diff --git a/.gitignore b/.gitignore
index 0023a53..80837be 100644
--- a/.gitignore
+++ b/.gitignore
@@ -3,6 +3,7 @@
 /Packages
 xcuserdata/
 DerivedData/
+.derived-data-log-*
 .swiftpm/configuration/registries.json
 .swiftpm/xcode/package.xcworkspace/contents.xcworkspacedata
 .netrc
diff --git a/Package.swift b/Package.swift
index b526725..197bbf4 100644
--- a/Package.swift
+++ b/Package.swift
@@ -14,6 +14,10 @@ let package = Package(
             name: "MaxVol",
             targets: ["MaxVol"]
         ),
+        .executable(
+            name: "MaxVolBenchmark",
+            targets: ["MaxVolBenchmark"]
+        ),
     ],
     targets: [
         // Targets are the basic building blocks of a package, defining a module or a test suite.
@@ -25,6 +29,13 @@ let package = Package(
                 .define("ACCELERATE_LAPACK_ILP64"),
             ]
         ),
+        .executableTarget(
+            name: "MaxVolBenchmark",
+            dependencies: ["MaxVol"],
+            resources: [
+                .copy("Resources/fixtures.json"),
+            ]
+        ),
         .testTarget(
             name: "MaxVolTests",
             dependencies: ["MaxVol"]
diff --git a/README.md b/README.md
index a06db8c..a2e3896 100644
--- a/README.md
+++ b/README.md
@@ -45,6 +45,39 @@ deprecated compatibility shims.
      points.
    - Consider complex support only after real-valued APIs are stable.
 
+## Benchmarking
+
+`MaxVolBenchmark` runs deterministic fixtures through the Swift implementation
+and prints one JSON object per result:
+
+```bash
+swift run -c release MaxVolBenchmark --iterations 20
+```
+
+The Python comparison harness reads the same checked-in fixture values and runs
+the official `maxvolpy` implementation from the PyPI source distribution:
+
+```bash
+uv run --python 3.11 scripts/compare_maxvolpy.py --iterations 20
+```
+
+To compare correctness-oriented fields, write both outputs as JSONL and run the
+parity checker:
+
+```bash
+swift run -c release MaxVolBenchmark --iterations 20 > /tmp/maxvol-swift.jsonl
+uv run --python 3.11 scripts/compare_maxvolpy.py --iterations 20 > /tmp/maxvol-python.jsonl
+python3 scripts/check_benchmark_parity.py /tmp/maxvol-swift.jsonl /tmp/maxvol-python.jsonl
+```
+
+For allocation profiling, build the executable once and record the workload with
+Instruments from the command line:
+
+```bash
+swift build -c release --product MaxVolBenchmark
+xcrun xctrace record --template 'Allocations' --output /tmp/MaxVolBenchmark.trace --launch -- .build/release/MaxVolBenchmark --iterations 100
+```
+
 ## Non-Goals For The First Pass
 
 - Exact exhaustive maximum-volume search.
diff --git a/ROADMAP.md b/ROADMAP.md
index 069c236..84a4e39 100644
--- a/ROADMAP.md
+++ b/ROADMAP.md
@@ -2,7 +2,7 @@
 
 ## Current Focus
 
-- Build from `v0.7.0` toward `v1.0.0` with real-valued `Double` and `Float`
+- Build from `v0.8.0` toward `v1.0.0` with real-valued `Double` and `Float`
   algorithms backed by modern Accelerate BLAS/LAPACK.
 - Keep Swift Testing as the package test surface and require reference fixtures
   before broadening the algorithm surface.
@@ -39,6 +39,8 @@
    - Reduce temporary allocations in square row swaps and rectangular appends.
    - Reuse workspace buffers where it improves measured throughput.
    - Add benchmark coverage for representative row counts and ranks.
+   - Compare Swift Release-mode results with official `maxvolpy` runs on shared
+     deterministic fixtures before changing allocation behavior.
 
 ## Test Coverage
 
@@ -51,6 +53,8 @@
   implementations when algorithm behavior changes.
 - Keep randomized orthonormal-matrix tests similar to `Maxvol.jl` across
   supported scalar types.
+- Keep benchmark fixture parity checks available for every supported scalar and
+  algorithm family.
 - Keep Release-mode validation in the release path for optimization-sensitive
   Accelerate calls.
 - Keep validation clean under the modern Accelerate `ACCELERATE_NEW_LAPACK` and
@@ -66,6 +70,8 @@
 - Keep public API docs aligned with tested behavior.
 - Expand DocC with algorithm notes, limitations, and reference-fixture
   provenance before `1.0.0`.
+- Keep benchmark and profiling commands documented so performance work remains
+  reproducible.
 
 ## Swift Package Index
 
@@ -95,3 +101,17 @@
 - Expand DocC with reference-fixture provenance and a short comparison with
   Python, Julia, and R implementations.
 - Verify Swift Package Index renders the tagged `v1.0.0` documentation cleanly.
+
+## Planned `v0.9.0`
+
+- Use `MaxVolBenchmark` and the `maxvolpy` comparison harness as the baseline
+  evidence source before changing performance-sensitive code.
+- Measure Release-mode square row-swap throughput and RectMaxVol append
+  throughput across the checked-in deterministic fixture set.
+- Capture allocation traces for the largest fixtures and identify temporary
+  buffers created inside coefficient construction, square row replacement, and
+  rectangular appends.
+- Decide whether reusable workspaces should remain an internal optimization or
+  become a public advanced API.
+- Implement only measured allocation reductions, then re-run parity, timing, and
+  allocation checks before tagging `v0.9.0`.
diff --git a/Sources/MaxVol/MaxVol.docc/BenchmarkingAndParity.md b/Sources/MaxVol/MaxVol.docc/BenchmarkingAndParity.md
new file mode 100644
index 0000000..6bf0466
--- /dev/null
+++ b/Sources/MaxVol/MaxVol.docc/BenchmarkingAndParity.md
@@ -0,0 +1,66 @@
+# Benchmarking and Parity
+
+Use the package benchmark executable and Python harness to compare MaxVol's
+Accelerate-backed implementation with `maxvolpy` on identical deterministic
+fixtures.
+
+## Swift Benchmark
+
+Build and run the benchmark executable in Release mode when measuring runtime:
+
+```bash
+swift run -c release MaxVolBenchmark --iterations 20
+```
+
+The executable reads bundled fixture values from `MaxVolBenchmark` resources and
+prints JSON Lines. Each record includes the fixture, algorithm, scalar type,
+selected row count, convergence status, algorithm iteration count, reconstruction
+residual, coefficient magnitude, and elapsed nanoseconds.
+
+Filter the workload when recording a focused trace:
+
+```bash
+swift run -c release MaxVolBenchmark --fixture gaussian-192x16 --algorithm square --scalar double --iterations 100
+```
+
+## Python Comparison
+
+The Python harness downloads the official `maxvolpy` source distribution from
+PyPI, imports its implementation, and runs it against the same checked-in fixture
+values:
+
+```bash
+uv run --python 3.11 scripts/compare_maxvolpy.py --iterations 20
+```
+
+Use the `pure` implementation mode for the Python reference path. The `api` mode
+uses `maxvolpy.maxvol` and `maxvolpy.rect_maxvol`, which may use the compiled
+extension if the package is installed with one available.
+
+## Parity Check
+
+Compare correctness-oriented fields by writing Swift and Python output to JSONL
+files:
+
+```bash
+swift run -c release MaxVolBenchmark --iterations 20 > /tmp/maxvol-swift.jsonl
+uv run --python 3.11 scripts/compare_maxvolpy.py --iterations 20 > /tmp/maxvol-python.jsonl
+python3 scripts/check_benchmark_parity.py /tmp/maxvol-swift.jsonl /tmp/maxvol-python.jsonl
+```
+
+The checker verifies that both runs produced the same fixture, algorithm, and
+scalar keys, then compares selected row counts, reconstruction residuals, and
+rectangular unselected-row norms.
