv-fnv = b4f647ee0ab928a3
 seed0.seven-60keV.rangeSensitivity = nil
@@ -983,6 +987,7 @@ seed0.four.quantification.fitSettings.escapePeaks = true
 seed0.four.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 seed0.four.quantification.fitSettings.method = .leastSquares
 seed0.four.quantification.fitSettings.lineTail = nil
+seed0.four.quantification.sumEscapeCounts = nil
 seed0.four.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 seed0.four.quantification.fitRange.toKeV = 4034000000000000 20
 seed0.four.quantification.fitRange.source = .defaultLimit
@@ -994,6 +999,7 @@ seed0.four.quantification.rangeSensitivity = nil
 seed0.four.quantification.unlistedCheck = nil
 seed0.four.quantification.unlistedCheckPending = false
 seed0.four.quantification.abundanceCaveat = nil
+seed0.four.quantification.appliedSumEscape = nil
 seed0.four.quantification.continuumDeadLayerMicrons = nil
 seed0.four.csv-fnv = 527d12db2afd525d
 seed0.four.rangeSensitivity.alternativeToKeV = 4053fdf036df3a38 79.967786520000004
diff --git a/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-unlisted-sim.txt b/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-unlisted-sim.txt
index d7b4b07..e0c5854 100644
--- a/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-unlisted-sim.txt
+++ b/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-unlisted-sim.txt
@@ -292,6 +292,7 @@ seed0.four.quantification.fitSettings.escapePeaks = true
 seed0.four.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 seed0.four.quantification.fitSettings.method = .leastSquares
 seed0.four.quantification.fitSettings.lineTail = nil
+seed0.four.quantification.sumEscapeCounts = nil
 seed0.four.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 seed0.four.quantification.fitRange.toKeV = 4034000000000000 20
 seed0.four.quantification.fitRange.source = .defaultLimit
@@ -303,6 +304,7 @@ seed0.four.quantification.rangeSensitivity = nil
 seed0.four.quantification.unlistedCheck = nil
 seed0.four.quantification.unlistedCheckPending = false
 seed0.four.quantification.abundanceCaveat = nil
+seed0.four.quantification.appliedSumEscape = nil
 seed0.four.quantification.continuumDeadLayerMicrons = nil
 seed0.four.csv-fnv = 39e1a8432149c423
 seed0.four.rangeSensitivity.alternativeToKeV = 4053fdc30de1dcc8 79.965030165261055
@@ -1525,6 +1527,7 @@ seed0.seven.quantification.fitSettings.escapePeaks = true
 seed0.seven.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 seed0.seven.quantification.fitSettings.method = .leastSquares
 seed0.seven.quantification.fitSettings.lineTail = nil
+seed0.seven.quantification.sumEscapeCounts = nil
 seed0.seven.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 seed0.seven.quantification.fitRange.toKeV = 4034000000000000 20
 seed0.seven.quantification.fitRange.source = .defaultLimit
@@ -1536,6 +1539,7 @@ seed0.seven.quantification.rangeSensitivity = nil
 seed0.seven.quantification.unlistedCheck = nil
 seed0.seven.quantification.unlistedCheckPending = false
 seed0.seven.quantification.abundanceCaveat = nil
+seed0.seven.quantification.appliedSumEscape = nil
 seed0.seven.quantification.continuumDeadLayerMicrons = nil
 seed0.seven.csv-fnv = 5312e03b97452089
 seed0.seven.rangeSensitivity.alternativeToKeV = 4053fdffd20951d7 79.968739041424996
diff --git a/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-weakline-sim.txt b/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-weakline-sim.txt
index 2b7857d..168481e 100644
--- a/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-weakline-sim.txt
+++ b/Tests/SpectroCoreTests/Fixtures/spectro-golden/eds-weakline-sim.txt
@@ -212,6 +212,7 @@ level0.quantification.fitSettings.escapePeaks = true
 level0.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 level0.quantification.fitSettings.method = .leastSquares
 level0.quantification.fitSettings.lineTail = nil
+level0.quantification.sumEscapeCounts = nil
 level0.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 level0.quantification.fitRange.toKeV = 40340160bc0314bd 20.005382300140571
 level0.quantification.fitRange.source = .defaultReach
@@ -223,6 +224,7 @@ level0.quantification.rangeSensitivity = nil
 level0.quantification.unlistedCheck = nil
 level0.quantification.unlistedCheckPending = false
 level0.quantification.abundanceCaveat = nil
+level0.quantification.appliedSumEscape = nil
 level0.quantification.continuumDeadLayerMicrons = nil
 level0.csv-fnv = 7bdff3fd070201e7
 level0.rangeSensitivity = nil
@@ -439,6 +441,7 @@ level4.quantification.fitSettings.escapePeaks = true
 level4.quantification.fitSettings.referenceShapes.shapes: n 0 sum 0000000000000000 0 fnv cbf29ce484222325
 level4.quantification.fitSettings.method = .leastSquares
 level4.quantification.fitSettings.lineTail = nil
+level4.quantification.sumEscapeCounts = nil
 level4.quantification.fitRange.fromKeV = 3fc999999999999a 0.20000000000000001
 level4.quantification.fitRange.toKeV = 403404cb90bd12c4 20.018731161270594
 level4.quantification.fitRange.source = .defaultReach
@@ -450,6 +453,7 @@ level4.quantification.rangeSensitivity = nil
 level4.quantification.unlistedCheck = nil
 level4.quantification.unlistedCheckPending = false
 level4.quantification.abundanceCaveat = nil
+level4.quantification.appliedSumEscape = nil
 level4.quantification.continuumDeadLayerMicrons = nil
 level4.csv-fnv = a32acb6ac2acfd15
 level4.rangeSensitivity = nil
diff --git a/Tests/SpectroEDXTests/DemoEDXPoolTests.swift b/Tests/SpectroEDXTests/DemoEDXPoolTests.swift
new file mode 100644
index 0000000..6ed4aa0
--- /dev/null
+++ b/Tests/SpectroEDXTests/DemoEDXPoolTests.swift
@@ -0,0 +1,266 @@
+import Foundation
+import Testing
+import SpectroTestSupport
+import SpectroCore
+import SpectroEDX
+
+/// The pooled quantification against PLANTED TRUTH ON SYNTHETIC DATA: five pools of the public AlMgSi demo set (mac4DSTEM `demo-edx`,
+/// `tools/demo-edx/sim_edx.py` v2.0; `tools/edx-sim/demo_pools.py` wrote `edx-demo-pools.json`) and the kit's own
+/// `eds-absorption-truth.json` pool. The truth is the simulation recipe, not a measurement, so every number here stays
+/// `validation: "none"`.
+///
+/// The generator plants what a real detector does and exSpy's line model leaves out: sum (pile-up) peaks whose parents lose the
+/// photons, a 1.5 % Al K-alpha tail (0.12 keV), Si escape, Si internal fluorescence and stray Cu K. Each pool is fitted on the
+/// generator's noise-free expected spectrum x100 (the fit's bias without noise) and, where said, on its Poisson counts. Setup as the
+/// apps run it: true axis locked, the generator's true k typed (weight convention, relative to the first quantified element), the
+/// truth geometry and thickness, absorption on. Cu and O are Fit only: the demo's Cu is a stray grid line (the test's choice).
+///
+/// Si planted counts include the Si internal-fluorescence peak at the same energy (the kit's convention, `SpectroscopyAbsorptionTruthTests`).
+///
+/// What the bounds are: MEASURED regression bounds on fixed inputs, not derived limits. The fit with the default sum peaks reads
+/// noise-free Si K-alpha -0.0 to -4.0 % on the pools at up to 300 counts/px and -7.9 % on L5 (the highest rate, where the
+/// generator's pile-up takes 11 % of the Al K-alpha photons); the bound is 5 % (10 % on L5). The fit without sum peaks read -8 to
+/// -57 % on the same pools: the Al+Al sum peak (2.97 keV) pulls the continuum segment above the Al K edge and Si K-alpha with it.
