diff --git a/Cargo.lock b/Cargo.lock
index 98a4ff5..2ab9514 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -20,6 +20,12 @@ dependencies = [
  "cc",
 ]
 
+[[package]]
+name = "allocation-counter"
+version = "0.8.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "beb9e990c0a33699f1984d85a6abead615ccc72dd8130bf3e15dcabe2ca149c9"
+
 [[package]]
 name = "anes"
 version = "0.1.6"
@@ -91,7 +97,7 @@ checksum = "fc0e56a716f1e132ff6bf4bdac1c944a3fcdc1cae65f70a4a2a1ac3b401d2d1f"
 dependencies = [
  "proc-macro2",
  "quote",
- "syn 3.0.4",
+ "syn 3.0.5",
 ]
 
 [[package]]
@@ -628,9 +634,9 @@ checksum = "8f42a60cbdf9a97f5d2305f08a87dc4e09308d1276d28c869c684d7777685682"
 
 [[package]]
 name = "js-sys"
-version = "0.3.104"
+version = "0.3.105"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0e0c1080212aad755ea003d18543e8768dd432c48819efd73a7bf1e39b7a5a3a"
+checksum = "ce57d20d1ea864ce2ac172ab472d409214f4fd359f0b2a2775abdf522e2af99e"
 dependencies = [
  "cfg-if",
  "futures-util",
@@ -641,6 +647,7 @@ dependencies = [
 name = "la-stack"
 version = "0.4.5"
 dependencies = [
+ "allocation-counter",
  "approx",
  "criterion",
  "faer",
@@ -1204,7 +1211,7 @@ checksum = "e7a5d71263a5a7d47b41f6b3f06ba276f10cc18b0931f1799f710578e2309348"
 dependencies = [
  "proc-macro2",
  "quote",
- "syn 3.0.4",
+ "syn 3.0.5",
 ]
 
 [[package]]
@@ -1268,9 +1275,9 @@ dependencies = [
 
 [[package]]
 name = "syn"
-version = "3.0.4"
+version = "3.0.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e6275cddf4610d1775e6d1fe9469b2e77d0f39fd98fb7450901b821e0c53649f"
+checksum = "12df2e0110f65b775f769bb17ef989067a1d931b2eb822bd4346631eeada89f9"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -1388,9 +1395,9 @@ dependencies = [
 
 [[package]]
 name = "wasm-bindgen"
-version = "0.2.127"
+version = "0.2.128"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1b70935747edd64d89de3efa29d73789b806c15798f8e7dca4d8ac356b50ce70"
+checksum = "aecb87a33d3b0c5e3b7aa46336eaf486cffafbd281b195e4c8b80d50df2351bf"
 dependencies = [
  "cfg-if",
  "once_cell",
@@ -1401,9 +1408,9 @@ dependencies = [
 
 [[package]]
 name = "wasm-bindgen-macro"
-version = "0.2.127"
+version = "0.2.128"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "77775f8f3f7217702089053b94958f8f54061a3f663417df76e19cbdcca29bc1"
+checksum = "a690d511e3c1a8b3a55e33511e3c2c00c78415cd23650f32b808627f5696b9ed"
 dependencies = [
  "quote",
  "wasm-bindgen-macro-support",
@@ -1411,31 +1418,31 @@ dependencies = [
 
 [[package]]
 name = "wasm-bindgen-macro-support"
-version = "0.2.127"
+version = "0.2.128"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e11d33f857dc2fb11b8bc75aee111aa9cbeb12cd9f25efd3d4c2a3dd4e235284"
+checksum = "411e4887f0071ef2d2164a9d5fdf2d20efbef78fccd3a78b0c10a1dc5295e48a"
 dependencies = [
  "bumpalo",
  "proc-macro2",
  "quote",
- "syn 2.0.119",
+ "syn 3.0.5",
  "wasm-bindgen-shared",
 ]
 
 [[package]]
 name = "wasm-bindgen-shared"
-version = "0.2.127"
+version = "0.2.128"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7ef64dbcc55df09c7e5a46182d181c2cfa3e925f3da937ea764728b4bbb9dcbf"
+checksum = "81941cd78d0c92026c33e5e01312845a4cb1e9af3407f9134b100dd03144103e"
 dependencies = [
  "unicode-ident",
 ]
 
 [[package]]
 name = "web-sys"
-version = "0.3.104"
+version = "0.3.105"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "c435338968042f4f59a557f690a253676d47ce13ceb55d70100e7facf6620a30"
+checksum = "9fbddc4a036f00ec4f18c83445bd3115cb306a91da554919a099d9222fe4a7f8"
 dependencies = [
  "js-sys",
  "wasm-bindgen",
diff --git a/Cargo.toml b/Cargo.toml
index 25a6a0d..c1adb68 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -42,6 +42,7 @@ num-rational = { version = "0.4.2", features = [ "num-bigint-std" ], optional =
 num-traits = { version = "0.2.19", optional = true }
 