+
+## Allocation Profiling
+
+Build before profiling so the trace captures benchmark work instead of package
+resolution or compilation:
+
+```bash
+swift build -c release --product MaxVolBenchmark
+xcrun xctrace record --template 'Allocations' --output /tmp/MaxVolBenchmark.trace --launch -- .build/release/MaxVolBenchmark --fixture gaussian-192x16 --iterations 100
+```
+
+Keep trace artifacts out of the repository unless a future performance report
+explicitly needs to preserve one as release evidence.
diff --git a/Sources/MaxVol/MaxVol.docc/MaxVol.md b/Sources/MaxVol/MaxVol.docc/MaxVol.md
index 6761a46..ebac45a 100644
--- a/Sources/MaxVol/MaxVol.docc/MaxVol.md
+++ b/Sources/MaxVol/MaxVol.docc/MaxVol.md
@@ -77,3 +77,4 @@ let rectangular = try rectMaxVol(matrix, options: RectMaxVolOptions(minRows: 3))
 ### Algorithm Notes
 
 - <doc:ToleranceAndConvergence>
+- <doc:BenchmarkingAndParity>
diff --git a/Sources/MaxVolBenchmark/Resources/fixtures.json b/Sources/MaxVolBenchmark/Resources/fixtures.json
new file mode 100644
index 0000000..b97db9d
--- /dev/null
+++ b/Sources/MaxVolBenchmark/Resources/fixtures.json
@@ -0,0 +1,4798 @@
+{
+  "fixtures": [
+    {
+      "columns": 2,
+      "description": "Small fixture that performs one square MaxVol row swap.",
+      "id": "square-swap-3x2",
+      "rowMajorValues": [
+        0.25,
+        0.0,
+        0.5,
+        1.0,
+        0.5,
+        1.5
+      ],
+      "rows": 3
+    },
+    {
+      "columns": 2,
+      "description": "Small fixture that appends one RectMaxVol row.",
+      "id": "rect-append-5x2",
+      "rowMajorValues": [
+        1.0,
+        0.0,
+        0.0,
+        1.0,
+        1.2,
+        0.2,
+        0.1,
+        1.3,
+        0.8,
+        0.8
+      ],
+      "rows": 5
+    },
+    {
+      "columns": 8,
+      "description": "Medium full-rank Gaussian-like tall matrix with a diagonal boost.",
+      "id": "gaussian-64x8",
+      "rowMajorValues": [
+        1.3555326985042249,
+        -0.3556249113960911,
+        0.028651929590178316,
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+        -0.4073471321777901,
+        -0.3361682528212281,
+        0.11189372946099818,
+        1.1683694586794084,
+        -0.5364987251507349,
+        -0.271635072969874,
+        -0.09609073676553787,
+        0.04398727575435113,
+        -0.17732146358588663,
+        0.6628393108883238,
+        0.7839332910491649,
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+        0.5937682776779967,
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+        0.03519327089821028,
+        0.09491141447466572,
+        0.02047564633469512,
+        -0.17939778250878124,
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+        0.022426483564250643,
+        1.0780355357129365,
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+        0.6674483479285728,
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+      "rows": 192
+    }
+  ],
+  "source": "Generated by scripts/generate_benchmark_fixtures.py.",
+  "version": 1
+}
diff --git a/Sources/MaxVolBenchmark/main.swift b/Sources/MaxVolBenchmark/main.swift
new file mode 100644
index 0000000..7770eda
--- /dev/null
+++ b/Sources/MaxVolBenchmark/main.swift
@@ -0,0 +1,432 @@
+import Foundation
+import MaxVol
+
+struct FixtureFile: Decodable {
+    let version: Int
+    let source: String
+    let fixtures: [BenchmarkFixture]
+}
+
+struct BenchmarkFixture: Decodable {
+    let id: String
+    let description: String
+    let rows: Int
+    let columns: Int
+    let rowMajorValues: [Double]
+}
+
+struct BenchmarkConfiguration {
+    var fixtureFilter: String?
+    var algorithmFilter = BenchmarkAlgorithm.all
+    var scalarFilter = BenchmarkScalar.all
+    var iterations = 10
+    var rectangularMinRows: Int?
+}
+
+enum BenchmarkAlgorithm: String, CaseIterable {
+    case all
+    case square
+    case rectangular
+
+    var selectedAlgorithms: [BenchmarkAlgorithm] {
+        switch self {
+            case .all:
+                [.square, .rectangular]
+            case .square, .rectangular:
+                [self]
+        }
+    }
+}
+
+enum BenchmarkScalar: String, CaseIterable {
+    case all
+    case double
+    case float
+
+    var selectedScalars: [BenchmarkScalar] {
+        switch self {
+            case .all:
+                [.double, .float]
+            case .double, .float:
+                [self]
+        }
+    }
+}
+
+struct BenchmarkRecord: Encodable {
+    let tool: String
+    let fixture: String
+    let algorithm: String
+    let scalar: String
+    let rows: Int
+    let columns: Int
+    let repetitions: Int
+    let elapsedNanoseconds: UInt64
+    let averageNanoseconds: Double
+    let selectedRowCount: Int
+    let algorithmIterations: Int
+    let converged: Bool
+    let maxCoefficientMagnitude: Double
+    let maxUnselectedRowNorm: Double?
+    let reconstructionResidual: Double
+}
+
+enum BenchmarkError: Error, CustomStringConvertible {
+    case invalidArgument(String)
+    case missingArgumentValue(String)
+    case missingFixtureResource
+    case fixtureNotFound(String)
+
+    var description: String {
+        switch self {
+            case let .invalidArgument(argument):
+                "Unrecognized MaxVolBenchmark argument '\(argument)'."
+            case let .missingArgumentValue(argument):
+                "MaxVolBenchmark argument '\(argument)' requires a value."
+            case .missingFixtureResource:
+                "MaxVolBenchmark could not find its bundled fixtures.json resource. Rebuild the MaxVolBenchmark product and verify the package resource is declared in Package.swift."
+            case let .fixtureNotFound(identifier):
+                "No benchmark fixture matched '\(identifier)'."