+struct DemoEDXPoolTests {
+    static let tables = try! QuantificationTables(directory: EDXFixtures.repoRoot.appendingPathComponent("Sources/SpectroEDX/Resources/Spectroscopy"))
+
+    private struct Axis: Decodable { let offset: Double; let scale: Double }
+    private struct DemoPool: Decodable {
+        let name: String; let npix: Int
+        let thicknessNm: Double
+        let truthAt: [String: Double]
+        let axisTrue: Axis
+        let counts: [Int]; let expected: [Double]; let planted: [String: Double]
+        enum CodingKeys: String, CodingKey {
+            case name, npix, counts, expected, planted
+            case thicknessNm = "thickness_nm", truthAt = "truth_at", axisTrue = "axis_true"
+        }
+    }
+    private struct DemoDoc: Decodable {
+        let trueK: [String: Double]; let mass: [String: Double]; let pools: [DemoPool]
+        enum CodingKeys: String, CodingKey { case pools; case trueK = "true_k_counts_per_atom_nm2"; case mass = "atomic_mass" }
+    }
+    private static let demo = try! JSONDecoder().decode(DemoDoc.self, from: Data(contentsOf: EDXFixtures.url("edx-demo-pools.json")))
+
+    /// One pool in the form the tests use.
+    struct Case {
+        let name: String
+        let axis: EnergyAxis
+        let npix: Int
+        let thicknessNm: Double
+        let quantified: [String]
+        let trueK: [String: Double]
+        let expected: [Double]
+        let counts: [Int]?
+        /// Planted Mg K-alpha, Si K-alpha (+ internal fluorescence) and Cu K-alpha (stray + sample), counts; nil when not planted or not known.
+        let mg: Double, si: Double, cu: Double?
+    }
+
+    static let cases: [Case] = {
+        var out: [Case] = demo.pools.map { p in
+            Case(name: p.name, axis: EnergyAxis(offset: p.axisTrue.offset, scale: p.axisTrue.scale, size: p.expected.count), npix: p.npix,
+                 thicknessNm: p.thicknessNm, quantified: p.truthAt["Al"] == nil ? ["Mg", "Si"] : ["Al", "Mg", "Si"], trueK: demo.trueK,
+                 expected: p.expected, counts: p.counts, mg: p.planted["Mg_Ka"]!, si: p.planted["Si_Ka"]! + p.planted["Si_Ka_internal"]!,
+                 cu: p.planted["Cu_Ka"]! + p.planted["Cu_Ka_stray"]!)
+        }
+        let fx = EDXFixtures.jsonObject("eds-absorption-truth.json")
+        let e = fx["expected"] as! [Double]
+        let with = fx["areas_with_absorption"] as! [String: Double]
+        out.append(Case(name: "absorption-truth", axis: EnergyAxis(offset: fx["offset"] as! Double, scale: fx["scale"] as! Double, size: e.count),
+                        npix: fx["npix"] as! Int, thicknessNm: fx["thickness_nm"] as! Double, quantified: ["Al", "Mg", "Si"],
+                        trueK: fx["true_k_counts_per_atom_nm2"] as! [String: Double], expected: e, counts: nil,
+                        mg: with["Mg_Ka"]!, si: with["Si_Ka"]! + (fx["area_si_ka_internal"] as! Double), cu: nil))
+        return out
+    }()
+
+    static func named(_ prefix: String) -> Case { cases.first { $0.name.hasPrefix(prefix) }! }
+
+    static func input(_ c: Case, noiseFree: Bool, policy: QuantificationPolicy = .default) -> PooledQuantificationInput {
+        let counts = noiseFree ? c.expected.map { UInt64(($0 * 100).rounded()) } : c.counts!.map { UInt64($0) }
+        var m = QuantificationMethod()
+        var roles: [(String, QuantificationMethod.ElementRole)] = c.quantified.map { ($0, .quantify) }
+        if !c.quantified.contains("Al") { roles.append(("Al", .fitOnly)) }
+        roles += [("Cu", .fitOnly), ("O", .fitOnly)]
+        m.elements = roles.map { .init(symbol: $0.0, role: $0.1, isManual: false) }
+        m.beamEnergyKeV = 200
+        m.lockEnergyAxis = true
+        m.kFactorSource = .typed
+        m.kSource = "demo generator true k (Gp x s x eps), weight convention"; m.kDate = "2026-10-31"; m.kReference = c.quantified[0]
+        let mass = demo.mass
+        let w = c.quantified.map { mass[$0]! / c.trueK[$0]! }
+        m.typedK = zip(c.quantified, w).map { .init(element: $0.0, k: $0.1 / w[0], relativeSigma: 0) }
+        m.thickness = .init(nanometres: c.thicknessNm, sigmaNanometres: 0)
+        m.absorptionCorrection = true
+        var meta = SpectrumImageMetadata(fileName: c.name, filePath: c.name, scanWidth: 1, scanHeight: 1, channelCount: counts.count,
+                                         energyOffsetEV: c.axis.offset * 1000, energyDispersionEV: c.axis.scale * 1000)
+        meta.origin = .veloxEMD
+        meta.alphaTiltDegrees = -16.87; meta.betaTiltDegrees = 0
+        meta.detectors = zip([45.0, 135, 225, 315], [0.4, 0.2, 0.1, 0.3]).enumerated().map { i, a in
+            SpectrumDetectorSegment(name: "SuperXG1\(i + 1)", azimuthDegrees: a.0, elevationDegrees: 22, solidAngle: a.1)
+        }
+        return PooledQuantificationInput(counts: counts, axis: c.axis, method: m, metadata: meta, regionName: c.name, pixelCount: c.npix,
+                                         resolutionMnKaEV: 130, policy: policy)
+    }
+
+    static var withoutSumPeaks: QuantificationPolicy { QuantificationPolicy(fit: .exspyEquivalent) }
+
+    static func net(_ q: PooledQuantification, _ group: String) -> Double { q.fit.groupIDs.firstIndex(of: group).map { q.fit.values[$0] } ?? .nan }
+    static func say(_ s: String) { FileHandle.standardError.write(Data(("DEMO " + s + "\n").utf8)) }
+
+    /// Red before sum peaks were the default: Si K-alpha read 8-57 % low noise-free. Now within 5 % (10 % at L5's rate), and the
+    /// footer names the decision with its number.
+    @Test(arguments: cases.map(\.name))
+    func defaultFitRecoversSiKAlphaNoiseFree(_ name: String) throws {
+        let c = Self.named(name)
+        let q = try PooledQuantifier.run(Self.input(c, noiseFree: true), tables: Self.tables)
+        let off = try PooledQuantifier.run(Self.input(c, noiseFree: true, policy: Self.withoutSumPeaks), tables: Self.tables)
+        let si = Self.net(q, "Si_Ka") / 100 / c.si - 1, siOff = Self.net(off, "Si_Ka") / 100 / c.si - 1
+        Self.say(String(format: "%@ Si %+.4f (without sum peaks %+.4f) | %@", name, si, siOff, q.footerLines.first { $0.hasPrefix("sum peaks") } ?? "-"))
+        #expect(abs(si) <= (name.hasPrefix("L5") ? 0.10 : 0.05), "\(name): Si K-alpha \(si)")
+        #expect(q.appliedSumEscape == SumEscapeModel(sumPeaks: true))
+        #expect(q.footerLines.contains { $0.hasPrefix("sum peaks kept") })
+        #expect(off.appliedSumEscape == nil)
+        #expect(off.footerLines.contains("policy (non-default): fit.sumPeaks = off"))
+        #expect(abs(si) < abs(siOff) || abs(siOff) < 0.01, "\(name): the default is not closer than the fit without sum peaks")
+        #expect(q.quality < off.quality, "\(name): the fit with sum peaks fits worse")
+    }
+
+    /// Cu K-alpha at high rate: the fit without sum peaks held it at 0 (L6) or read 40 % of it (L5, L7), noise-free; the default
+    /// reads 92-97 %. At the map pools' low rate both fits read it within 5 %.
+    @Test func cuKAlphaIsRecoveredAtHighRate() throws {
+        for c in Self.cases where c.cu != nil {
+            let q = try PooledQuantifier.run(Self.input(c, noiseFree: true), tables: Self.tables)
+            let off = try PooledQuantifier.run(Self.input(c, noiseFree: true, policy: Self.withoutSumPeaks), tables: Self.tables)
+            let cu = Self.net(q, "Cu_Ka") / 100 / c.cu!, cuOff = Self.net(off, "Cu_Ka") / 100 / c.cu!
+            Self.say(String(format: "%@ Cu read %.3f of planted (without sum peaks %.3f)", c.name, cu, cuOff))
+            if c.name.hasPrefix("L") {
+                #expect(cu >= 0.85, "\(c.name): Cu \(cu)")
+                #expect(cuOff <= 0.45, "\(c.name): without sum peaks Cu \(cuOff)")
+            } else {
+                #expect(abs(cu - 1) <= 0.05 && abs(cuOff - 1) <= 0.05, "\(c.name): Cu \(cu), without sum peaks \(cuOff)")
+            }
+        }
+        // On the Poisson counts of L6 (300 counts/px): 123 counts of stray Cu above the window background.