 [dev-dependencies]
+allocation-counter = "0.8.1"
 approx = "0.5.1"
 criterion = { version = "0.8.2", features = [ "html_reports" ] }
 faer = { version = "0.24.4", default-features = false, features = [ "std", "linalg" ] }
diff --git a/benches/common/rational.rs b/benches/common/rational.rs
new file mode 100644
index 0000000..e8597d0
--- /dev/null
+++ b/benches/common/rational.rs
@@ -0,0 +1,223 @@
+#![forbid(unsafe_code)]
+
+//! Independently validated rational inputs shared by timing and allocation probes.
+
+use la_stack::{BigInt, BigRational, DeterminantSign, RationalMatrix, RationalVector};
+
+use super::bench_utils::OrAbort;
+
+/// Fixed rational component-size families.
+#[derive(Clone, Copy, Debug)]
+pub enum RationalInputKind {
+    /// Original small-integer components from the rational-input benchmark.
+    Small,
+    /// Row factors with at least 256-bit numerator/denominator inputs.
+    Wide256,
+    /// Row factors with at least 1024-bit numerator/denominator inputs.
+    Wide1024,
+}
+
+impl RationalInputKind {
+    /// Stable fixture families, in registration order.
+    pub const ALL: [Self; 3] = [Self::Small, Self::Wide256, Self::Wide1024];
+
+    /// Stable family name used in benchmark and allocation output.
+    #[must_use]
+    pub const fn name(self) -> &'static str {
+        match self {
+            Self::Small => "small",
+            Self::Wide256 => "wide256",
+            Self::Wide1024 => "wide1024",
+        }
+    }
+
+    const fn component_bits(self) -> Option<usize> {
+        match self {
+            Self::Small => None,
+            Self::Wide256 => Some(256),
+            Self::Wide1024 => Some(1024),
+        }
+    }
+}
+
+/// Independently validated exact-input rational benchmark fixture.
+#[must_use]
+pub struct ValidatedRationalInput<const D: usize> {
+    matrix: RationalMatrix<D>,
+    rhs: RationalVector<D>,
+}
+
+impl<const D: usize> ValidatedRationalInput<D> {
+    /// Borrow the independently checked matrix.
+    pub const fn matrix(&self) -> &RationalMatrix<D> {
+        &self.matrix
+    }
+
+    /// Borrow the independently checked right-hand side.
+    pub const fn rhs(&self) -> &RationalVector<D> {
+        &self.rhs
+    }
+}
+
+/// Deterministic, strictly diagonally-dominant exact-input rational fixture.
+///
+/// # Panics
+/// Panics if construction or the independent determinant/solve checks fail.
+pub fn rational_input<const D: usize>(kind: RationalInputKind) -> ValidatedRationalInput<D> {
+    let mut rows = std::array::from_fn(|row| {
+        std::array::from_fn(|col| {
+            if row == col {
+                let diagonal = 2 * D + row + 1;
+                BigRational::from_integer(BigInt::from(diagonal))
+            } else {
+                let raw_numerator = (row * 3 + col * 5) % 5;
+                let numerator = i64::try_from(raw_numerator).or_abort("rational numerator") - 2;
+                let denominator = (row + col) % 7 + 2;
+                BigRational::new(BigInt::from(numerator), BigInt::from(denominator))
+            }
+        })
+    });
+    if let Some(bits) = kind.component_bits() {
+        for (row, entries) in rows.iter_mut().enumerate() {
+            let shift = bits + 16 * row;
+            let factor = BigRational::new(
+                (BigInt::from(1) << shift) + BigInt::from(1),
+                (BigInt::from(1) << (shift + 1)) - BigInt::from(1),
+            );
+            for entry in entries {
+                *entry *= &factor;
+            }
+        }
+    }
+    let expected_solution = std::array::from_fn(|index| {
+        BigRational::new(BigInt::from(index + 1), BigInt::from(index + 2))
+    });
+    let rhs_data = rational_matvec(&rows, &expected_solution);
+    let matrix = RationalMatrix::try_from_rows(rows.clone())
+        .or_abort("rational benchmark matrix construction");
+    let rhs =
+        RationalVector::try_new(rhs_data.clone()).or_abort("rational benchmark RHS construction");
+
+    let reference_determinant = rational_determinant_gaussian(rows.clone());
+    assert_eq!(matrix.det(), reference_determinant);
+    assert_eq!(matrix.det_sign(), determinant_sign(&reference_determinant));
+    let reference_solution = rational_solve_gaussian(rows, rhs_data)
+        .or_abort("rational Gaussian benchmark validation solve");
+    assert_eq!(reference_solution, expected_solution);
+    assert_eq!(
+        matrix
+            .solve(&rhs)
+            .or_abort("row-cleared Bareiss benchmark validation solve")
+            .into_array(),
+        expected_solution
+    );
+
+    ValidatedRationalInput { matrix, rhs }
+}
+
+/// Exact rational matrix-vector multiplication used only to assemble and
+/// validate benchmark fixtures.
+fn rational_matvec<const D: usize>(
+    rows: &[[BigRational; D]; D],
+    vector: &[BigRational; D],
+) -> [BigRational; D] {
+    std::array::from_fn(|row| {
+        rows[row]
+            .iter()
+            .zip(vector.iter())
+            .map(|(coefficient, component)| coefficient * component)
+            .sum()
+    })
+}
+
+/// Straightforward cubic rational Gaussian determinant reference.
+#[must_use]
+pub fn rational_determinant_gaussian<const D: usize>(
+    mut rows: [[BigRational; D]; D],
+) -> BigRational {
+    let zero = BigRational::from_integer(BigInt::from(0));
+    let mut determinant = BigRational::from_integer(BigInt::from(1));
+    let mut odd_swaps = false;
+
+    for pivot_col in 0..D {
+        let Some(pivot_row) = (pivot_col..D).find(|&row| rows[row][pivot_col] != zero) else {
+            return zero;
+        };
+        if pivot_row != pivot_col {
+            rows.swap(pivot_col, pivot_row);
+            odd_swaps = !odd_swaps;
+        }
+
+        let (pivot_rows, rows_below) = rows.split_at_mut(pivot_col + 1);
+        let pivot_entries = &pivot_rows[pivot_col];
+        let pivot = &pivot_entries[pivot_col];
+        determinant *= pivot;
+        for row_entries in rows_below {
+            let factor = &row_entries[pivot_col] / pivot;
+            for (entry, pivot_entry) in row_entries
+                .iter_mut()
+                .zip(pivot_entries.iter())
+                .skip(pivot_col + 1)
+            {
+                *entry -= &factor * pivot_entry;
+            }
+            row_entries[pivot_col] = zero.clone();
+        }
+    }
+
+    if odd_swaps { -determinant } else { determinant }
+}
+
+/// Straightforward cubic rational Gaussian solve reference.
+#[must_use]
+pub fn rational_solve_gaussian<const D: usize>(
+    mut rows: [[BigRational; D]; D],
+    mut rhs: [BigRational; D],
+) -> Option<[BigRational; D]> {
+    let zero = BigRational::from_integer(BigInt::from(0));
+    for pivot_col in 0..D {
+        let pivot_row = (pivot_col..D).find(|&row| rows[row][pivot_col] != zero)?;
+        if pivot_row != pivot_col {
+            rows.swap(pivot_col, pivot_row);
+            rhs.swap(pivot_col, pivot_row);
+        }
+
+        let (pivot_rows, rows_below) = rows.split_at_mut(pivot_col + 1);
+        let pivot_entries = &pivot_rows[pivot_col];
+        let pivot = &pivot_entries[pivot_col];
+        let (pivot_rhs_entries, rhs_below) = rhs.split_at_mut(pivot_col + 1);
+        let pivot_rhs = &pivot_rhs_entries[pivot_col];
+        for (row_entries, rhs_entry) in rows_below.iter_mut().zip(rhs_below) {
+            let factor = &row_entries[pivot_col] / pivot;
+            for (entry, pivot_entry) in row_entries
+                .iter_mut()
+                .zip(pivot_entries.iter())
+                .skip(pivot_col + 1)
+            {
+                *entry -= &factor * pivot_entry;
+            }
+            let rhs_update = &factor * pivot_rhs;
+            *rhs_entry -= rhs_update;
+            row_entries[pivot_col] = zero.clone();
+        }
+    }
+
+    let mut solution = std::array::from_fn(|_| zero.clone());
+    for row in (0..D).rev() {
+        let mut value = rhs[row].clone();
+        for (coefficient, component) in rows[row].iter().zip(solution.iter()).skip(row + 1) {
+            value -= coefficient * component;
+        }
+        solution[row] = value / &rows[row][row];
+    }
+    Some(solution)
+}
+
+fn determinant_sign(value: &BigRational) -> DeterminantSign {
+    let zero = BigRational::from_integer(BigInt::from(0));
+    match value.cmp(&zero) {
+        std::cmp::Ordering::Less => DeterminantSign::Negative,
+        std::cmp::Ordering::Equal => DeterminantSign::Zero,
+        std::cmp::Ordering::Greater => DeterminantSign::Positive,
+    }
+}
diff --git a/benches/exact.rs b/benches/exact.rs
index 2bc2335..22aaaf7 100644
--- a/benches/exact.rs
+++ b/benches/exact.rs
@@ -37,8 +37,6 @@ use std::hint::black_box;
 use criterion::BatchSize;
 use criterion::{BenchmarkGroup, Criterion, Throughput, measurement::WallTime};
 