+        }
+    }
+}
+
+let configuration = try parseArguments(Array(CommandLine.arguments.dropFirst()))
+let fixtureFile = try loadFixtureFile()
+let fixtures = try selectedFixtures(from: fixtureFile, configuration: configuration)
+let encoder = JSONEncoder()
+encoder.outputFormatting = [.sortedKeys]
+
+for fixture in fixtures {
+    for algorithm in configuration.algorithmFilter.selectedAlgorithms {
+        for scalar in configuration.scalarFilter.selectedScalars {
+            let record = try runBenchmark(
+                fixture: fixture,
+                algorithm: algorithm,
+                scalar: scalar,
+                configuration: configuration
+            )
+            let data = try encoder.encode(record)
+            print(String(decoding: data, as: UTF8.self))
+        }
+    }
+}
+
+func parseArguments(_ arguments: [String]) throws -> BenchmarkConfiguration {
+    var configuration = BenchmarkConfiguration()
+    var index = 0
+
+    while index < arguments.count {
+        let argument = arguments[index]
+        switch argument {
+            case "--fixture":
+                configuration.fixtureFilter = try value(after: argument, at: &index, in: arguments)
+            case "--algorithm":
+                let rawValue = try value(after: argument, at: &index, in: arguments)
+                guard let algorithm = BenchmarkAlgorithm(rawValue: rawValue) else {
+                    throw BenchmarkError.invalidArgument("\(argument) \(rawValue)")
+                }
+
+                configuration.algorithmFilter = algorithm
+            case "--scalar":
+                let rawValue = try value(after: argument, at: &index, in: arguments)
+                guard let scalar = BenchmarkScalar(rawValue: rawValue) else {
+                    throw BenchmarkError.invalidArgument("\(argument) \(rawValue)")
+                }
+
+                configuration.scalarFilter = scalar
+            case "--iterations":
+                let rawValue = try value(after: argument, at: &index, in: arguments)
+                guard let iterations = Int(rawValue), iterations > 0 else {
+                    throw BenchmarkError.invalidArgument("\(argument) \(rawValue)")
+                }
+
+                configuration.iterations = iterations
+            case "--rectangular-min-rows":
+                let rawValue = try value(after: argument, at: &index, in: arguments)
+                guard let minRows = Int(rawValue), minRows > 0 else {
+                    throw BenchmarkError.invalidArgument("\(argument) \(rawValue)")
+                }
+
+                configuration.rectangularMinRows = minRows
+            case "--help", "-h":
+                printUsage()
+                Foundation.exit(0)
+            default:
+                throw BenchmarkError.invalidArgument(argument)
+        }
+        index += 1
+    }
+
+    return configuration
+}
+
+func value(after argument: String, at index: inout Int, in arguments: [String]) throws -> String {
+    let valueIndex = index + 1
+    guard valueIndex < arguments.count else {
+        throw BenchmarkError.missingArgumentValue(argument)
+    }
+
+    index = valueIndex
+    return arguments[valueIndex]
+}
+
+func printUsage() {
+    print(
+        """
+        Usage: MaxVolBenchmark [--fixture <id>] [--algorithm all|square|rectangular] [--scalar all|double|float] [--iterations <count>] [--rectangular-min-rows <count>]
+
+        Prints one JSON object per benchmark result. Build with:
+          swift build -c release --product MaxVolBenchmark
+        """
+    )
+}
+
+func loadFixtureFile() throws -> FixtureFile {
+    guard let url = Bundle.module.url(forResource: "fixtures", withExtension: "json") else {
+        throw BenchmarkError.missingFixtureResource
+    }
+
+    let data = try Data(contentsOf: url)
+    return try JSONDecoder().decode(FixtureFile.self, from: data)
+}
+
+func selectedFixtures(
+    from fixtureFile: FixtureFile,
+    configuration: BenchmarkConfiguration
+) throws -> [BenchmarkFixture] {
+    guard let fixtureFilter = configuration.fixtureFilter else {
+        return fixtureFile.fixtures
+    }
+
+    let fixtures = fixtureFile.fixtures.filter { $0.id == fixtureFilter }
+    guard !fixtures.isEmpty else {
+        throw BenchmarkError.fixtureNotFound(fixtureFilter)
+    }
+
+    return fixtures
+}
+
+func runBenchmark(
+    fixture: BenchmarkFixture,
+    algorithm: BenchmarkAlgorithm,
+    scalar: BenchmarkScalar,
+    configuration: BenchmarkConfiguration
+) throws -> BenchmarkRecord {
+    switch scalar {
+        case .double:
+            return try runDoubleBenchmark(
+                fixture: fixture,
+                algorithm: algorithm,
+                configuration: configuration
+            )
+        case .float:
+            return try runFloatBenchmark(
+                fixture: fixture,
+                algorithm: algorithm,
+                configuration: configuration
+            )
+        case .all:
+            preconditionFailure("Expanded scalar filters should not include .all.")
+    }
+}
+
+func runDoubleBenchmark(
+    fixture: BenchmarkFixture,
+    algorithm: BenchmarkAlgorithm,
+    configuration: BenchmarkConfiguration
+) throws -> BenchmarkRecord {
+    let matrix = try DenseColumnMajorMatrix<Double>(
+        rows: fixture.rows,
+        columns: fixture.columns,
+        rowMajorValues: fixture.rowMajorValues
+    )
+    _ = try runDoubleAlgorithm(matrix, algorithm: algorithm, configuration: configuration)
+
+    let start = DispatchTime.now().uptimeNanoseconds
+    var latest = try runDoubleAlgorithm(matrix, algorithm: algorithm, configuration: configuration)
+    for _ in 1..<configuration.iterations {
+        latest = try runDoubleAlgorithm(matrix, algorithm: algorithm, configuration: configuration)
+    }
+    let elapsed = DispatchTime.now().uptimeNanoseconds - start
+
+    return try BenchmarkRecord(
+        tool: "MaxVolBenchmark",
+        fixture: fixture.id,
+        algorithm: algorithm.rawValue,
+        scalar: BenchmarkScalar.double.rawValue,
+        rows: fixture.rows,
+        columns: fixture.columns,
+        repetitions: configuration.iterations,
+        elapsedNanoseconds: elapsed,
+        averageNanoseconds: Double(elapsed) / Double(configuration.iterations),
+        selectedRowCount: latest.selectedRows.count,
+        algorithmIterations: latest.iterations,
+        converged: latest.converged,
+        maxCoefficientMagnitude: maximumAbsoluteCoefficient(in: latest.coefficients),
+        maxUnselectedRowNorm: algorithm == .rectangular ? maximumUnselectedRowNorm(in: latest) : nil,
+        reconstructionResidual: reconstructionResidual(matrix: matrix, result: latest)
+    )
+}
+
+func runFloatBenchmark(
+    fixture: BenchmarkFixture,
+    algorithm: BenchmarkAlgorithm,
+    configuration: BenchmarkConfiguration
+) throws -> BenchmarkRecord {
+    let matrix = try DenseColumnMajorMatrix<Float>(
+        rows: fixture.rows,
+        columns: fixture.columns,
+        rowMajorValues: fixture.rowMajorValues.map(Float.init)
+    )
+    _ = try runFloatAlgorithm(matrix, algorithm: algorithm, configuration: configuration)
+
+    let start = DispatchTime.now().uptimeNanoseconds
+    var latest = try runFloatAlgorithm(matrix, algorithm: algorithm, configuration: configuration)
+    for _ in 1..<configuration.iterations {
+        latest = try runFloatAlgorithm(matrix, algorithm: algorithm, configuration: configuration)
+    }
+    let elapsed = DispatchTime.now().uptimeNanoseconds - start
+
+    return try BenchmarkRecord(
+        tool: "MaxVolBenchmark",
+        fixture: fixture.id,
+        algorithm: algorithm.rawValue,
+        scalar: BenchmarkScalar.float.rawValue,
+        rows: fixture.rows,
+        columns: fixture.columns,
+        repetitions: configuration.iterations,
+        elapsedNanoseconds: elapsed,
+        averageNanoseconds: Double(elapsed) / Double(configuration.iterations),
+        selectedRowCount: latest.selectedRows.count,
+        algorithmIterations: latest.iterations,
+        converged: latest.converged,
+        maxCoefficientMagnitude: maximumAbsoluteCoefficient(in: latest.coefficients),
+        maxUnselectedRowNorm: algorithm == .rectangular ? maximumUnselectedRowNorm(in: latest) : nil,
+        reconstructionResidual: Double(reconstructionResidual(matrix: matrix, result: latest))
+    )
+}
+
+func runDoubleAlgorithm(
+    _ matrix: DenseColumnMajorMatrix<Double>,
+    algorithm: BenchmarkAlgorithm,
+    configuration: BenchmarkConfiguration
+) throws -> MaxVolResult<Double> {
+    switch algorithm {
+        case .square:
+            try maxVol(matrix, options: MaxVolOptions(tolerance: 1.05, maxIterations: 200))
+        case .rectangular:
+            try rectMaxVol(
+                matrix,
+                options: RectMaxVolOptions(
+                    tolerance: 1.0,
+                    minRows: configuration.rectangularMinRows,
+                    startMaxVolIterations: 10
+                )
+            )
+        case .all:
+            preconditionFailure("Expanded algorithm filters should not include .all.")