+        let l6 = Self.named("L6")
+        let q = try PooledQuantifier.run(Self.input(l6, noiseFree: false), tables: Self.tables)
+        let off = try PooledQuantifier.run(Self.input(l6, noiseFree: false, policy: Self.withoutSumPeaks), tables: Self.tables)
+        #expect(Self.net(q, "Cu_Ka") / l6.cu! >= 0.85)
+        #expect(Self.net(off, "Cu_Ka") / l6.cu! <= 0.05)
+    }
+
+    /// The Poisson counts of every demo pool: the fit without sum peaks has a reduced chi2 of 2.1-31; with them 0.7-1.1.
+    @Test func reducedChiSquareOnThePoissonCounts() throws {
+        for c in Self.cases where c.counts != nil {
+            let q = try PooledQuantifier.run(Self.input(c, noiseFree: false), tables: Self.tables)
+            let off = try PooledQuantifier.run(Self.input(c, noiseFree: false, policy: Self.withoutSumPeaks), tables: Self.tables)
+            Self.say(String(format: "%@ chi2_red %.3f (without sum peaks %.3f) | %@", c.name, q.quality, off.quality,
+                            q.footerLines.first { $0.hasPrefix("sum peaks") } ?? "-"))
+            #expect(q.appliedSumEscape == SumEscapeModel(sumPeaks: true), "\(c.name): the self pair did not pass on the Poisson counts")
+            #expect(q.quality <= 1.2, "\(c.name): \(q.quality)")
+            #expect(off.quality >= 2, "\(c.name): \(off.quality)")
+        }
+    }
+
+    /// The Al K-alpha tail is a detector calibration, not part of the default. Measured once on a high-count spectrum of the same
+    /// detector (the absorption-truth pool, 1e4 px) with `TailEstimate`, then typed into `FitPolicy.lineTail`, it takes the noise-free
+    /// Mg K-alpha bias next to Al K-alpha (-22 % on L5, -32 % on recipe A, -45 % on the matrix map) to within 5 % on L5 and recipe A,
+    /// and to -15 % on the matrix map (which
+    /// pools seven recipes and thicknesses; not explained). Without it the default fit leaves Mg where it was (the tail is not a sum peak).
+    @Test func aCalibratedTailTakesTheMgBiasOut() throws {
+        let fx = Self.named("absorption-truth")
+        var s = FitSettings.standard(elements: ["Al", "Mg", "Si", "Cu", "O"], axis: fx.axis, resolutionMnKaEV: 130, beamEnergy: 200)
+        s.method = .leastSquares
+        let tail = try TailEstimate.measure(counts: fx.expected.map { $0.rounded() }, axis: fx.axis, settings: s, elements: ["Al", "Mg", "Si", "Cu", "O"]).tail
+        Self.say(String(format: "tail measured on the absorption-truth pool: f %.4f, slope %.3f keV (planted 0.015, 0.12)", tail.fraction, tail.slopeKeV))
+        #expect(tail.fraction > 0.005 && tail.fraction < 0.02)
+        var calibrated = QuantificationPolicy.default
+        calibrated.fit.lineTail = tail
+        for (name, bound) in [("L5", 0.05), ("L6", 0.05), ("L7", 0.05), ("M_A", 0.05), ("M_matrix", 0.16)] {
+            let c = Self.named(name)
+            let q = try PooledQuantifier.run(Self.input(c, noiseFree: true, policy: calibrated), tables: Self.tables)
+            let plain = try PooledQuantifier.run(Self.input(c, noiseFree: true), tables: Self.tables)
+            let off = try PooledQuantifier.run(Self.input(c, noiseFree: true, policy: Self.withoutSumPeaks), tables: Self.tables)
+            let mg = Self.net(q, "Mg_Ka") / 100 / c.mg - 1, mgPlain = Self.net(plain, "Mg_Ka") / 100 / c.mg - 1
+            let mgOff = Self.net(off, "Mg_Ka") / 100 / c.mg - 1
+            Self.say(String(format: "%@ Mg with the calibrated tail %+.4f, default %+.4f, without sum peaks %+.4f", name, mg, mgPlain, mgOff))
+            #expect(abs(mg) <= bound, "\(name): Mg \(mg)")
+            #expect(abs(mgPlain - mgOff) <= 0.03, "\(name): sum peaks moved Mg from \(mgOff) to \(mgPlain)")
+        }
+    }
+
+    /// The unlisted-line check on the Poisson counts of the Al-rich pools: without sum peaks the Al+Al sum (2.973 keV) is left in
+    /// the residual (Ar K-alpha 2.957 keV, Ag L-alpha 2.984 keV); with the default it is a modelled sum peak, explained to the proposer,
+    /// and neither Ar nor Ag is named.
+    @Test(arguments: ["L5", "M_A", "M_matrix"])
+    func theAlAlSumIsNotNamedAsArOrAg(_ name: String) throws {
+        let c = Self.named(name)
+        let input = Self.input(c, noiseFree: false)
+        let q = try PooledQuantifier.run(input, tables: Self.tables)
+        let proposal = try UnlistedLineChecker.propose(counts: input.counts.map { Double($0) }, quantification: q)
+        let check = UnlistedLineChecker.check(proposal: proposal, input: input, quantification: q)
+        Self.say("\(name) unlisted check, default: \(check.summary)")
+        #expect(!check.names.contains("Ar") && !check.names.contains("Ag"), "\(name): \(check.summary)")
+        // The other side of the same coin: a real Ar or Ag line there would be read as pile-up, and the result says so.
+        #expect(q.warnings.contains { $0.contains("Ar_Ka") && $0.contains("read as pile-up") }, "\(name): \(q.warnings)")
+        #expect(q.footerLines.contains { $0.contains("Ar_Ka") }, "\(name): \(q.footerLines)")
+    }
+
+    /// `.off` is the fit as it ran before, bit for bit: the same as a caller's explicit `SumEscapeModel()` (both off).
+    @Test func theSwitchGivesTheFitWithoutSumPeaksBitForBit() throws {
+        let c = Self.named("L6")
+        let off = try PooledQuantifier.run(Self.input(c, noiseFree: false, policy: Self.withoutSumPeaks), tables: Self.tables)
+        var explicit = Self.input(c, noiseFree: false)
+        explicit.sumEscape = SumEscapeModel()
+        let e = try PooledQuantifier.run(explicit, tables: Self.tables)
+        #expect(off.fit.values == e.fit.values)
+        #expect(off.fit.model == e.fit.model)
+        #expect(off.rows == e.rows)
+        #expect(FitPolicy.exspyEquivalent.sumPeaks == .off)
+        #expect(FitPolicy.default.sumPeaks == .whenSignificant)
+    }
+
+    /// A policy stored before `sumPeaks` existed reads `.off` (the fit it was stored with); the new fields round-trip.
+    @Test func aStoredPolicyWithoutTheFieldReadsOff() throws {
+        var o = try #require(try JSONSerialization.jsonObject(with: Data(QuantificationPolicy.default.canonicalJSON.utf8)) as? [String: Any])
+        var fit = try #require(o["fit"] as? [String: Any])
+        #expect(fit["sumPeaks"] as? String == "whenSignificant")
+        fit.removeValue(forKey: "sumPeaks"); fit.removeValue(forKey: "sumPeakSignificance")
+        o["fit"] = fit
+        let old = try JSONDecoder().decode(QuantificationPolicy.self, from: JSONSerialization.data(withJSONObject: o))
+        #expect(old.fit.sumPeaks == .off)
+        #expect(old.fit.sumPeakSignificance == 3)
+        var p = QuantificationPolicy.default
+        p.fit.sumPeaks = .always; p.fit.sumPeakSignificance = 5
+        #expect(try JSONDecoder().decode(QuantificationPolicy.self, from: Data(p.canonicalJSON.utf8)) == p)
+        p.fit.sumPeakSignificance = -1
+        #expect(p.problem != nil)
+    }
+
+    /// No pile-up planted (`eds-unlisted-sim.json`, noise-free, the one such spectrum tested): the default keeps the fit without sum
+    /// peaks bit for bit, and says so. With Cu, Ga
+    /// and Ge left out of the list the four-parent model would keep c at 48 sigma (Ni K-alpha + O K-alpha lies on Cu K-alpha); the
+    /// self-pair test (Si + Si) reads 0, so nothing is kept.