-#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-use la_stack::{BigInt, BigRational, DeterminantSign, RationalMatrix, RationalVector};
 use la_stack::{Matrix, Vector};
 
 #[path = "common/bench_utils.rs"]
@@ -46,6 +44,15 @@ mod bench_utils;
 #[path = "common/exact.rs"]
 pub mod exact_bench;
 
+#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
+#[path = "common/rational.rs"]
+pub mod rational_bench;
+
+#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
+use rational_bench::{
+    RationalInputKind, rational_determinant_gaussian, rational_input, rational_solve_gaussian,
+};
+
 use bench_utils::OrAbort;
 use exact_bench::{
     ExactInput, RANDOM_INPUT_ARRAY_LEN, ValidatedExactInput, hilbert_input,
@@ -98,188 +105,35 @@ const CORPUS_AND_EXTREME_OPERATIONS: &[ExactOperation] = &[
     ExactOperation::SolveExactRoundedF64,
 ];
 
-/// Independently validated exact-input rational benchmark fixture.
-#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-#[must_use]
-struct ValidatedRationalInput<const D: usize> {
-    matrix: RationalMatrix<D>,
-    rhs: RationalVector<D>,
-}
-
-/// Deterministic, strictly diagonally-dominant exact-input rational fixture.
-#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-fn rational_input<const D: usize>() -> ValidatedRationalInput<D> {
-    let rows = std::array::from_fn(|row| {
-        std::array::from_fn(|col| {
-            if row == col {
-                let diagonal = 2 * D + row + 1;
-                BigRational::from_integer(BigInt::from(diagonal))
-            } else {
-                let raw_numerator = (row * 3 + col * 5) % 5;
-                let numerator = i64::try_from(raw_numerator).or_abort("rational numerator") - 2;
-                let denominator = (row + col) % 7 + 2;
-                BigRational::new(BigInt::from(numerator), BigInt::from(denominator))
-            }
-        })
-    });
-    let expected_solution = std::array::from_fn(|index| {
-        BigRational::new(BigInt::from(index + 1), BigInt::from(index + 2))
-    });
-    let rhs_data = rational_matvec(&rows, &expected_solution);
-    let matrix = RationalMatrix::try_from_rows(rows.clone())
-        .or_abort("rational benchmark matrix construction");
-    let rhs =
-        RationalVector::try_new(rhs_data.clone()).or_abort("rational benchmark RHS construction");
-
-    let reference_determinant = rational_determinant_gaussian(rows.clone());
-    assert_eq!(matrix.det(), reference_determinant);
-    assert_eq!(matrix.det_sign(), determinant_sign(&reference_determinant));
-    let reference_solution = rational_solve_gaussian(rows, rhs_data)
-        .or_abort("rational Gaussian benchmark validation solve");
-    assert_eq!(reference_solution, expected_solution);
-    assert_eq!(
-        matrix
-            .solve(&rhs)
-            .or_abort("row-cleared Bareiss benchmark validation solve")
-            .into_array(),
-        expected_solution
-    );
-
-    ValidatedRationalInput { matrix, rhs }
-}
-
-/// Exact rational matrix-vector multiplication used only to assemble and
-/// validate benchmark fixtures.
-#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-fn rational_matvec<const D: usize>(
-    rows: &[[BigRational; D]; D],
-    vector: &[BigRational; D],
-) -> [BigRational; D] {
-    std::array::from_fn(|row| {
-        rows[row]
-            .iter()
-            .zip(vector.iter())
-            .map(|(coefficient, component)| coefficient * component)
-            .sum()
-    })
-}
-
-/// Straightforward cubic rational Gaussian determinant reference.
-#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-fn rational_determinant_gaussian<const D: usize>(mut rows: [[BigRational; D]; D]) -> BigRational {
-    let zero = BigRational::from_integer(BigInt::from(0));
-    let mut determinant = BigRational::from_integer(BigInt::from(1));
-    let mut odd_swaps = false;
-
-    for pivot_col in 0..D {
-        let Some(pivot_row) = (pivot_col..D).find(|&row| rows[row][pivot_col] != zero) else {
-            return zero;
-        };
-        if pivot_row != pivot_col {
-            rows.swap(pivot_col, pivot_row);
-            odd_swaps = !odd_swaps;
-        }
-
-        let (pivot_rows, rows_below) = rows.split_at_mut(pivot_col + 1);
-        let pivot_entries = &pivot_rows[pivot_col];
-        let pivot = &pivot_entries[pivot_col];
-        determinant *= pivot;
-        for row_entries in rows_below {
-            let factor = &row_entries[pivot_col] / pivot;
-            for (entry, pivot_entry) in row_entries
-                .iter_mut()
-                .zip(pivot_entries.iter())
-                .skip(pivot_col + 1)
-            {
-                *entry -= &factor * pivot_entry;
-            }
-            row_entries[pivot_col] = zero.clone();
-        }
-    }
-
-    if odd_swaps { -determinant } else { determinant }
-}
-
-/// Straightforward cubic rational Gaussian solve reference.
-#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-fn rational_solve_gaussian<const D: usize>(
-    mut rows: [[BigRational; D]; D],
-    mut rhs: [BigRational; D],
-) -> Option<[BigRational; D]> {
-    let zero = BigRational::from_integer(BigInt::from(0));
-    for pivot_col in 0..D {
-        let pivot_row = (pivot_col..D).find(|&row| rows[row][pivot_col] != zero)?;
-        if pivot_row != pivot_col {
-            rows.swap(pivot_col, pivot_row);
-            rhs.swap(pivot_col, pivot_row);
-        }
-