+    }
+}
+
+func runFloatAlgorithm(
+    _ matrix: DenseColumnMajorMatrix<Float>,
+    algorithm: BenchmarkAlgorithm,
+    configuration: BenchmarkConfiguration
+) throws -> MaxVolResult<Float> {
+    switch algorithm {
+        case .square:
+            try maxVol(matrix, options: MaxVolOptions(tolerance: 1.05, maxIterations: 200))
+        case .rectangular:
+            try rectMaxVol(
+                matrix,
+                options: RectMaxVolOptions(
+                    tolerance: 1.0,
+                    minRows: configuration.rectangularMinRows,
+                    startMaxVolIterations: 10
+                )
+            )
+        case .all:
+            preconditionFailure("Expanded algorithm filters should not include .all.")
+    }
+}
+
+func maximumAbsoluteCoefficient(
+    in coefficients: DenseColumnMajorMatrix<Double>
+) -> Double {
+    coefficients.values.map(abs).max() ?? 0
+}
+
+func maximumAbsoluteCoefficient(
+    in coefficients: DenseColumnMajorMatrix<Float>
+) -> Double {
+    coefficients.values.map { Double(abs($0)) }.max() ?? 0
+}
+
+func maximumUnselectedRowNorm(in result: MaxVolResult<Double>) -> Double {
+    let selected = Set(result.selectedRows)
+    return (0..<result.coefficients.rows)
+        .filter { !selected.contains($0) }
+        .map { row in
+            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
+                let coefficient = result.coefficients.values[
+                    column * result.coefficients.leadingDimension + row
+                ]
+                return total + coefficient * coefficient
+            }
+            return normSquared.squareRoot()
+        }
+        .max() ?? 0
+}
+
+func maximumUnselectedRowNorm(in result: MaxVolResult<Float>) -> Double {
+    let selected = Set(result.selectedRows)
+    return (0..<result.coefficients.rows)
+        .filter { !selected.contains($0) }
+        .map { row in
+            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
+                let coefficient = Double(result.coefficients.values[
+                    column * result.coefficients.leadingDimension + row
+                ])
+                return total + coefficient * coefficient
+            }
+            return normSquared.squareRoot()
+        }
+        .max() ?? 0
+}
+
+func reconstructionResidual(
+    matrix: DenseColumnMajorMatrix<Double>,
+    result: MaxVolResult<Double>
+) throws -> Double {
+    var residual = 0.0
+    for row in 0..<matrix.rows {
+        for column in 0..<matrix.columns {
+            var reconstructed = 0.0
+            for selectedColumn in 0..<result.selectedRows.count {
+                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
+                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
+            }
+            residual = try max(residual, abs(matrix.value(row: row, column: column) - reconstructed))
+        }
+    }
+    return residual
+}
+
+func reconstructionResidual(
+    matrix: DenseColumnMajorMatrix<Float>,
+    result: MaxVolResult<Float>
+) throws -> Float {
+    var residual: Float = 0
+    for row in 0..<matrix.rows {
+        for column in 0..<matrix.columns {
+            var reconstructed: Float = 0
+            for selectedColumn in 0..<result.selectedRows.count {
+                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
+                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
+            }
+            residual = try max(residual, abs(matrix.value(row: row, column: column) - reconstructed))
+        }
+    }
+    return residual
+}
diff --git a/Tests/MaxVolTests/FloatMaxVolTests.swift b/Tests/MaxVolTests/FloatMaxVolTests.swift
index 71e37c3..348d6e5 100644
--- a/Tests/MaxVolTests/FloatMaxVolTests.swift
+++ b/Tests/MaxVolTests/FloatMaxVolTests.swift
@@ -259,133 +259,3 @@ struct FloatMaxVolTests {
         }
     }
 }
-
-private func expectReconstruction(
-    of matrix: DenseColumnMajorMatrix<Float>,
-    using result: MaxVolResult<Float>,
-    tolerance: Float = 1e-5
-) throws {
-    for row in 0..<matrix.rows {
-        for column in 0..<matrix.columns {
-            var reconstructed: Float = 0
-            for selectedColumn in 0..<result.selectedRows.count {
-                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
-                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
-            }
-
-            let expected = try matrix.value(row: row, column: column)
-            #expect(abs(reconstructed - expected) <= tolerance)
-        }
-    }
-}
-
-private func expectCoefficients(
-    _ coefficients: DenseColumnMajorMatrix<Float>,
-    rowMajorValues: [Float],
-    tolerance: Float = 5e-6
-) throws {
-    let expected = try DenseColumnMajorMatrix(
-        rows: coefficients.rows,
-        columns: coefficients.columns,
-        rowMajorValues: rowMajorValues
-    )
-
-    for row in 0..<coefficients.rows {
-        for column in 0..<coefficients.columns {
-            let actualValue = try coefficients.value(row: row, column: column)
-            let expectedValue = try expected.value(row: row, column: column)
-            #expect(abs(actualValue - expectedValue) <= tolerance)
-        }
-    }
-}
-
-private func expectSelectedRowsAreIdentity(_ result: MaxVolResult<Float>) throws {
-    for (identityColumn, selectedRow) in result.selectedRows.enumerated() {
-        for column in 0..<result.coefficients.columns {
-            let expected: Float = column == identityColumn ? 1 : 0
-            let actual = try result.coefficients.value(row: selectedRow, column: column)
-            #expect(abs(actual - expected) <= 1e-6)
-        }
-    }
-}
-
-private func maximumAbsoluteCoefficient(
-    in coefficients: DenseColumnMajorMatrix<Float>
-) -> Double {
-    coefficients.values.map { Double(abs($0)) }.max() ?? 0
-}
-
-private func maximumUnselectedRowNorm(in result: MaxVolResult<Float>) -> Double {
-    let selected = Set(result.selectedRows)
-    return (0..<result.coefficients.rows)
-        .filter { !selected.contains($0) }
-        .map { row in
-            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
-                let coefficient = result.coefficients[row: row, column: column]
-                return total + Double(coefficient * coefficient)
-            }
-            return normSquared.squareRoot()
-        }
-        .max() ?? 0
-}
-
-private func orthonormalColumns(
-    rows: Int,
-    columns: Int,
-    seed: UInt64
-) throws -> DenseColumnMajorMatrix<Double> {
-    var generator = SeededGenerator(state: seed)
-    var columnVectors = (0..<columns).map { column -> [Double] in
-        (0..<rows).map { row in
-            generator.nextDouble() + (row == column ? 1.0 : 0.0)
-        }
-    }
-
-    for column in 0..<columns {
-        for priorColumn in 0..<column {
-            let projection = dot(columnVectors[column], columnVectors[priorColumn])
-            for row in 0..<rows {
-                columnVectors[column][row] -= projection * columnVectors[priorColumn][row]
-            }
-        }
-
-        let norm = dot(columnVectors[column], columnVectors[column]).squareRoot()
-        for row in 0..<rows {
-            columnVectors[column][row] /= norm
-        }
-    }
-
-    return try DenseColumnMajorMatrix(
-        rows: rows,
-        columns: columns,
-        columnMajorValues: columnVectors.flatMap { $0 }
-    )
-}
-
-private func dot(_ left: [Double], _ right: [Double]) -> Double {
-    zip(left, right).reduce(0) { total, pair in
-        total + pair.0 * pair.1
-    }
-}
-
-private struct SeededGenerator {
-    var state: UInt64
-
-    mutating func nextDouble() -> Double {
-        state = state &* 6_364_136_223_846_793_005 &+ 1_442_695_040_888_963_407
-        let scaled = Double(state >> 11) / Double(UInt64.max >> 11)
-        return scaled * 2 - 1
-    }
-}
-
-private extension DenseColumnMajorMatrix where Scalar == Double {
-    func mapValues<Output: Sendable>(
-        _ transform: (Double) -> Output
-    ) throws -> DenseColumnMajorMatrix<Output> {
-        try DenseColumnMajorMatrix<Output>(
-            rows: rows,
-            columns: columns,
-            columnMajorValues: values.map(transform)
-        )
-    }
-}
diff --git a/Tests/MaxVolTests/NumericalBehaviorTests.swift b/Tests/MaxVolTests/NumericalBehaviorTests.swift