+    @Test(arguments: [false, true])
+    func noPileUpKeepsTheDefaultFit(incompleteList: Bool) throws {
+        let o = EDXFixtures.jsonObject("eds-unlisted-sim.json")
+        let e = o["expected"] as! [Double]
+        let axis = EnergyAxis(offset: o["offset"] as! Double, scale: o["scale"] as! Double, size: e.count)
+        var m = QuantificationMethod()
+        let listed = incompleteList ? ["O", "Si", "Ti", "Ni"] : ["O", "Si", "Ti", "Ni", "Ge", "Cu", "Ga"]
+        m.elements = listed.map { .init(symbol: $0, role: .quantify, isManual: false) }
+        m.beamEnergyKeV = 200
+        m.absorptionCorrection = false
+        m.lockEnergyAxis = true
+        let meta = SpectrumImageMetadata(fileName: "eds-unlisted-sim.json", filePath: "", scanWidth: 1, scanHeight: 1, channelCount: e.count,
+                                         energyOffsetEV: axis.offset * 1000, energyDispersionEV: axis.scale * 1000)
+        var input = PooledQuantificationInput(counts: e.map { UInt64($0.rounded()) }, axis: axis, method: m, metadata: meta,
+                                              regionName: "synthetic", pixelCount: 1)
+        let q = try PooledQuantifier.run(input, tables: Self.tables)
+        input.policy = Self.withoutSumPeaks
+        let off = try PooledQuantifier.run(input, tables: Self.tables)
+        #expect(q.appliedSumEscape == nil)
+        #expect(q.fit.values == off.fit.values)
+        #expect(q.rows == off.rows)
+        #expect(q.footerLines.contains { $0.hasPrefix("sum peaks tested, not kept: Si_Ka + Si_Ka alone") }, "\(q.footerLines)")
+    }
+}
diff --git a/Tests/SpectroEDXTests/Fixtures/edx-demo-pools.json b/Tests/SpectroEDXTests/Fixtures/edx-demo-pools.json
new file mode 100644
index 0000000..c89df08
--- /dev/null
+++ b/Tests/SpectroEDXTests/Fixtures/edx-demo-pools.json
@@ -0,0 +1 @@
+{"atomic_mass":{"Al":26.9815,"Mg":24.305,"Si":28.0855},"generator":"mac4DSTEM demo-edx, tools/demo-edx/sim_edx.py v2.0 (seed 42, ladder seed 52); truth is the simulation 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8,9,3,7,10,5,5,8,6,5,3,11,6,3,3,4,1,3,8,7,5,15,1,3,9,4,3,12,4,5,8,7,3,7,2,4,5,5,2,4,4,7,5,3,7,3,6,7,6,6,5,5,7,4,4,4,3,2,4,3,8,2,6,5,3,3,3,7,5,5,9,2,4,3,8,9,4,10,5,7,5,2,2,5,3,2,6,2,3,4,4,8,8,3,0,1,9,8,5,4,6,4,7,2,7,2,5,2,2,8,5,2,8,4,2,3,5,1,5,3,5,2,10,2,5,5,11,5,3,8,7,4,6,5,4,5,4,3,7,5,4,5,2,4,3,3,6,2,6,7,5,1,8,2,3,3,4,5,4,4,5,5,4,2,10,9,5,5,4,5,7,4,3,3,2,6,4,5,4,6,5,2,1,5,4,1,7,9,4,6,3,6,3,3,2,4,4,5,4,6,4,1,7,3,3,4,6,5,2,6,6,3,4,4,4,4,3,4,4,2,6,5,5,5,6,2,9,2,5,6,3,4,9,1,6,3,4,5,8,5,7,6,5,5,11,5,5,8,3,5,6,2,3,6,5,8,6,4,8,4,6,6,6,5,2,4,6,3,4,6,4,4,6,5,4,2,4,6,2,2,1,4,4,2,4,2,4,4,5,4,6,4,2,3,5,2,2,12,3,7,3,7,4,4,5,8,5,4,6,6,2,6,3,8,5,4,3,4,0,5,4,11,5,8,6,5,3,5,7,7,5,3,7,4,9,4,10,7,6,6,6,0,6,3,6,3,2,0,2,2,6,4,3,6,7,5,4,4,6,4,3,4,3,3,6,2,5,7,4,7,3,9,4,2,4,4,3,2,4,4,2,7,6,2,3,2,6,6,3,4,3,3,3,4,0,4,11,4,2,4,7,9,3,2,3,3,2,3,5,6,5,6,1,5,7,5,5,10,5,7,4,4,5,3,4,4,3,2,2,6,6,3,3,4,3,6,3,5,3,5,5,3,7,3,2,4,4,2,8,6,2,2,2,3,5,7,5,5,9,3,5,4,2,6,1,1,2,5,2,3,10,4,1,7,7,4,3,0,7,5,3,1,5,4,2,8,5,3,4,5,7,3,3,1,4,4,1,9,2,3,4,4,4,5,1,7,3,5,2,4,2,3,3,5,5,6,6,3,6,6,4,7,6,5,5,4,4,2,7,3,8,3,7,5,8,4,5,5,2,9,7,3,5,12,9,6,7,5,4,11,6,7,11,5,6,5,7,7,3,6,6,12,5,8,5,6,6,3,8,6,5,8,2,2,4,3,4,6,5,1,1,5,3,3,4,4,2,6,2,2,4,8,3,1,3,1,4,0,2,5,4,1,2,2,8,4,2,4,3,4,1,5,2,3,5,2,6,2,4,1,6,6,7,7,2,4,4,1,2,2,5,3,4,1,4,2,6,4,4,3,1,3,2,1,1,5,9,2,6,4,0,6,3,4,1,3,2,3,3,0,3,2,0,2,3,2,3,1,4,4,0,4,2,6,1,5,2,4,3,4,2,2,5,2,1,3,5,3,5,2,5,4,2,3,5,3,2,3,3,4,4,4,1,3,2,4,2,5,1,4,7,0,5,4,4,4,5,4,6,3,4,5,3,3,4,7,3,7,3,4,3,5,2,2,4,2,2,4,2,2,3,2,2,1,4,1,2,0,0,3,4,4,3,4,0,3,5,0,1,3,4,4,1,1,1,3,3,1,2,1,3,3,5,2,5,3,1,3,4,5,1,2,0,3,3,1,4,3,3,4,3,4,6,5,6,4,3,3,0,2,2,2,5,4,1,2,4,1,2,6,2,1,1,4,3,4,1,3,4,2,2,6,4,3,4,6,1,4,1,7,3,1,1,2,3,3,2,1,2,1,5,3,2,5,4,5,3,2,2,2,4,4,2,1,1,2,4,0,1,3,4,5,0,2,2,4,2,3,2,6,3,2,2,2,1,3,5,2,2,3,3,9,3,5,8,1,4,4,2,2,3,3,3,3,4,4,5,1,2,3,3,1,2,1,3,6,2,4,3,4,0,0,2,2,7,4,4,4,2,2,1,7,9,4,1,0,3,3,5,1,1,2,5,0,3,2,0,4,9,4,4,4,3,1,3,5,2,2,1,3,5,5,3,1,4,6,3,5,4,4,1,2,6,2,5,1,4,4,0,3,6,1,4,3,4,2,2,2,2,2,3,5,3,3,2,0,5,2,1,2,2,2,4,1,1,5,1,1,4,4,0,3,0,5,4,3,0,2,1,3,3,3,2,2,3,1,2,4,6,2,4,0,1,2,1,3,2,5,0,1,3,3,3,2,5,4,5,5,1,2,4,2,5,3,2,2,5,4,2,4,2,4,2,3,5,2,2,4,1,2,3,6,2,6,2,4,2,8,1,2,0,2,4,4,4,3,1,1,2,0,3,3,2,1,1,2,2,2,1,3,4,0,3,1,3,3,4,1,3,2,4,3,2,2,6,1,2,3,1,3,1,2,2,3,2,2,3,2,2,2,2,3,4,3,3,3,3,2,3,2,5,2,2,2,3,0,0,3,3,1,1,2,1,6,2,1,6,4,0,5,2,3,0,3,3,2,1,3,4,3,3,3,2,4,1,1,2,2,5,2,1,1,3,4,1,6,4,1,3,5,0,1,5,1,1,1,3,1,2,2,2,2,0,3,3,2,1,0,3,5,2,3,1,2,3,1,0,5,2,3,3,3,3,0,2,0,3,1,3,1,4,3,5,3,1,3,1,3,2,4,2,5,2,2,5,4,3,2,0,1,2,2,3,3,2,2,5,3,5,1,4,3,1,2,8,0,4,3,1,3,1,2,1,3,4,4,0,1,0,2,1,5,2,2,2,5,2,1,2,7,3,4,1,1,2,4,2,4,5,3,1,0,4,1,0,0,4,3,0,2,2,2,2,3,0,4,3,0,2,4,3,2,2,3,1,1,3,1,4,1,1,1,1,1,2,2,2,1,3,1,2,2,2,3,0,0,3,3,0,3,3,4,5,1,2,2,7,0,2,2,1,3,4,0,1,2,4,4,4,4,2,0,6,2,2,3,3,2,2,3,0,3,4,3,0,2,4,2,1,3,1,2,7,3,1,0,3,3,0,5,3,1,1,0,2,3,1,1,2,1,6,2,3,2,1,3,1,3,0,5,0,2,4,2,3,2,0,7,4,5,0,1,2,2,5,4,5,1,0,1,3,6,1,1,0,1,1,1,4,5,1,4,0,3,3,0,0,5,1,5,3,2,2,0,4,2,1,1,4,2,2,4,0,2,3,1,0,3,1,2,3,0,2,2,3,1,2,2,3,5,1,1,1,2,5,1,3,3,0,2,2,5,1,2,1,3,1,2,1,2,1,5,3,2,1,2,3,0,2,0,3,4,5,0,4,3,4,0,3,2,1,2,1,1,1,2,3,