-        let (pivot_rows, rows_below) = rows.split_at_mut(pivot_col + 1);
-        let pivot_entries = &pivot_rows[pivot_col];
-        let pivot = &pivot_entries[pivot_col];
-        let (pivot_rhs_entries, rhs_below) = rhs.split_at_mut(pivot_col + 1);
-        let pivot_rhs = &pivot_rhs_entries[pivot_col];
-        for (row_entries, rhs_entry) in rows_below.iter_mut().zip(rhs_below) {
-            let factor = &row_entries[pivot_col] / pivot;
-            for (entry, pivot_entry) in row_entries
-                .iter_mut()
-                .zip(pivot_entries.iter())
-                .skip(pivot_col + 1)
-            {
-                *entry -= &factor * pivot_entry;
-            }
-            let rhs_update = &factor * pivot_rhs;
-            *rhs_entry -= rhs_update;
-            row_entries[pivot_col] = zero.clone();
-        }
-    }
-
-    let mut solution = std::array::from_fn(|_| zero.clone());
-    for row in (0..D).rev() {
-        let mut value = rhs[row].clone();
-        for (coefficient, component) in rows[row].iter().zip(solution.iter()).skip(row + 1) {
-            value -= coefficient * component;
-        }
-        solution[row] = value / &rows[row][row];
-    }
-    Some(solution)
-}
-
-#[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-fn determinant_sign(value: &BigRational) -> DeterminantSign {
-    let zero = BigRational::from_integer(BigInt::from(0));
-    match value.cmp(&zero) {
-        std::cmp::Ordering::Less => DeterminantSign::Negative,
-        std::cmp::Ordering::Equal => DeterminantSign::Zero,
-        std::cmp::Ordering::Greater => DeterminantSign::Positive,
-    }
-}
-
 /// Compare exact-input row clearing and Bareiss elimination with direct
 /// `BigRational` Gaussian elimination.
 ///
 /// The consuming Gaussian references clone their inputs in Criterion's untimed
 /// setup phase, so both sides estimate computation over already-accepted input.
 #[cfg(not(any(la_stack_pre_rational_input_api, la_stack_v0_4_3_api)))]
-fn bench_rational_input<const D: usize>(criterion: &mut Criterion) {
-    let input = rational_input::<D>();
-    let mut group = criterion.benchmark_group(format!("rational_input_d{D}"));
+fn bench_rational_input<const D: usize>(criterion: &mut Criterion, kind: RationalInputKind) {
+    let input = rational_input::<D>(kind);
+    let group_name = match kind {
+        RationalInputKind::Small => format!("rational_input_d{D}"),
+        _ => format!("rational_input_{}_d{D}", kind.name()),
+    };
+    let mut group = criterion.benchmark_group(group_name);
 
     group.bench_function("det_sign_row_cleared_bareiss", |bencher| {
         bencher.iter(|| {
-            let sign = black_box(&input.matrix).det_sign();
+            let sign = black_box(input.matrix()).det_sign();
             let _ = black_box(sign);
         });
     });
     group.bench_function("det_row_cleared_bareiss", |bencher| {
         bencher.iter(|| {
-            let determinant = black_box(&input.matrix).det();
+            let determinant = black_box(input.matrix()).det();
             black_box(determinant);
         });
     });
     group.bench_function("det_big_rational_gaussian", |bencher| {
         bencher.iter_batched(
-            || black_box(input.matrix.as_rows()).clone(),
+            || black_box(input.matrix().as_rows()).clone(),
             |rows| {
                 let determinant = rational_determinant_gaussian(rows);
                 black_box(determinant);
@@ -289,8 +143,8 @@ fn bench_rational_input<const D: usize>(criterion: &mut Criterion) {
     });
     group.bench_function("solve_row_cleared_bareiss", |bencher| {
         bencher.iter(|| {
-            let solution = black_box(&input.matrix)
-                .solve(black_box(&input.rhs))
+            let solution = black_box(input.matrix())
+                .solve(black_box(input.rhs()))
                 .or_abort("row-cleared Bareiss rational benchmark solve");
             let _ = black_box(solution);
         });
@@ -299,8 +153,8 @@ fn bench_rational_input<const D: usize>(criterion: &mut Criterion) {
         bencher.iter_batched(
             || {
                 (
-                    black_box(input.matrix.as_rows()).clone(),
-                    black_box(input.rhs.as_array()).clone(),
+                    black_box(input.matrix().as_rows()).clone(),
+                    black_box(input.rhs().as_array()).clone(),
                 )
             },
             |(rows, rhs)| {
@@ -557,13 +411,15 @@ fn main() {
         // These compare the production row-cleared integer Bareiss backend with
         // straightforward BigRational Gaussian elimination on dimensions needed
         // by downstream geometric predicates and runtime-selected basis systems.
-        bench_rational_input::<2>(&mut c);
-        bench_rational_input::<3>(&mut c);
-        bench_rational_input::<4>(&mut c);
-        bench_rational_input::<5>(&mut c);
-        bench_rational_input::<6>(&mut c);
-        bench_rational_input::<7>(&mut c);
-        bench_rational_input::<8>(&mut c);
+        for kind in RationalInputKind::ALL {
+            bench_rational_input::<2>(&mut c, kind);
+            bench_rational_input::<3>(&mut c, kind);
+            bench_rational_input::<4>(&mut c, kind);
+            bench_rational_input::<5>(&mut c, kind);
+            bench_rational_input::<6>(&mut c, kind);
+            bench_rational_input::<7>(&mut c, kind);
+            bench_rational_input::<8>(&mut c, kind);
+        }
     }
 