index bf9b587..679f997 100644
--- a/Tests/MaxVolTests/NumericalBehaviorTests.swift
+++ b/Tests/MaxVolTests/NumericalBehaviorTests.swift
@@ -74,142 +74,3 @@ struct NumericalBehaviorTests {
         }
     }
 }
-
-private func expectReconstruction(
-    of matrix: DenseColumnMajorMatrix<Double>,
-    using result: MaxVolResult<Double>,
-    tolerance: Double
-) throws {
-    for row in 0..<matrix.rows {
-        for column in 0..<matrix.columns {
-            var reconstructed = 0.0
-            for selectedColumn in 0..<result.selectedRows.count {
-                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
-                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
-            }
-
-            let expected = try matrix.value(row: row, column: column)
-            #expect(abs(reconstructed - expected) <= tolerance)
-        }
-    }
-}
-
-private func expectReconstruction(
-    of matrix: DenseColumnMajorMatrix<Float>,
-    using result: MaxVolResult<Float>,
-    tolerance: Float
-) throws {
-    for row in 0..<matrix.rows {
-        for column in 0..<matrix.columns {
-            var reconstructed: Float = 0
-            for selectedColumn in 0..<result.selectedRows.count {
-                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
-                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
-            }
-
-            let expected = try matrix.value(row: row, column: column)
-            #expect(abs(reconstructed - expected) <= tolerance)
-        }
-    }
-}
-
-private func maximumAbsoluteCoefficient(
-    in coefficients: DenseColumnMajorMatrix<Double>
-) -> Double {
-    coefficients.values.map(abs).max() ?? 0
-}
-
-private func maximumAbsoluteCoefficient(
-    in coefficients: DenseColumnMajorMatrix<Float>
-) -> Double {
-    coefficients.values.map { Double(abs($0)) }.max() ?? 0
-}
-
-private func maximumUnselectedRowNorm(in result: MaxVolResult<Double>) -> Double {
-    let selected = Set(result.selectedRows)
-    return (0..<result.coefficients.rows)
-        .filter { !selected.contains($0) }
-        .map { row in
-            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
-                let coefficient = result.coefficients[row: row, column: column]
-                return total + coefficient * coefficient
-            }
-            return normSquared.squareRoot()
-        }
-        .max() ?? 0
-}
-
-private func maximumUnselectedRowNorm(in result: MaxVolResult<Float>) -> Double {
-    let selected = Set(result.selectedRows)
-    return (0..<result.coefficients.rows)
-        .filter { !selected.contains($0) }
-        .map { row in
-            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
-                let coefficient = result.coefficients[row: row, column: column]
-                return total + Double(coefficient * coefficient)
-            }
-            return normSquared.squareRoot()
-        }
-        .max() ?? 0
-}
-
-private func orthonormalColumns(
-    rows: Int,
-    columns: Int,
-    seed: UInt64
-) throws -> DenseColumnMajorMatrix<Double> {
-    var generator = SeededGenerator(state: seed)
-    var columnVectors = (0..<columns).map { column -> [Double] in
-        (0..<rows).map { row in
-            generator.nextDouble() + (row == column ? 1.0 : 0.0)
-        }
-    }
-
-    for column in 0..<columns {
-        for priorColumn in 0..<column {
-            let projection = dot(columnVectors[column], columnVectors[priorColumn])
-            for row in 0..<rows {
-                columnVectors[column][row] -= projection * columnVectors[priorColumn][row]
-            }
-        }
-
-        let norm = dot(columnVectors[column], columnVectors[column]).squareRoot()
-        for row in 0..<rows {
-            columnVectors[column][row] /= norm
-        }
-    }
-
-    return try DenseColumnMajorMatrix(
-        rows: rows,
-        columns: columns,
-        columnMajorValues: columnVectors.flatMap { $0 }
-    )
-}
-
-private func dot(_ left: [Double], _ right: [Double]) -> Double {
-    zip(left, right).reduce(0) { total, pair in
-        total + pair.0 * pair.1
-    }
-}
-
-private struct SeededGenerator {
-    var state: UInt64
-
-    mutating func nextDouble() -> Double {
-        state = state &* 6_364_136_223_846_793_005 &+ 1_442_695_040_888_963_407
-        let scaled = Double(state >> 11) / Double(UInt64.max >> 11)
-        return scaled * 2 - 1
-    }
-}
-
-private extension DenseColumnMajorMatrix where Scalar == Double {
-    func mapValues<Output: Sendable>(
-        _ transform: (Double) -> Output
-    ) throws -> DenseColumnMajorMatrix<Output> {
-        try DenseColumnMajorMatrix<Output>(
-            rows: rows,
-            columns: columns,
-            columnMajorValues: values.map(transform)
-        )
-    }
-}
diff --git a/Tests/MaxVolTests/RectMaxVolTests.swift b/Tests/MaxVolTests/RectMaxVolTests.swift
index bfe5b9f..bcf7dc8 100644
--- a/Tests/MaxVolTests/RectMaxVolTests.swift
+++ b/Tests/MaxVolTests/RectMaxVolTests.swift
@@ -199,121 +199,3 @@ struct RectMaxVolTests {
         try expectSelectedRowsAreIdentity(rectangular)
     }
 }
-
-private func expectReconstruction(
-    of matrix: DenseColumnMajorMatrix<Double>,
-    using result: MaxVolResult<Double>,
-    tolerance: Double = 1e-10
-) throws {
-    for row in 0..<matrix.rows {
-        for column in 0..<matrix.columns {
-            var reconstructed = 0.0
-            for selectedColumn in 0..<result.selectedRows.count {
-                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
-                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
-            }
-
-            let expected = try matrix.value(row: row, column: column)
-            #expect(abs(reconstructed - expected) <= tolerance)
-        }
-    }
-}
-
-private func expectCoefficients(
-    _ coefficients: DenseColumnMajorMatrix<Double>,
-    rowMajorValues: [Double],
-    tolerance: Double = 1e-12
-) throws {
-    let expected = try DenseColumnMajorMatrix(
-        rows: coefficients.rows,
-        columns: coefficients.columns,
-        rowMajorValues: rowMajorValues
-    )
-
-    for row in 0..<coefficients.rows {
-        for column in 0..<coefficients.columns {
-            let actualValue = try coefficients.value(row: row, column: column)
-            let expectedValue = try expected.value(row: row, column: column)
-            #expect(abs(actualValue - expectedValue) <= tolerance)
-        }
-    }
-}
-
-private func expectSelectedRowsAreIdentity(_ result: MaxVolResult<Double>) throws {
-    for (identityColumn, selectedRow) in result.selectedRows.enumerated() {
-        for column in 0..<result.coefficients.columns {
-            let expected = column == identityColumn ? 1.0 : 0.0
-            let actual = try result.coefficients.value(row: selectedRow, column: column)
-            #expect(abs(actual - expected) <= 1e-12)
-        }
-    }
-}
-
-private func maximumAbsoluteCoefficient(
-    in coefficients: DenseColumnMajorMatrix<Double>
-) -> Double {
-    coefficients.values.map(abs).max() ?? 0
-}
-
-private func maximumUnselectedRowNorm(in result: MaxVolResult<Double>) -> Double {
-    let selected = Set(result.selectedRows)
-    return (0..<result.coefficients.rows)
-        .filter { !selected.contains($0) }
-        .map { row in
-            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
-                let coefficient = result.coefficients[row: row, column: column]
-                return total + coefficient * coefficient
-            }
-            return normSquared.squareRoot()
-        }
-        .max() ?? 0
-}
-
-private func orthonormalColumns(
-    rows: Int,
-    columns: Int,
-    seed: UInt64
-) throws -> DenseColumnMajorMatrix<Double> {
-    var generator = SeededGenerator(state: seed)
-    var columnVectors = (0..<columns).map { column -> [Double] in
-        (0..<rows).map { row in
-            generator.nextDouble() + (row == column ? 1.0 : 0.0)
-        }
-    }
-
-    for column in 0..<columns {
-        for priorColumn in 0..<column {
-            let projection = dot(columnVectors[column], columnVectors[priorColumn])
-            for row in 0..<rows {
-                columnVectors[column][row] -= projection * columnVectors[priorColumn][row]