3,0,5,2,1,2,1,2,3,3,1,2,4,2,1,4,2,0,2,5,3,4,1,2,1,1,1,2,1,2,2,2,3,1,3,4,2,0,0,1,2,5,1,0,0,2,3,3,2,0,5,2,0,1,3,1,4,2,0,3,1,3,0,3,3,1,1,2,3,3,1,3,3,3,2,0,5,2,1,1,2,0,2,2,3,4,1,3,4,0,0,3,0,3,4,4,2,3,0,2,1,5,2,4,2,3,0,2,1,0,3,2,5,3,0,2,4,1,2,3,4,4,4,6,1,1,1,2,5,1,3,3,3,2,2,0,2,4,2,0,1,7,1,3,1,1,0,2,3,1,3,0,2,4,3,1,2,2,1,4,5,5,3,2,4,1,1,0,4,2,0,3,4,4,1,2,1,3,3,2,1,2,3,0,2,5,2,2,2,0,2,1,1,2,1,4,0,1,3,0,0,3,2,1,2,3,1,1,2,4,4,3,1,1,1,0,0,1,1,1,5,2,1,2,3,1,4,3,1,1,0,2,2,4,3,1,0,2,3,2,3,0,3,3,2,2,1,4,1,2,5,1,3,1,1,3,0,1,2,3,4,1,1,1,2,3,0,2,1,3,3,1,3,1,4,0,2,0,1,2,2,1,1,0,2,3,1,2,0,3,1,1,1,5,4,3,1,0,3,2,3,2,3,3,2,1,2,0,1,2,3,3,2,2,1,2,2,1,0,2,3,2,2,2,1,2,4,5,2,4,2,1,1,1,2,3,2,2,1,1,3,5,2,3,6,2,2,2,4,4,0,1,3,2,1,3,1,2,0,2,1,5,1,1,3,1,4,3,1,1,1,1,1,0,2,0,5,3,3,3,2,1,2,1,4,1,3,2,2,1,2,3,0,2,1,2,1,5,3,2,2,0,3,1,1,4,2,0,5,4,2,1,1,3,1,0,5,1,2,2,1,2,0,5,2,4,2,2,2,1,2,2,2,1,4,3,2,1,2,2,1,1,4,1,2,2,2,4,1,2,0,1,3,2,1,3,0,3,0,2,2,1,2,0,4,1,2,5,3,0,2,4,1,2,2,1,3,0,0,3,6,1,1,1,2,2,1,2,1,3,2,1,4,4,3,3,1,0,4,2,1,1,0,2,2,2,1,2,4,0,1,0,0,2,1,1,1,0,2,0,1,2,2,1,2,0,5,2,3,2,3,1,3,3,2,0,2,1,1,2,0,0,3,0,2,3,1,3,1,3,1,2,0,3,2,1,1,1,2,2,2,1,0,3,3,4,2,0,2,1,1,2,3,2,1,1,2,1,1,2,3,1,2,3,0,1,2,0,3,1,3,2,1,0,1,2,0,5,1,2,2,1,1,5,4,1,2,1,3,1,0,1,0,1,0,1,3,0,3,3,3,2,3,2,2,1,0,3,1,1,2,0,0,3,0,2,3,0,3,3,1,1,1,3,1,2,0,1,2,4,1,1,5,1,1,1,1,1,4,1,2,1,3,3,2,4,1,3,2,1,1,0,0,1,3,2,3,2,4,2,2,1,2,1,0,3,0,5,3,3,1,3,1,1,0,2,0,2,2,3,2,2,3,1,0,0,0,4,3,0,2,2,0,1,2,1,2,0,1,0,3,2,1,4,3,1,1,1,0,3,2,2,2,3,3,0,0,2,3,2,1,1,2,2,3,5,3,3,1,0,0,1,0,1,3,1,2,1,2,0,1,0,1,3,1,1,3,1,2,4,1,3,1,0,2,1,2,1,1,0,3,1,2,2,1,1,0,1,2,0,1,0,3,3,0,0,2,3,5,4,3,1,3,2,0,1,2,3,2,3,4,0,0,2,0,0,1,2,1,0,2,3,2,0,1,2,2,1,4,1,3,0,1,2,1,1,2,0,4,0,2,0,1,2,3,3,2,1,3,5,0,1,1,2,3,2,2,0,3,1,3,4,1,1,3,0,2,1,2,0,4,3,0,0,0,4,2,0,3,4,0,2,1,2,0,2,2,1,4,3,2,0,1,1,1,4,2,1,3,1,4,0,1,7,1,2,2,2,3,3,1,2,2,2,3,1,6,3,4,0,0,0,4,2,1,2,1,1,5,0,2,1,1,2,1,0,3,1,0,0,2,0,0,2,1,2,1,3,0,0,0,3,4,1,1,4,1,0,2,1,3,5,0,3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2916,1.2911,1.2906,1.29,1.2895,1.2889,1.2884,1.2878,1.2873,1.2868,1.2862,1.2857,1.2851,1.2846,1.2841,1.2835,1.283,1.2824,1.2819,1.2814,1.2808,1.2803,1.2797,1.2792,1.2787,1.2781,1.2776,1.277,1.2765,1.276,1.2754,1.2749,1.2743,1.2738,1.2733,1.2727,1.2722,1.2717,1.2711,1.2706,1.27,1.2695,1.269,1.2684,1.2679,1.2673,1.2668,1.2663,1.2657,1.2652,1.2647,1.2641,1.2636,1.263,1.2625,1.262,1.2614,1.2609,1.2604,1.2598,1.2593,1.2588,1.2582,1.2577,1.2571,1.2566,1.2561,1.2555,1.255,1.2545,1.2539,1.2534,1.2529,1.2523,1.2518,1.2512,1.2507,1.2502,1.2496,1.2491,1.2486,1.248,1.2475,1.247,1.2464,1.2459,1.2454,1.2448,1.2443,1.2438,1.2432,1.2427,1.2422,1.2416,1.2411,1.2406,1.24,1.2395,1.239,1.2384,1.2379,1.2374,1.2368,1.2363,1.2358,1.2352,1.2347,1.2342,1.2336,1.2331,1.2326,1.232,1.2315,1.231,1.2304,1.2299,1.2294,1.2288,1.2283,1.2278,1.2272,1.2267,1.2262,1.2257,1.2251,1.2246,1.2241,1.2235,1.223,1.2225,1.2219,1.2214,1.2209,1.2203,1.2198,1.2193,1.2188,1.2182,1.2177,1.2172,1.2166,1.2161,1.2156,1.215,1.2145,1.214,1.2135,1.2129,1.2124,1.2119,1.2113,1.2108,1.2103,1.2098,1.2092,1.2087,1.2082,1.2076,1.2071,1.2066,1.2061,1.2055,1.205,1.2045,1.2039,1.2034,1.2029,1.2024,1.2018,1.2013,1.2008,1.2003,1.1997,1.1992,1.1987,1.1981,1.1976,1.1971,1.1966,1.196,1.1955,1.195,1.1945,1.1939,1.1934,1.1929,1.1924,1.1918,1.1913,1.1908,1.1903,1.1897,1.1892,1.1887,1.1882,1.1876,1.1871,1.1866,1.1861,1.1855,1.185,1.1845,1.184,1.1834,1.1829,1.1824,1.1819,1.1813,1.1808,1.1803,1.1798,1.1793,1.1787,1.1782,1.1777,1.1772,1.1766,1.1761,1.1756,1.1751,1.1745,1.174,1.1735,1.173,1.1725,1.1719,1.1714,1.1709,1.1704,1.1699,1.1693,1.1688,1.1683,1.1678,1.1672,1.1667,1.1662,1.1657,1.1652,1.1646,1.1641,1.1636,1.1631,1.1626,1.162,1.1615,1.161,1.1605,1.16,1.1594,1.1589,1.1584,1.1579,1.1574,1.1568,1.1563,1.1558,1.1553,1.1548,1.1543,1.1537,1.1532,1.1527,1.1522,1.1517,1.1511],"name":"M_matrix","npix":2897,"planted":{"Al_Ka":74726.2304,"Al_Ka_tail":1137.9629,"Cu_Ka":0.0,"Cu_Ka_stray":127.7478,"Mg_Ka":245.9678,"O_Ka":262.3691,"Si_Ka":484.8118,"Si_Ka_internal":59.8995},"source":"map","thickness_nm":80.878071,"truth_at":{"Al":98.8,"Mg":0.6,"Si":0.6}}],"true_k_counts_per_atom_nm2":{"Al":0.006802201645893394,"Mg":0.0036712336182256246,"Si":0.008262366164884884}}
diff --git a/Tests/SpectroEDXTests/SpectroscopyAbsorptionTruthTests.swift b/Tests/SpectroEDXTests/SpectroscopyAbsorptionTruthTests.swift
index 61d751b..1b5c6a1 100644
--- a/Tests/SpectroEDXTests/SpectroscopyAbsorptionTruthTests.swift
+++ b/Tests/SpectroEDXTests/SpectroscopyAbsorptionTruthTests.swift
@@ -160,7 +160,7 @@ final class SpectroscopyAbsorptionTruthTests {
         }
     }
 
-    private static func input(seed: UInt64, absorption: Bool) -> PooledQuantificationInput {
+    private static func input(seed: UInt64, absorption: Bool, policy: QuantificationPolicy = .default) -> PooledQuantificationInput {
         let p = pool
         var rng = SplitMix64(state: seed)
         let counts = p.expected.map { poisson($0, &rng) }
@@ -183,7 +183,7 @@ final class SpectroscopyAbsorptionTruthTests {
             SpectrumDetectorSegment(name: "SuperXG1\(i + 1)", azimuthDegrees: a.0, elevationDegrees: 22, solidAngle: a.1)