     // === Adversarial / extreme-input groups ===
diff --git a/docs/BENCHMARKING.md b/docs/BENCHMARKING.md
index e80e586..69708de 100644
--- a/docs/BENCHMARKING.md
+++ b/docs/BENCHMARKING.md
@@ -525,8 +525,13 @@ random-corpus groups, and adversarial-input groups:
   calls using row-denominator clearing plus integer Bareiss elimination with
   straightforward cubic `BigRational` Gaussian determinant and solve
   references on identical matrices and right-hand sides \[7, 11-12\].
+- `rational_input_wide{256,1024}_d{2..8}` — diagnostic rational groups with
+  large positive rational row factors. These retain exact solutions and strict
+  diagonal dominance while exercising heap-backed numerator and denominator
+  storage. See the [row-clearing study](performance/rational-row-clearing.md)
+  for fixtures, allocation evidence, focused timing commands, and limitations.
 
-Each random-corpus and adversarial group runs the same exact-arithmetic
+The f64-input random-corpus and adversarial groups run the same exact-arithmetic
 benches (`det_sign_exact`, `det_exact`, `solve_exact`,
 `solve_exact_f64_result`, `solve_exact_rounded_f64`) so tables are comparable
 across input classes.
@@ -542,7 +547,10 @@ and first failing component. These checks run outside timed Criterion closures.
 Any disagreement or unexpected error fails setup instead of becoming an
 artificially fast measurement.
 
-The rational-input groups are part of the canonical exact release signal.
+The original `rational_input_d{2..8}` groups are part of the canonical exact
+release signal. The wide-component
+diagnostics remain local Criterion evidence and are not included in the release
+report's group registry.
 Releases produced with the rational-input harness include their Criterion point
 estimates and confidence intervals. When the comparison baseline predates the
 rational-input API, the report retains current-only rows with an explicit
@@ -570,8 +578,8 @@ being compared to the historical lossy `*_exact_f64` benchmark. Rows such as
 `det_exact_f64_result (vs det_exact_f64)` intentionally show the overhead of the
 new strict conversion contract against that same historical baseline.
 