-            }
-        }
-
-        let norm = dot(columnVectors[column], columnVectors[column]).squareRoot()
-        for row in 0..<rows {
-            columnVectors[column][row] /= norm
-        }
-    }
-
-    return try DenseColumnMajorMatrix(
-        rows: rows,
-        columns: columns,
-        columnMajorValues: columnVectors.flatMap { $0 }
-    )
-}
-
-private func dot(_ left: [Double], _ right: [Double]) -> Double {
-    zip(left, right).reduce(0) { total, pair in
-        total + pair.0 * pair.1
-    }
-}
-
-private struct SeededGenerator {
-    var state: UInt64
-
-    mutating func nextDouble() -> Double {
-        state = state &* 6_364_136_223_846_793_005 &+ 1_442_695_040_888_963_407
-        let scaled = Double(state >> 11) / Double(UInt64.max >> 11)
-        return scaled * 2 - 1
-    }
-}
diff --git a/Tests/MaxVolTests/TestSupport.swift b/Tests/MaxVolTests/TestSupport.swift
new file mode 100644
index 0000000..e3183bc
--- /dev/null
+++ b/Tests/MaxVolTests/TestSupport.swift
@@ -0,0 +1,207 @@
+@testable import MaxVol
+import Testing
+
+func expectReconstruction(
+    of matrix: DenseColumnMajorMatrix<Double>,
+    using result: MaxVolResult<Double>,
+    tolerance: Double = 1e-10
+) throws {
+    for row in 0..<matrix.rows {
+        for column in 0..<matrix.columns {
+            var reconstructed = 0.0
+            for selectedColumn in 0..<result.selectedRows.count {
+                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
+                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
+            }
+
+            let expected = try matrix.value(row: row, column: column)
+            #expect(abs(reconstructed - expected) <= tolerance)
+        }
+    }
+}
+
+func expectReconstruction(
+    of matrix: DenseColumnMajorMatrix<Float>,
+    using result: MaxVolResult<Float>,
+    tolerance: Float = 1e-5
+) throws {
+    for row in 0..<matrix.rows {
+        for column in 0..<matrix.columns {
+            var reconstructed: Float = 0
+            for selectedColumn in 0..<result.selectedRows.count {
+                reconstructed += try result.coefficients.value(row: row, column: selectedColumn)
+                    * matrix.value(row: result.selectedRows[selectedColumn], column: column)
+            }
+
+            let expected = try matrix.value(row: row, column: column)
+            #expect(abs(reconstructed - expected) <= tolerance)
+        }
+    }
+}
+
+func expectCoefficients(
+    _ coefficients: DenseColumnMajorMatrix<Double>,
+    rowMajorValues: [Double],
+    tolerance: Double = 1e-12
+) throws {
+    let expected = try DenseColumnMajorMatrix(
+        rows: coefficients.rows,
+        columns: coefficients.columns,
+        rowMajorValues: rowMajorValues
+    )
+
+    for row in 0..<coefficients.rows {
+        for column in 0..<coefficients.columns {
+            let actualValue = try coefficients.value(row: row, column: column)
+            let expectedValue = try expected.value(row: row, column: column)
+            #expect(abs(actualValue - expectedValue) <= tolerance)
+        }
+    }
+}
+
+func expectCoefficients(
+    _ coefficients: DenseColumnMajorMatrix<Float>,
+    rowMajorValues: [Float],
+    tolerance: Float = 5e-6
+) throws {
+    let expected = try DenseColumnMajorMatrix(
+        rows: coefficients.rows,
+        columns: coefficients.columns,
+        rowMajorValues: rowMajorValues
+    )
+
+    for row in 0..<coefficients.rows {
+        for column in 0..<coefficients.columns {
+            let actualValue = try coefficients.value(row: row, column: column)
+            let expectedValue = try expected.value(row: row, column: column)
+            #expect(abs(actualValue - expectedValue) <= tolerance)
+        }
+    }
+}
+
+func expectSelectedRowsAreIdentity(
+    _ result: MaxVolResult<Double>,
+    tolerance: Double = 1e-12
+) throws {
+    for (identityColumn, selectedRow) in result.selectedRows.enumerated() {
+        for column in 0..<result.coefficients.columns {
+            let expected = column == identityColumn ? 1.0 : 0.0
+            let actual = try result.coefficients.value(row: selectedRow, column: column)
+            #expect(abs(actual - expected) <= tolerance)
+        }
+    }
+}
+
+func expectSelectedRowsAreIdentity(
+    _ result: MaxVolResult<Float>,
+    tolerance: Float = 1e-6
+) throws {
+    for (identityColumn, selectedRow) in result.selectedRows.enumerated() {
+        for column in 0..<result.coefficients.columns {
+            let expected: Float = column == identityColumn ? 1 : 0
+            let actual = try result.coefficients.value(row: selectedRow, column: column)
+            #expect(abs(actual - expected) <= tolerance)
+        }
+    }
+}
+
+func maximumAbsoluteCoefficient(
+    in coefficients: DenseColumnMajorMatrix<Double>
+) -> Double {
+    coefficients.values.map(abs).max() ?? 0
+}
+
+func maximumAbsoluteCoefficient(
+    in coefficients: DenseColumnMajorMatrix<Float>
+) -> Double {
+    coefficients.values.map { Double(abs($0)) }.max() ?? 0
+}
+
+func maximumUnselectedRowNorm(in result: MaxVolResult<Double>) -> Double {
+    let selected = Set(result.selectedRows)
+    return (0..<result.coefficients.rows)
+        .filter { !selected.contains($0) }
+        .map { row in
+            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
+                let coefficient = result.coefficients[row: row, column: column]
+                return total + coefficient * coefficient
+            }
+            return normSquared.squareRoot()
+        }
+        .max() ?? 0
+}
+
+func maximumUnselectedRowNorm(in result: MaxVolResult<Float>) -> Double {
+    let selected = Set(result.selectedRows)
+    return (0..<result.coefficients.rows)
+        .filter { !selected.contains($0) }
+        .map { row in
+            let normSquared = (0..<result.coefficients.columns).reduce(0.0) { total, column in
+                let coefficient = Double(result.coefficients[row: row, column: column])
+                return total + coefficient * coefficient
+            }
+            return normSquared.squareRoot()
+        }
+        .max() ?? 0
+}
+
+func orthonormalColumns(
+    rows: Int,
+    columns: Int,
+    seed: UInt64
+) throws -> DenseColumnMajorMatrix<Double> {
+    var generator = SeededGenerator(state: seed)
+    var columnVectors = (0..<columns).map { column -> [Double] in
+        (0..<rows).map { row in
+            generator.nextDouble() + (row == column ? 1.0 : 0.0)
+        }
+    }
+
+    for column in 0..<columns {
+        for priorColumn in 0..<column {
+            let projection = dot(columnVectors[column], columnVectors[priorColumn])
+            for row in 0..<rows {
+                columnVectors[column][row] -= projection * columnVectors[priorColumn][row]
+            }
+        }
+
+        let norm = dot(columnVectors[column], columnVectors[column]).squareRoot()
+        for row in 0..<rows {
+            columnVectors[column][row] /= norm
+        }
+    }
+
+    return try DenseColumnMajorMatrix(
+        rows: rows,
+        columns: columns,
+        columnMajorValues: columnVectors.flatMap { $0 }
+    )
+}
+
+func dot(_ left: [Double], _ right: [Double]) -> Double {
+    zip(left, right).reduce(0) { total, pair in
+        total + pair.0 * pair.1
+    }
+}
+
+struct SeededGenerator {
+    var state: UInt64
+
+    mutating func nextDouble() -> Double {
+        state = state &* 6_364_136_223_846_793_005 &+ 1_442_695_040_888_963_407
+        let scaled = Double(state >> 11) / Double(UInt64.max >> 11)
+        return scaled * 2 - 1
+    }
+}
+
+extension DenseColumnMajorMatrix where Scalar == Double {
+    func mapValues<Output: Sendable>(
+        _ transform: (Double) -> Output
+    ) throws -> DenseColumnMajorMatrix<Output> {
+        try DenseColumnMajorMatrix<Output>(
+            rows: rows,
+            columns: columns,
+            columnMajorValues: values.map(transform)
+        )
+    }
+}
diff --git a/scripts/check_benchmark_parity.py b/scripts/check_benchmark_parity.py
new file mode 100755
index 0000000..772362e
--- /dev/null
+++ b/scripts/check_benchmark_parity.py
@@ -0,0 +1,78 @@
+#!/usr/bin/env python3
+"""Compare MaxVolBenchmark JSONL with maxvolpy JSONL for correctness parity."""