         }
         return PooledQuantificationInput(counts: counts, axis: p.axis, method: m, metadata: meta, regionName: "recipe A pool",
-                                         pixelCount: p.npix, resolutionMnKaEV: 130)
+                                         pixelCount: p.npix, resolutionMnKaEV: 130, policy: policy)
     }
 
     private static let seeds: [UInt64] = [11, 12, 13, 14]
@@ -223,7 +223,13 @@ final class SpectroscopyAbsorptionTruthTests {
     /// sqrt(4) (3 x 56 / 2 / 2116 = 0.040, about 85 counts). The seeds are fixed, so this is a regression pin, not a confidence
     /// interval and not validation. A known deviation: pinned so that a change either way fails and is looked at. It is the real
     /// Si gate; the per-seed tolerance above only bounds each draw.
-    private static let siBiasFraction = -0.203, siBiasBand = 0.040
+    /// Those numbers are the fit WITHOUT sum peaks (`SumPeakRule.off`, the default before sum peaks were; the envelope above is
+    /// kept, it bounds both fits). With the default sum peaks (`SumPeakRule.whenSignificant`, the pile-up coefficient kept on every
+    /// seed) the nets are 2061 / 1912 / 1917 / 2006, mean 1974, -6.7 %, sd 72 counts, band 3 x 72 / 2 / 2116 = 0.051 (noise-free the
+    /// same fit reads -4.0 %). The Al+Al sum peak at 2.97 keV had pulled the continuum segment above the Al K edge, and Si K-alpha
+    /// with it (`DemoEDXPoolTests`). `siBiasFractionWithoutSumPeaks` keeps the old pin on the `.off` fit.
+    private static let siBiasFraction = -0.067, siBiasBand = 0.051
+    private static let siBiasFractionWithoutSumPeaks = -0.203, siBiasBandWithoutSumPeaks = 0.040
 
     /// Per-seed numbers go to stderr: `print` stays in the hosted app's stdout and never reaches the xcodebuild log.
     /// Also kept as an attachment (read it from the xcresult: `xcresulttool export attachments`, or the test run's attachments folder).
@@ -285,6 +291,17 @@ final class SpectroscopyAbsorptionTruthTests {
         note(String(format: "L2 Si bias against the planted K-alpha peak %.4f (pinned %.3f +- %.3f); against the sample line alone %.4f",
                     siBias, Self.siBiasFraction, Self.siBiasBand, siNet.reduce(0, +) / Double(siNet.count) / p.areasWithAbsorption["Si_Ka"]! - 1))
         #expect(abs(siBias - Self.siBiasFraction) <= Self.siBiasBand, "Si bias against the planted K-alpha peak: \(siBias), nets \(siNet)")
+        // The fit without sum peaks (the exSpy-equivalent line model) keeps its own pin.
+        var off = QuantificationPolicy.default
+        off.fit.sumPeaks = .off
+        var offNet: [Double] = []
+        for seed in Self.seeds {
+            let r = try PooledQuantifier.run(Self.input(seed: seed, absorption: true, policy: off), tables: Self.tables)
+            offNet.append(try #require(r.rows.first { $0.element == "Si" }).net)
+        }
+        let offBias = offNet.reduce(0, +) / Double(offNet.count) / Self.plantedSiKa - 1
+        note(String(format: "L2 Si bias without sum peaks %.4f (pinned %.3f +- %.3f)", offBias, Self.siBiasFractionWithoutSumPeaks, Self.siBiasBandWithoutSumPeaks))
+        #expect(abs(offBias - Self.siBiasFractionWithoutSumPeaks) <= Self.siBiasBandWithoutSumPeaks, "without sum peaks: \(offBias), nets \(offNet)")
         // The Si correction is a property of the geometry, not of the draw: the same on every seed (predicted +0.078 at%).
         let spread = (siGain.max() ?? 0) - (siGain.min() ?? 0)
         #expect(spread < 0.01, "Si correction by seed: \(siGain)")
diff --git a/Tests/SpectroEDXTests/SumEscapeExplainedTests.swift b/Tests/SpectroEDXTests/SumEscapeExplainedTests.swift
new file mode 100644
index 0000000..f3737b4
--- /dev/null
+++ b/Tests/SpectroEDXTests/SumEscapeExplainedTests.swift
@@ -0,0 +1,149 @@
+//
+//  SumEscapeExplainedTests.swift
+//  Role: the sum/escape model's peaks are explained counts for the element proposer and the unlisted-line check. Before, a Quantify fit
+//        with `SumEscapeModel` on modelled the pile-up and escape peaks, but the check proposed on the bare spectrum and named
+//        them as elements (measured on the tools/edx-sim pool below: Ar, Ag, Pd at 100 counts/px; Rh, Ar, In, Sn, Pd, Ag, Cd, Ru,
+//        Bi, K at 300 counts/px; La, Ce, Cr, Cs at the planted Fe escape with the free escape columns off). Planted truth only; the
+//        model is `validation: "none"` and eXSpy has no sum or escape model to compare with.
+//
+
+import Foundation
+import Testing
+import SpectroTestSupport
+import SpectroCore
+import SpectroEDX
+
+struct SumEscapeExplainedTests {
+
+    private struct SimPools: Decodable {
+        struct Region: Decodable { let label: String; let expected: [Double]; let components: [String: Double] }
+        let offset: Double, scale: Double, size: Int
+        let regions: [Region]
+        var axis: EnergyAxis { EnergyAxis(offset: offset, scale: scale, size: size) }
+    }
+
+    /// tools/edx-sim/proposer_sim.py: region 1 is the Al matrix at 100 counts/px (Al+Al sum 1845 counts), region 2 the beta''
+    /// pixel at 300 counts/px (six sum peaks, 454 to 8553 counts).