-The default `release-signal` scope includes all exact-arithmetic groups because
-their inputs and execution order are fixed across revisions. Historical
+The default `release-signal` scope includes the canonical exact-arithmetic
+groups because their inputs and execution order are fixed across revisions. Historical
 baselines created before the `exact_random_corpus_d*` names were introduced do
 not have comparable full-corpus rows, so those rows appear once both sides of a
 comparison provide the stable group.
diff --git a/docs/assets/rational-row-clearing-allocations.csv b/docs/assets/rational-row-clearing-allocations.csv
new file mode 100644
index 0000000..770b967
--- /dev/null
+++ b/docs/assets/rational-row-clearing-allocations.csv
@@ -0,0 +1,190 @@
+family,dimension,operation,cloned_allocations,borrowed_allocations,cloned_bytes,borrowed_bytes
+small,2,det,0,0,0,0
+small,2,det_sign,0,0,0,0
+small,2,solve,0,0,0,0
+small,2,matrix_component_clones,0,0,0,0
+small,2,matrix_scaled_cloned,0,0,0,0
+small,2,matrix_scaled_borrowed,0,0,0,0
+small,2,augmented_component_clones,0,0,0,0
+small,2,augmented_scaled_cloned,0,0,0,0
+small,2,augmented_scaled_borrowed,0,0,0,0
+wide256,2,det,51,47,2376,2216
+wide256,2,det_sign,43,39,1896,1736
+wide256,2,solve,103,97,4952,4712
+wide256,2,matrix_component_clones,8,8,320,320
+wide256,2,matrix_scaled_cloned,16,16,672,672
+wide256,2,matrix_scaled_borrowed,12,12,512,512
+wide256,2,augmented_component_clones,12,12,480,480
+wide256,2,augmented_scaled_cloned,28,28,1184,1184
+wide256,2,augmented_scaled_borrowed,22,22,944,944
+wide1024,2,det,55,51,8136,7592
+wide1024,2,det_sign,43,39,6216,5672
+wide1024,2,solve,104,98,16592,15776
+wide1024,2,matrix_component_clones,8,8,1088,1088
+wide1024,2,matrix_scaled_cloned,16,16,2208,2208
+wide1024,2,matrix_scaled_borrowed,12,12,1664,1664
+wide1024,2,augmented_component_clones,12,12,1632,1632
+wide1024,2,augmented_scaled_cloned,28,28,3872,3872
+wide1024,2,augmented_scaled_borrowed,22,22,3056,3056
+small,3,det,0,0,0,0
+small,3,det_sign,0,0,0,0
+small,3,solve,0,0,0,0
+small,3,matrix_component_clones,0,0,0,0
+small,3,matrix_scaled_cloned,0,0,0,0
+small,3,matrix_scaled_borrowed,0,0,0,0
+small,3,augmented_component_clones,0,0,0,0
+small,3,augmented_scaled_cloned,0,0,0,0
+small,3,augmented_scaled_borrowed,0,0,0,0
+wide256,3,det,164,155,7864,7504
+wide256,3,det_sign,153,144,7032,6672
+wide256,3,solve,274,262,15064,14584
+wide256,3,matrix_component_clones,18,18,720,720
+wide256,3,matrix_scaled_cloned,54,54,2304,2304
+wide256,3,matrix_scaled_borrowed,45,45,1944,1944
+wide256,3,augmented_component_clones,24,24,960,960
+wide256,3,augmented_scaled_cloned,64,64,2720,2720
+wide256,3,augmented_scaled_borrowed,52,52,2240,2240
+wide1024,3,det,166,157,25872,24648
+wide1024,3,det_sign,153,144,22872,21648
+wide1024,3,solve,294,282,53912,52280
+wide1024,3,matrix_component_clones,18,18,2448,2448
+wide1024,3,matrix_scaled_cloned,54,54,7488,7488
+wide1024,3,matrix_scaled_borrowed,45,45,6264,6264
+wide1024,3,augmented_component_clones,24,24,3264,3264
+wide1024,3,augmented_scaled_cloned,64,64,8864,8864
+wide1024,3,augmented_scaled_borrowed,52,52,7232,7232
+small,4,det,0,0,0,0
+small,4,det_sign,0,0,0,0
+small,4,solve,5,5,80,80
+small,4,matrix_component_clones,0,0,0,0
+small,4,matrix_scaled_cloned,0,0,0,0
+small,4,matrix_scaled_borrowed,0,0,0,0
+small,4,augmented_component_clones,0,0,0,0
+small,4,augmented_scaled_cloned,0,0,0,0
+small,4,augmented_scaled_borrowed,0,0,0,0
+wide256,4,det,334,318,17592,16952
+wide256,4,det_sign,322,306,16384,15744
+wide256,4,solve,517,497,32976,32176
+wide256,4,matrix_component_clones,32,32,1280,1280
+wide256,4,matrix_scaled_cloned,96,96,4096,4096
+wide256,4,matrix_scaled_borrowed,80,80,3456,3456
+wide256,4,augmented_component_clones,40,40,1600,1600
+wide256,4,augmented_scaled_cloned,108,108,4592,4592
+wide256,4,augmented_scaled_borrowed,88,88,3792,3792
+wide1024,4,det,338,322,57624,55448
+wide1024,4,det_sign,322,306,53152,50976
+wide1024,4,solve,586,566,124696,121976
+wide1024,4,matrix_component_clones,32,32,4352,4352
+wide1024,4,matrix_scaled_cloned,96,96,13312,13312
+wide1024,4,matrix_scaled_borrowed,80,80,11136,11136
+wide1024,4,augmented_component_clones,40,40,5440,5440
+wide1024,4,augmented_scaled_cloned,108,108,14960,14960
+wide1024,4,augmented_scaled_borrowed,88,88,12240,12240
+small,5,det,2,2,32,32
+small,5,det_sign,2,2,32,32
+small,5,solve,17,17,272,272
+small,5,matrix_component_clones,0,0,0,0
+small,5,matrix_scaled_cloned,0,0,0,0
+small,5,matrix_scaled_borrowed,0,0,0,0
+small,5,augmented_component_clones,0,0,0,0
+small,5,augmented_scaled_cloned,0,0,0,0
+small,5,augmented_scaled_borrowed,0,0,0,0
+wide256,5,det,489,468,32416,31568
+wide256,5,det_sign,474,453,30704,29856
+wide256,5,solve,723,697,52768,51712
+wide256,5,matrix_component_clones,42,42,1696,1696
+wide256,5,matrix_scaled_cloned,126,126,5408,5408
+wide256,5,matrix_scaled_borrowed,105,105,4560,4560
+wide256,5,augmented_component_clones,52,52,2112,2112
+wide256,5,augmented_scaled_cloned,140,140,6032,6032
+wide256,5,augmented_scaled_borrowed,114,114,4976,4976
+wide1024,5,det,572,551,127272,124408
+wide1024,5,det_sign,555,534,121336,118472
+wide1024,5,solve,859,833,206416,202864
+wide1024,5,matrix_component_clones,42,42,5728,5728
+wide1024,5,matrix_scaled_cloned,126,126,17504,17504
+wide1024,5,matrix_scaled_borrowed,105,105,14640,14640
+wide1024,5,augmented_component_clones,52,52,7104,7104
+wide1024,5,augmented_scaled_cloned,140,140,19472,19472
+wide1024,5,augmented_scaled_borrowed,114,114,15920,15920
+small,6,det,24,24,384,384
+small,6,det_sign,24,24,384,384
+small,6,solve,78,78,1368,1368
+small,6,matrix_component_clones,0,0,0,0
+small,6,matrix_scaled_cloned,0,0,0,0
+small,6,matrix_scaled_borrowed,0,0,0,0
+small,6,augmented_component_clones,0,0,0,0
+small,6,augmented_scaled_cloned,0,0,0,0
+small,6,augmented_scaled_borrowed,0,0,0,0
+wide256,6,det,774,743,58192,56896
+wide256,6,det_sign,758,727,56016,54720
+wide256,6,solve,1124,1087,86984,85432
+wide256,6,matrix_component_clones,62,62,2592,2592