+
+from __future__ import annotations
+
+import argparse
+import json
+from pathlib import Path
+from typing import Any
+
+
+def load_records(path: Path) -> dict[tuple[str, str, str], dict[str, Any]]:
+    records: dict[tuple[str, str, str], dict[str, Any]] = {}
+    for line in path.read_text(encoding="utf-8").splitlines():
+        if not line.strip():
+            continue
+        record = json.loads(line)
+        key = (record["fixture"], record["algorithm"], record["scalar"])
+        records[key] = record
+    return records
+
+
+def tolerance_for(scalar: str) -> float:
+    return 1e-4 if scalar == "float" else 1e-8
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("swift_jsonl", type=Path)
+    parser.add_argument("python_jsonl", type=Path)
+    args = parser.parse_args()
+
+    swift_records = load_records(args.swift_jsonl)
+    python_records = load_records(args.python_jsonl)
+
+    missing_from_python = sorted(set(swift_records) - set(python_records))
+    missing_from_swift = sorted(set(python_records) - set(swift_records))
+    if missing_from_python or missing_from_swift:
+        raise SystemExit(
+            "Benchmark result keys differ. "
+            f"Missing from Python: {missing_from_python}. "
+            f"Missing from Swift: {missing_from_swift}."
+        )
+
+    failures: list[str] = []
+    for key in sorted(swift_records):
+        swift = swift_records[key]
+        python = python_records[key]
+        tolerance = tolerance_for(swift["scalar"])
+
+        if swift["selectedRowCount"] != python["selectedRowCount"]:
+            failures.append(
+                f"{key}: selected row count differs "
+                f"Swift={swift['selectedRowCount']} Python={python['selectedRowCount']}"
+            )
+
+        residual_delta = abs(swift["reconstructionResidual"] - python["reconstructionResidual"])
+        if residual_delta > tolerance:
+            failures.append(
+                f"{key}: reconstruction residual differs by {residual_delta}, tolerance {tolerance}"
+            )
+
+        swift_norm = swift.get("maxUnselectedRowNorm")
+        python_norm = python.get("maxUnselectedRowNorm")
+        if swift_norm is not None and python_norm is not None and abs(swift_norm - python_norm) > tolerance:
+            failures.append(
+                f"{key}: rectangular row norm differs "
+                f"Swift={swift_norm} Python={python_norm}, tolerance {tolerance}"
+            )
+
+    if failures:
+        raise SystemExit("\n".join(failures))
+
+    print(f"Benchmark parity passed for {len(swift_records)} result keys.")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/compare_maxvolpy.py b/scripts/compare_maxvolpy.py
new file mode 100755
index 0000000..bc8acd6
--- /dev/null
+++ b/scripts/compare_maxvolpy.py
@@ -0,0 +1,173 @@
+#!/usr/bin/env -S uv run
+# /// script
+# requires-python = ">=3.11,<3.12"
+# dependencies = [
+#   "numpy==1.26.4",
+#   "scipy==1.11.4",
+# ]
+# ///
+"""Run the official maxvolpy implementation against MaxVol benchmark fixtures."""
+
+from __future__ import annotations
+
+import argparse
+import contextlib
+import importlib
+import json
+import sys
+import tarfile
+import time
+import urllib.request
+from pathlib import Path
+from tempfile import TemporaryDirectory
+from typing import Any
+
+import numpy as np
+
+
+MAXVOLPY_VERSION = "0.3.8"
+MAXVOLPY_SDIST_URL = (
+    "https://files.pythonhosted.org/packages/4a/cd/"
+    "142dc96f91db394c4a9c212c59ee17e67e3324dba6ff05346d269d5b6731/"
+    "maxvolpy-0.3.8.tar.gz"
+)
+
+
+def safe_extract(source: tarfile.TarFile, destination: Path) -> None:
+    destination = destination.resolve()
+    for member in source.getmembers():
+        target = (destination / member.name).resolve()
+        if not target.is_relative_to(destination):
+            raise RuntimeError(f"Refusing to extract unsafe maxvolpy archive member: {member.name}")
+    source.extractall(destination)
+
+
+def load_maxvol_module(source_dir: Path | None):
+    if source_dir is None:
+        with TemporaryDirectory(prefix="maxvolpy-") as temporary_directory:
+            source_dir = Path(temporary_directory)
+            archive = source_dir / "maxvolpy.tar.gz"
+            urllib.request.urlretrieve(MAXVOLPY_SDIST_URL, archive)
+            with tarfile.open(archive) as tar:
+                safe_extract(tar, source_dir)
+            package_root = source_dir / f"maxvolpy-{MAXVOLPY_VERSION}"
+            sys.path.insert(0, str(package_root))
+            with contextlib.redirect_stdout(sys.stderr):
+                return importlib.import_module("maxvolpy.maxvol")
+
+    sys.path.insert(0, str(source_dir))
+    with contextlib.redirect_stdout(sys.stderr):
+        return importlib.import_module("maxvolpy.maxvol")
+
+
+def run_algorithm(module: Any, matrix: np.ndarray, algorithm: str, implementation: str):
+    if algorithm == "square":
+        function = module.py_maxvol if implementation == "pure" else module.maxvol
+        return function(matrix, tol=1.05, max_iters=200)
+
+    function = module.py_rect_maxvol if implementation == "pure" else module.rect_maxvol
+    return function(matrix, tol=1.0, start_maxvol_iters=10)
+
+
+def reconstruction_residual(matrix: np.ndarray, pivots: np.ndarray, coefficients: np.ndarray) -> float:
+    reconstructed = coefficients.dot(matrix[pivots])
+    return float(np.max(np.abs(matrix - reconstructed)))
+
+
+def max_unselected_row_norm(pivots: np.ndarray, coefficients: np.ndarray) -> float | None:
+    selected = set(int(row) for row in pivots)
+    norms = [
+        float(np.linalg.norm(coefficients[row], ord=2))
+        for row in range(coefficients.shape[0])
+        if row not in selected
+    ]
+    return max(norms) if norms else 0.0
+
+
+def benchmark_fixture(
+    module: Any,
+    fixture: dict[str, Any],
+    algorithm: str,
+    scalar: str,
+    implementation: str,
+    repetitions: int,
+) -> dict[str, Any]:
+    dtype = np.float32 if scalar == "float" else np.float64
+    matrix = np.array(fixture["rowMajorValues"], dtype=dtype).reshape(fixture["rows"], fixture["columns"])
+    run_algorithm(module, matrix, algorithm, implementation)
+
+    start = time.perf_counter_ns()
+    pivots, coefficients = run_algorithm(module, matrix, algorithm, implementation)
+    for _ in range(1, repetitions):
+        pivots, coefficients = run_algorithm(module, matrix, algorithm, implementation)
+    elapsed = time.perf_counter_ns() - start
+
+    return {
+        "tool": "maxvolpy",
+        "implementation": implementation,
+        "fixture": fixture["id"],
+        "algorithm": algorithm,
+        "scalar": scalar,
+        "rows": fixture["rows"],
+        "columns": fixture["columns"],
+        "repetitions": repetitions,
+        "elapsedNanoseconds": elapsed,
+        "averageNanoseconds": elapsed / repetitions,