+    private static let sim: SimPools = {
+        let url = EDXFixtures.dir.appendingPathComponent("eds-proposer-sim.json")
+        return try! JSONDecoder().decode(SimPools.self, from: Data(contentsOf: url))
+    }()
+
+    private static func input(counts: [Double], axis: EnergyAxis, elements: [String], sumEscape: SumEscapeModel?,
+                              policy: QuantificationPolicy = .default) -> PooledQuantificationInput {
+        var m = QuantificationMethod()
+        m.elements = elements.map { .init(symbol: $0, role: .quantify, isManual: false) }
+        m.beamEnergyKeV = 200
+        m.absorptionCorrection = false
+        m.lockEnergyAxis = true
+        let meta = SpectrumImageMetadata(fileName: "planted", filePath: "", scanWidth: 1, scanHeight: 1, channelCount: axis.size,
+                                         energyOffsetEV: axis.offset * 1000, energyDispersionEV: axis.scale * 1000)
+        return PooledQuantificationInput(counts: counts.map { UInt64(max($0, 0).rounded()) }, axis: axis, method: m, metadata: meta,
+                                         regionName: "planted", pixelCount: 1, policy: policy, sumEscape: sumEscape)
+    }
+
+    private static func check(_ input: PooledQuantificationInput) throws -> (UnlistedLineCheck, PooledQuantification) {
+        let q = try PooledQuantifier.run(input, tables: QuantificationTables.bundled())
+        let proposal = try UnlistedLineChecker.propose(counts: input.counts.map { Double($0) }, quantification: q)
+        return (UnlistedLineChecker.check(proposal: proposal, input: input, quantification: q), q)
+    }
+
+    private static func simCounts(_ region: Int, plant: [String: Double] = [:]) -> [Double] {
+        var expected = sim.regions[region].expected
+        if !plant.isEmpty {
+            let axis = sim.axis
+            let symbols = Array(Set(plant.keys.map { String($0.split(separator: "_")[0]) }))
+            let model = EDSLineModel.build(elements: symbols, axis: axis, beamEnergy: 200, resolutionMnKaEV: 130, escapePeaks: false)
+            let energies = (0..<axis.size).map { axis.energy(ofChannel: $0) }
+            for g in model.groups { if let a = plant[g.id] {
+                let col = EDSLineModel.column(of: g.lines, energies: energies, scale: axis.scale)
+                for i in expected.indices { expected[i] += a * col[i] }
+            } }
+        }
+        var rng = Xoshiro256StarStar(seed: UInt64(77 + region))
+        return expected.map { rng.poisson($0) }
+    }
+
+    private static let listed = ["Al", "Mg", "Si", "O", "Cu"]
+
+    /// Red before: with the model on, the check named the sum peaks as Ar, Ag, Pd (100 counts/px) and Rh, Ar, In, Sn, Pd, Ag, Cd,
+    /// Ru, Bi, K (300 counts/px). With the model off nothing changes: the proposer's own sum columns win those peaks and the check
+    /// still names the elements it lost them to as sum-peak questions (D6).
+    @Test(arguments: [1, 2])
+    func simSumPeaksTheModelCoversAreNotNamed(region: Int) throws {
+        let counts = Self.simCounts(region)
+        // Off: an explicit model with both terms off (the default runs sum peaks when the data support them, below).
+        let (off, qOff) = try Self.check(Self.input(counts: counts, axis: Self.sim.axis, elements: Self.listed, sumEscape: SumEscapeModel()))
+        #expect(qOff.sumEscapeCounts == nil)
+        #expect(off.names.contains("Ar"), "premise: without the model the Al+Al sum is named as Ar: \(off.summary)")
+        // The default (`SumPeakRule.whenSignificant`): the Al+Al self pair is significant, the sum peaks are kept and explained.
+        let (byDefault, qDefault) = try Self.check(Self.input(counts: counts, axis: Self.sim.axis, elements: Self.listed, sumEscape: nil))
+        #expect(qDefault.appliedSumEscape == SumEscapeModel(sumPeaks: true))
+        #expect(qDefault.sumEscapeCounts != nil)
+        #expect(!byDefault.names.contains("Ar") && !byDefault.names.contains("Ag"), "the default explains the Al+Al sum: \(byDefault.summary)")
+        let (on, q) = try Self.check(Self.input(counts: counts, axis: Self.sim.axis, elements: Self.listed, sumEscape: .both))
+        let sumCounts = try #require(q.sumEscapeCounts)
+        #expect(sumCounts.reduce(0, +) > 0.5 * Self.sim.regions[region].components.filter { $0.key.hasPrefix("sum_") }.values.reduce(0, +))
+        #expect(on.candidates.isEmpty, "the modelled sum peaks are explained: \(on.summary)")
+    }
+
+    /// A real line between two sum peaks is still found with the model on: K K-alpha (3.314 keV, between Al+Si 3.226 and Si+Si 3.479),
+    /// the strongest candidate. (The elements its peak was tested against, In and Cd among them, are named beside it as the check
+    /// always names every tested candidate at or above L_D; that is the check's rule, not pile-up.)
+    @Test func aRealLineBesideTheSumPeaksIsStillNamed() throws {
+        let counts = Self.simCounts(2, plant: ["K_Ka": 3000])
+        let (on, _) = try Self.check(Self.input(counts: counts, axis: Self.sim.axis, elements: Self.listed, sumEscape: .both))
+        #expect(on.elementNames.first == "K", "\(on.summary)")
+    }
+
+    /// Red before: a common escape fraction with the free escape columns off left the Fe K-alpha escape (4.66 keV) to the proposer,
+    /// which named it La (L-alpha 4.651 keV), with Ce, Cr and Cs beside it.
+    @Test func theCommonEscapeIsExplained() throws {
+        let axis = EnergyAxis(offset: 0, scale: 0.01, size: 2000)
+        let energies = (0..<axis.size).map { axis.energy(ofChannel: $0) }
+        var mu = energies.map { e -> Double in
+            let x = max(e, 0.05)
+            return e >= 0.2 ? 2.0 * max(200 - e, 0) / x * exp(-pow(0.3 / x, 3)) / 40 : 0
+        }
+        let model = EDSLineModel.build(elements: ["Al", "Fe"], axis: axis, beamEnergy: 200, resolutionMnKaEV: 130, escapePeaks: true)
+        for g in model.groups where g.id == "Al_Ka" || g.id == "Fe_Ka" {
+            let col = EDSLineModel.column(of: g.lines, energies: energies, scale: axis.scale)
+            for i in mu.indices { mu[i] += 300_000 * col[i] }
+            if !g.escapes.isEmpty {
+                let ec = EDSLineModel.column(of: g.escapes, energies: energies, scale: axis.scale)
+                for i in mu.indices { mu[i] += 0.01 * 300_000 * ec[i] }
+            }
+        }
+        var rng = Xoshiro256StarStar(seed: 3)
+        let counts = mu.map { rng.poisson($0) }
+        var policy = QuantificationPolicy.default
+        policy.fit.escapePeaks = false
+        let (on, q) = try Self.check(Self.input(counts: counts, axis: axis, elements: ["Al", "Fe"],
+                                                sumEscape: SumEscapeModel(commonEscapeFraction: true), policy: policy))
+        #expect(q.sumEscapeCounts != nil)
+        #expect(on.candidates.isEmpty, "the modelled Fe escape is explained: \(on.summary)")
+    }
+
+    /// The proposer itself: the sum/escape fit's components as `explained` remove the sum peaks from what it can propose; nil runs it
+    /// as before (the same result as no argument).
+    @Test func theProposerTakesTheComponentsAsExplained() throws {
+        let axis = Self.sim.axis
+        let counts = Self.simCounts(2)
+        let st = FitSettings.standard(elements: Self.listed, axis: axis, resolutionMnKaEV: 130, beamEnergy: 200)
+        let r = try EDSSumEscapeFit.run(counts: counts, axis: axis, settings: st, model: .both)
+        #expect(r.componentCounts.count == r.fit.channels.count)
+        var explained = [Double](repeating: 0, count: axis.size)
+        for (k, ch) in r.fit.channels.enumerated() { explained[ch] = r.componentCounts[k] }
+        let bare = try ElementProposer().propose(counts: counts, axis: axis, settings: st)
+        let none = try ElementProposer().propose(counts: counts, axis: axis, settings: st, explained: nil)
+        #expect(bare.candidates == none.candidates)
+        #expect(bare.candidates.contains { $0.aboveDetectionLimit })
+        let shared = try ElementProposer().propose(counts: counts, axis: axis, settings: st, explained: explained)
+        #expect(!shared.candidates.contains { $0.aboveDetectionLimit }, "\(shared.candidates.map(\.group))")
+        #expect(throws: ProposerError.lengthMismatch) {
+            _ = try ElementProposer().propose(counts: counts, axis: axis, settings: st, explained: [1, 2])
+        }
+        let off = try EDSSumEscapeFit.run(counts: counts, axis: axis, settings: st, model: SumEscapeModel())
+        #expect(off.componentCounts.allSatisfy { $0 == 0 } && off.componentCounts.count == off.fit.channels.count)
+    }
+}
diff --git a/Tests/SpectroEDXTests/SumEscapeFitTests.swift b/Tests/SpectroEDXTests/SumEscapeFitTests.swift
index 3b116b2..e4081b9 100644
--- a/Tests/SpectroEDXTests/SumEscapeFitTests.swift
+++ b/Tests/SpectroEDXTests/SumEscapeFitTests.swift
@@ -148,11 +148,14 @@ struct SumEscapeFitTests {
                                          energyOffsetEV: 0, energyDispersionEV: 10)
         let tables = QuantificationTables.bundled()
         var input = PooledQuantificationInput(counts: y, axis: Self.axis, method: m, metadata: meta, regionName: "planted", pixelCount: 1)
+        input.sumEscape = SumEscapeModel()   // both off: the fit without sum peaks, whatever the policy says
         let plain = try PooledQuantifier.run(input, tables: tables)
         #expect(!plain.footerLines.contains { $0.hasPrefix("sum peaks") })
+        #expect(plain.appliedSumEscape == nil)
         input.sumEscape = .both
         let on = try PooledQuantifier.run(input, tables: tables)
         #expect(on.footerLines.contains { $0.hasPrefix("sum peaks") })
+        #expect(on.appliedSumEscape == .both)
         let truth = Self.areas["Ag_La"]!