+wide256,6,matrix_scaled_cloned,187,187,8304,8304
+wide256,6,matrix_scaled_borrowed,156,156,7008,7008
+wide256,6,augmented_component_clones,74,74,3104,3104
+wide256,6,augmented_scaled_cloned,215,215,9584,9584
+wide256,6,augmented_scaled_borrowed,178,178,8032,8032
+wide1024,6,det,1022,991,260440,256168
+wide1024,6,det_sign,1002,971,252792,248520
+wide1024,6,solve,1521,1484,397856,392752
+wide1024,6,matrix_component_clones,62,62,8544,8544
+wide1024,6,matrix_scaled_cloned,187,187,26256,26256
+wide1024,6,matrix_scaled_borrowed,156,156,21984,21984
+wide1024,6,augmented_component_clones,74,74,10208,10208
+wide1024,6,augmented_scaled_cloned,215,215,30224,30224
+wide1024,6,augmented_scaled_borrowed,178,178,25120,25120
+small,7,det,72,72,1184,1184
+small,7,det_sign,70,70,1152,1152
+small,7,solve,254,254,5120,5120
+small,7,matrix_component_clones,0,0,0,0
+small,7,matrix_scaled_cloned,0,0,0,0
+small,7,matrix_scaled_borrowed,0,0,0,0
+small,7,augmented_component_clones,0,0,0,0
+small,7,augmented_scaled_cloned,0,0,0,0
+small,7,augmented_scaled_borrowed,0,0,0,0
+wide256,7,det,1149,1106,96504,94664
+wide256,7,det_sign,1132,1089,93768,91928
+wide256,7,solve,1631,1581,149976,147832
+wide256,7,matrix_component_clones,86,86,3680,3680
+wide256,7,matrix_scaled_cloned,260,260,11808,11808
+wide256,7,matrix_scaled_borrowed,217,217,9968,9968
+wide256,7,augmented_component_clones,100,100,4296,4296
+wide256,7,augmented_scaled_cloned,291,291,13304,13304
+wide256,7,augmented_scaled_borrowed,241,241,11160,11160
+wide1024,7,det,1764,1721,519136,513168
+wide1024,7,det_sign,1743,1700,509696,503728
+wide1024,7,solve,2563,2513,799792,792848
+wide1024,7,matrix_component_clones,86,86,11936,11936
+wide1024,7,matrix_scaled_cloned,260,260,36768,36768
+wide1024,7,matrix_scaled_borrowed,217,217,30800,30800
+wide1024,7,augmented_component_clones,100,100,13896,13896
+wide1024,7,augmented_scaled_cloned,291,291,41336,41336
+wide1024,7,augmented_scaled_borrowed,241,241,34392,34392
+small,8,det,141,141,2464,2464
+small,8,det_sign,139,139,2432,2432
+small,8,solve,461,461,10240,10240
+small,8,matrix_component_clones,0,0,0,0
+small,8,matrix_scaled_cloned,0,0,0,0
+small,8,matrix_scaled_borrowed,0,0,0,0
+small,8,augmented_component_clones,0,0,0,0
+small,8,augmented_scaled_cloned,0,0,0,0
+small,8,augmented_scaled_borrowed,0,0,0,0
+wide256,8,det,1644,1587,162992,160520
+wide256,8,det_sign,1626,1569,159640,157168
+wide256,8,solve,2226,2161,232192,229368
+wide256,8,matrix_component_clones,114,114,4952,4952
+wide256,8,matrix_scaled_cloned,345,345,15856,15856
+wide256,8,matrix_scaled_borrowed,288,288,13384,13384
+wide256,8,augmented_component_clones,130,130,5664,5664
+wide256,8,augmented_scaled_cloned,371,371,17144,17144
+wide256,8,augmented_scaled_borrowed,306,306,14320,14320
+wide1024,8,det,2959,2902,1039840,1031896
+wide1024,8,det_sign,2937,2880,1028424,1020480
+wide1024,8,solve,4203,4138,1561032,1551968
+wide1024,8,matrix_component_clones,114,114,15896,15896
+wide1024,8,matrix_scaled_cloned,345,345,48976,48976
+wide1024,8,matrix_scaled_borrowed,288,288,41032,41032
+wide1024,8,augmented_component_clones,130,130,18144,18144
+wide1024,8,augmented_scaled_cloned,371,371,52952,52952
+wide1024,8,augmented_scaled_borrowed,306,306,43888,43888
diff --git a/docs/assets/rational-row-clearing-timings.csv b/docs/assets/rational-row-clearing-timings.csv
new file mode 100644
index 0000000..5084feb
--- /dev/null
+++ b/docs/assets/rational-row-clearing-timings.csv
@@ -0,0 +1,66 @@
+run,family,dimension,operation,cloned_mean_ns,cloned_lower_95_ns,cloned_upper_95_ns,borrowed_mean_ns,borrowed_lower_95_ns,borrowed_upper_95_ns,change_pct
+initial,small,2,det_row_cleared_bareiss,253.57996602286676,251.96233109059892,255.04279379555084,240.09172332068007,239.68896652674255,240.497109951427,-5.31912789237079
+initial,small,2,det_sign_row_cleared_bareiss,148.14185815945484,147.6334757091275,148.65083771167528,142.18300290610006,141.4753237356683,142.9555694001452,-4.022398076673827
+initial,small,2,solve_row_cleared_bareiss,934.8261988000057,931.5700652199237,938.3629864625598,935.1289940035239,932.1982732004009,938.6304464889907,0.0323905346156117
+initial,small,3,det_row_cleared_bareiss,692.8203575919379,689.1890648032097,696.3196203901136,684.3753106575886,682.6786084312726,686.0754923596298,-1.2189374694043464
+initial,small,3,det_sign_row_cleared_bareiss,483.9731143083831,480.6555687245251,487.33367139791756,470.25877061014023,468.9244820488141,471.73477895412253,-2.8336994954443306
+initial,small,3,solve_row_cleared_bareiss,2428.1495869333858,2415.5923180930426,2440.6810646904914,2356.626156687433,2349.201778640446,2364.172751396604,-2.9455940701035077
+initial,small,4,det_row_cleared_bareiss,1421.6166379336328,1417.5998579343288,1425.6836793333596,1423.7600908964494,1421.2002068412194,1426.3283118111437,0.15077573697590552
+initial,small,4,det_sign_row_cleared_bareiss,1049.4218658115506,1042.1732456845484,1057.3132069056956,1033.9447768550845,1030.9407562154147,1037.4259512358142,-1.474820514102515
+initial,small,4,solve_row_cleared_bareiss,5240.309187965997,5222.235035716053,5260.991009197907,5239.541006748381,5219.774497195444,5260.018951147271,-0.014659081936996277
+initial,small,5,det_row_cleared_bareiss,2206.486054640564,2194.872216601879,2218.0293565014185,2136.3396833684014,2132.1194427147243,2140.4354701036186,-3.1790987812786886
+initial,small,5,det_sign_row_cleared_bareiss,1648.5518483486487,1646.14546041875,1650.902536307032,1638.659555086847,1635.7774740124396,1641.507365025709,-0.6000595778477225
+initial,small,5,solve_row_cleared_bareiss,9358.726122771854,9311.279654313166,9414.174220386622,9087.67277903307,9057.693035825745,9117.086275658014,-2.8962632326556825
+initial,small,6,det_row_cleared_bareiss,3742.6766210949822,3722.258597008504,3764.9707740236,3709.3586507024793,3702.95943450328,3716.227941921543,-0.8902177175744153
+initial,small,6,det_sign_row_cleared_bareiss,3096.8749833531574,3083.4692392212646,3110.7771110991725,3066.1203151986165,3060.230529540134,3072.2637455138793,-0.993087170772422