+        "selectedRowCount": int(len(pivots)),
+        "algorithmIterations": None,
+        "converged": None,
+        "maxCoefficientMagnitude": float(np.max(np.abs(coefficients))),
+        "maxUnselectedRowNorm": (
+            max_unselected_row_norm(pivots, coefficients)
+            if algorithm == "rectangular"
+            else None
+        ),
+        "reconstructionResidual": reconstruction_residual(matrix, pivots, coefficients),
+    }
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--fixtures", default="Sources/MaxVolBenchmark/Resources/fixtures.json")
+    parser.add_argument("--fixture")
+    parser.add_argument("--algorithm", choices=["all", "square", "rectangular"], default="all")
+    parser.add_argument("--scalar", choices=["all", "double", "float"], default="all")
+    parser.add_argument("--implementation", choices=["pure", "api"], default="pure")
+    parser.add_argument("--iterations", type=int, default=10)
+    parser.add_argument("--maxvolpy-source-dir", type=Path)
+    args = parser.parse_args()
+
+    if args.iterations <= 0:
+        raise SystemExit("--iterations must be greater than zero.")
+
+    fixtures_file = json.loads(Path(args.fixtures).read_text(encoding="utf-8"))
+    fixtures = fixtures_file["fixtures"]
+    if args.fixture is not None:
+        fixtures = [fixture for fixture in fixtures if fixture["id"] == args.fixture]
+        if not fixtures:
+            raise SystemExit(f"No benchmark fixture matched '{args.fixture}'.")
+
+    algorithms = ["square", "rectangular"] if args.algorithm == "all" else [args.algorithm]
+    scalars = ["double", "float"] if args.scalar == "all" else [args.scalar]
+    module = load_maxvol_module(args.maxvolpy_source_dir)
+
+    for fixture in fixtures:
+        for algorithm in algorithms:
+            for scalar in scalars:
+                print(
+                    json.dumps(
+                        benchmark_fixture(
+                            module,
+                            fixture,
+                            algorithm,
+                            scalar,
+                            args.implementation,
+                            args.iterations,
+                        ),
+                        sort_keys=True,
+                    )
+                )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/generate_benchmark_fixtures.py b/scripts/generate_benchmark_fixtures.py
new file mode 100755
index 0000000..be45499
--- /dev/null
+++ b/scripts/generate_benchmark_fixtures.py
@@ -0,0 +1,137 @@
+#!/usr/bin/env python3
+"""Generate deterministic benchmark fixtures shared by Swift and Python harnesses."""
+
+from __future__ import annotations
+
+import argparse
+import json
+from pathlib import Path
+
+
+def next_double(state: int) -> tuple[int, float]:
+    state = (state * 6_364_136_223_846_793_005 + 1_442_695_040_888_963_407) & ((1 << 64) - 1)
+    scaled = (state >> 11) / float((1 << 53) - 1)
+    return state, scaled * 2.0 - 1.0
+
+
+def gaussian_like(rows: int, columns: int, seed: int, diagonal_boost: float) -> list[float]:
+    state = seed
+    values: list[float] = []
+    for row in range(rows):
+        for column in range(columns):
+            state, first = next_double(state)
+            state, second = next_double(state)
+            value = 0.5 * first + 0.5 * second
+            if row == column:
+                value += diagonal_boost
+            values.append(value)
+    return values
+
+
+def dot(left: list[float], right: list[float]) -> float:
+    return sum(a * b for a, b in zip(left, right))
+
+
+def orthonormal(rows: int, columns: int, seed: int) -> list[float]:
+    state = seed
+    vectors: list[list[float]] = []
+    for column in range(columns):
+        vector: list[float] = []
+        for row in range(rows):
+            state, value = next_double(state)
+            vector.append(value + (1.0 if row == column else 0.0))
+        vectors.append(vector)
+
+    for column in range(columns):
+        for prior in range(column):
+            projection = dot(vectors[column], vectors[prior])
+            for row in range(rows):
+                vectors[column][row] -= projection * vectors[prior][row]
+
+        norm = dot(vectors[column], vectors[column]) ** 0.5
+        for row in range(rows):
+            vectors[column][row] /= norm
+
+    return [vectors[column][row] for row in range(rows) for column in range(columns)]
+
+
+def fixture(identifier: str, rows: int, columns: int, values: list[float], description: str) -> dict:
+    return {
+        "id": identifier,
+        "description": description,
+        "rows": rows,
+        "columns": columns,
+        "rowMajorValues": values,
+    }
+
+
+def build_fixtures() -> dict:
+    return {
+        "version": 1,
+        "source": "Generated by scripts/generate_benchmark_fixtures.py.",
+        "fixtures": [
+            fixture(
+                "square-swap-3x2",
+                3,
+                2,
+                [
+                    0.25, 0.0,
+                    0.5, 1.0,
+                    0.5, 1.5,
+                ],
+                "Small fixture that performs one square MaxVol row swap.",
+            ),
+            fixture(
+                "rect-append-5x2",
+                5,
+                2,
+                [
+                    1.0, 0.0,
+                    0.0, 1.0,
+                    1.2, 0.2,
+                    0.1, 1.3,
+                    0.8, 0.8,
+                ],
+                "Small fixture that appends one RectMaxVol row.",
+            ),
+            fixture(
+                "gaussian-64x8",
+                64,
+                8,
+                gaussian_like(64, 8, 0x6408_2026, 1.0),
+                "Medium full-rank Gaussian-like tall matrix with a diagonal boost.",
+            ),
+            fixture(
+                "orthonormal-96x12",
+                96,
+                12,
+                orthonormal(96, 12, 0x9612_2026),
+                "Medium tall matrix with deterministic orthonormal columns.",
+            ),
+            fixture(
+                "gaussian-192x16",
+                192,
+                16,
+                gaussian_like(192, 16, 0x1921_62026, 1.0),
+                "Larger full-rank Gaussian-like tall matrix for timing and profiling.",
+            ),
+        ],
+    }
+
+
+def main() -> None:
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument(
+        "--output",
+        default="Sources/MaxVolBenchmark/Resources/fixtures.json",
+        help="Fixture JSON path to write.",
+    )
+    args = parser.parse_args()
+
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    output.write_text(json.dumps(build_fixtures(), indent=2, sort_keys=True) + "\n", encoding="utf-8")
+
+
+if __name__ == "__main__":
+    main()