         let ag = try #require(on.rows.first { $0.element == "Ag" }), agPlain = try #require(plain.rows.first { $0.element == "Ag" })
         #expect(abs(ag.net - truth) < 0.1 * abs(agPlain.net - truth))
diff --git a/Tests/SpectroKitParityTests/SpectroGoldenTests.swift b/Tests/SpectroKitParityTests/SpectroGoldenTests.swift
index 3f0115c..b7cef4e 100644
--- a/Tests/SpectroKitParityTests/SpectroGoldenTests.swift
+++ b/Tests/SpectroKitParityTests/SpectroGoldenTests.swift
@@ -164,8 +164,9 @@ enum GoldenQ {
     }
 
     static func input(_ method: QuantificationMethod, image: LoadedSpectrumImage) -> PooledQuantificationInput {
+        // The fit without sum peaks (an explicit off model): the baseline records the exSpy-equivalent line model.
         PooledQuantificationInput(counts: image.sum(mask: nil), axis: image.energyAxis, method: method, metadata: image.metadata,
-                                  regionName: "Whole map", pixelCount: image.metadata.pixelCount)
+                                  regionName: "Whole map", pixelCount: image.metadata.pixelCount, sumEscape: SumEscapeModel())
     }
 }
 
@@ -224,7 +225,9 @@ enum SpectroGolden {
     static func pooledInput(counts: [UInt64], axis: EnergyAxis, method: QuantificationMethod, name: String) -> PooledQuantificationInput {
         let meta = SpectrumImageMetadata(fileName: name, filePath: "", scanWidth: 1, scanHeight: 1, channelCount: axis.size,
                                          energyOffsetEV: axis.offset * 1000, energyDispersionEV: axis.scale * 1000)
-        return PooledQuantificationInput(counts: counts, axis: axis, method: method, metadata: meta, regionName: "synthetic", pixelCount: 1)
+        // The fit without sum peaks (an explicit off model): the baseline records the exSpy-equivalent line model.
+        return PooledQuantificationInput(counts: counts, axis: axis, method: method, metadata: meta, regionName: "synthetic", pixelCount: 1,
+                                         sumEscape: SumEscapeModel())
     }
 
     /// The fit, its CSV, the range-sensitivity statement, the proposer on the fit's own settings and the unlisted-line check.
diff --git a/tools/edx-sim/demo_pools.py b/tools/edx-sim/demo_pools.py
new file mode 100644
index 0000000..6819cfe
--- /dev/null
+++ b/tools/edx-sim/demo_pools.py
@@ -0,0 +1,75 @@
+"""Pooled spectra of the public synthetic AlMgSi demo set, with their planted truth, for `DemoEDXPoolTests`.
+
+The demo set is mac4DSTEM's `demo-edx` (generator `tools/demo-edx/sim_edx.py` v2.0, seed 42, ladder seed 52). Its truth is the
+simulation recipe, not a measurement. Read-only on the demo folder.
+
+    python -I -B tools/edx-sim/demo_pools.py <demo-edx folder> Tests/SpectroEDXTests/Fixtures/edx-demo-pools.json
+
+Needs numpy and h5py. Each pool: the Poisson counts summed over its pixels, the generator's noise-free expected spectrum of the
+same pixels (`expected`, counts, 4 decimals), and the generator's planted component areas (`planted`, counts).
+"""
+import json
+import sys
+
+import h5py
+import numpy as np
+
+D = sys.argv[1].rstrip('/') + '/'
+OUT = sys.argv[2]
+T = json.load(open(D + 'truth_edx.json'))
+TA = np.load(D + 'truth_edx_arrays.npz')
+L = json.load(open(D + 'truth_edx_ladder.json'))
+LA = np.load(D + 'truth_edx_ladder_arrays.npz')
+comps = T['component_names']
+kc = T['forward_model']['line_model']['true_k']['counts_per_atom_nm2_per_family_(Gp*s*eps)']
+true_axis = dict(offset=-0.478, scale=0.005)
+keys = ['Al_Ka', 'Mg_Ka', 'Si_Ka', 'Si_Ka_internal', 'O_Ka', 'Al_Ka_tail', 'Cu_Ka_stray', 'Cu_Ka']
+
+
+def metals(af):
+    m = {k: v for k, v in af.items() if k != 'O'}
+    s = sum(m.values())
+    return {k: round(100 * v / s, 10) for k, v in m.items()}
+
+
+def spectrum(x):
+    return [round(float(v), 4) for v in x]
+
+
+pools = []
+recipes_af = {k: v['atom_fraction_incl_oxide'] for k, v in T['recipes'].items()}
+recipes_af['beta_pure'] = {'Mg': 5 / 11, 'Si': 6 / 11}
+
+with h5py.File(D + 'AlMgSi_edx_ladder.hspy', 'r') as f:
+    lad = f['Experiments/__unnamed__/data'][()]          # (16, 128, 4096)
+for ri in (5, 6, 7):
+    r = L['regions'][ri]
+    c0, c1 = r['columns']
+    block = lad[:, c0:c1 + 1, :].astype(np.int64)
+    c = r['components_expected_total_counts']
+    pools.append(dict(name='L%d_%s' % (ri, r['recipe']), source='ladder', npix=int(block.shape[0] * block.shape[1]),
+                      thickness_nm=r['thickness_nm'], truth_at=metals(recipes_af[r['recipe']]), axis_true=true_axis,
+                      counts=block.sum(axis=(0, 1)).tolist(), expected=spectrum(LA['expected_spectrum_sum_by_region'][ri]),
+                      planted={k: round(float(c.get(k, 0.0)), 4) for k in keys}))
+
+with h5py.File(D + 'AlMgSi_4D_EDX_EDS.hspy', 'r') as f:
+    m = f['Experiments/__unnamed__/data'][()].astype(np.int64)   # (48, 64, 4096), the file axis carries a planted error
+rm = np.array(T['recipe_map'])
+order = T['recipe_names_in_map_order']
+thick = TA['thickness_nm']
+cexp = TA['component_expected_counts']
+for name, idx in (('M_A', [0]), ('M_matrix', [0, 1, 2, 3, 4, 5, 6])):
+    mask = np.isin(rm, idx)
+    w = TA['expected_total_counts_per_pixel'][mask]
+    pools.append(dict(name=name, source='map', npix=int(mask.sum()),
+                      thickness_nm=round(float((thick[mask] * w).sum() / w.sum()), 6), truth_at=metals(recipes_af[order[idx[0]]]),
+                      axis_true=true_axis, counts=m[mask].sum(axis=0).tolist(),
+                      expected=spectrum(sum(TA['expected_spectrum_sum_by_recipe'][i] for i in idx)),
+                      planted={k: round(float(cexp[comps.index(k)][mask].sum()), 4) for k in keys}))
+
+out = dict(generator='mac4DSTEM demo-edx, tools/demo-edx/sim_edx.py v2.0 (seed 42, ladder seed 52); truth is the simulation recipe',
+           true_k_counts_per_atom_nm2={k: kc[k + '_K'] for k in ('Al', 'Mg', 'Si')},
+           atomic_mass={'Al': 26.9815, 'Mg': 24.305, 'Si': 28.0855}, pools=pools)
+with open(OUT, 'w') as fh:
+    json.dump(out, fh, separators=(',', ':'), sort_keys=True)
+    fh.write('\n')