+initial,small,6,solve_row_cleared_bareiss,17921.256426024887,17837.570604368004,18018.398889566866,16845.38343614974,16764.349665624974,16935.64994028919,-6.003334611700472
+initial,small,7,det_row_cleared_bareiss,5984.321715079504,5976.7222336995965,5992.614175568864,6079.288623048817,6064.0040892789,6095.369331214466,1.5869285190669435
+initial,small,7,det_sign_row_cleared_bareiss,5137.968719307963,5130.350889156592,5146.419128014786,5179.314648764177,5158.480119822258,5202.670065907994,0.8047135300929487
+initial,small,7,solve_row_cleared_bareiss,28748.124722412427,28680.189422873147,28821.275748153945,28842.567433066582,28781.916352354525,28903.681667646855,0.32851781313070205
+initial,small,8,det_row_cleared_bareiss,9027.476654049626,8993.09945625195,9064.87673649973,9081.470098171674,9045.937224412008,9119.54735671373,0.5981011770086031
+initial,small,8,det_sign_row_cleared_bareiss,8294.164705598829,8259.575585194452,8330.68695396005,8334.572391224432,8314.869134246012,8353.771486188693,0.48718209801557055
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+initial,wide256,7,det_sign_row_cleared_bareiss,59848.71974345715,59740.22457442797,59960.21900966058,59271.00755393324,59118.60860265242,59431.173828763945,-0.9652874647950505
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+initial,wide256,8,det_row_cleared_bareiss,148409.984607296,147336.76823238845,149650.54109030575,145935.82405576986,145775.91488136782,146105.51459694983,-1.6671119251665978
+initial,wide256,8,det_sign_row_cleared_bareiss,104036.49845363051,103829.41331378683,104250.44637532049,103602.19807549684,103321.91316432835,103904.15791994733,-0.4174500147438587
+initial,wide256,8,solve_row_cleared_bareiss,285550.81273397425,284954.9646277508,286193.4876907683,291018.82417213346,289828.5814214202,292384.94267804286,1.914899623575339
+repeat,small,8,solve_row_cleared_bareiss,42048.84657584045,41926.943649787136,42174.46105046291,41833.37102734208,41617.73126706454,42060.07120394692,-0.5124410442739036
+repeat,wide256,2,det_row_cleared_bareiss,9571.799337584047,9524.037117801725,9619.550393113404,9698.927944880726,9621.179023807637,9781.197317790604,1.328157881428882
diff --git a/docs/performance/rational-row-clearing.md b/docs/performance/rational-row-clearing.md
new file mode 100644
index 0000000..e095b29
--- /dev/null
+++ b/docs/performance/rational-row-clearing.md
@@ -0,0 +1,214 @@
+# Rational row-clearing allocation study (#233)
+
+## Decision and scope
+
+The component borrowing proposed in #233 was already implemented in
+`a62e72a` (#219). This study isolates that change, supplies missing allocation
+evidence, and adds reproducible wide-component fixtures. It makes no further
+production-code or public-API change.
+
+The baseline is current source with only `integer_at_scale` replaced by the
+former positive-canonical cloning expression:
+
+```rust
+let denominator = value.denom().clone();
+let multiplier = scale / denominator;
+let numerator = value.numer().clone();
+numerator * multiplier
+```
+
+The comparison uses the existing production expression:
+
+```rust
+value.numer() * (scale / value.denom())
+```
+
+Both use canonical positive denominators and the same exactly divisible row
+scales. The GCD/LCM calculation, elimination, pivoting, reconstruction, and error
+contracts are identical. This is an isolated component-cloning experiment, not
+a comparison against the entire revision preceding #219 (which also changed
+denominator handling in the LCM calculation).
+
+## Fixtures and independent validation
+
+Every family covers D=2 through D=8:
+
+- `small`: the unchanged `rational_input_d{2..8}` diagonally-dominant fixture.
+- `wide256`: multiply row `r` by `(2^k + 1) / (2^(k+1) - 1)`, with
+  `k = 256 + 16r`.
+- `wide1024`: the same construction with `k = 1024 + 16r`.
+
+The positive row factors preserve strict diagonal dominance and existing zeros.
+Non-zero entries stress large canonical numerators and denominators; reduction
+can remove small factors. Right-hand sides are rebuilt exactly from the known
+solution `x[i] = (i+1)/(i+2)`. The shared private-field
+`ValidatedRationalInput` is constructed only after independent rational Gaussian
+determinant/sign and solve checks agree with the production results and known
+solution. Construction and validation run outside measured closures.
+
+These deterministic families isolate component size. They are not a random
+rational corpus or a survey of unrelated large coprime denominators, and they
+do not establish performance for all exact-input workloads.
+
+## Allocation evidence
+
+The [complete allocation CSV](../assets/rational-row-clearing-allocations.csv)
+retains total allocation counts and requested bytes for both implementations.
+`det`, `det_sign`, and `solve` rows measure complete public calls, including
+dropping their results. The remaining rows isolate component cloning and
+integer scaling, with matrix-only or augmented matrix/RHS row scales computed
+before measurement. Those scaling rows model the private expressions above;
+they are not public row-clearing APIs and exclude LCM construction.
+
+The small family allocates nothing for either component cloning or isolated
+scaling. The pinned num-bigint 0.4.8 supports inline single-digit storage, which
+these fixtures use, so counting `.clone()` calls would overstate their heap
+cost. Larger small-family public calls still allocate during arithmetic.
+
+For both wide families, borrowing saves the following allocations per public
+call. The public-call differences exactly match the isolated scaling
+differences, separating component copies from the remaining arithmetic cost.
+
+| D | Saved per determinant/sign | Saved per solve |
+|---|----------------------------|-----------------|
+| 2 | 4 | 6 |
+| 3 | 9 | 12 |
+| 4 | 16 | 20 |
+| 5 | 21 | 26 |
+| 6 | 31 | 37 |
+| 7 | 43 | 50 |
+| 8 | 57 | 65 |
+
+The net saving is smaller than the two explicit component clones per non-zero
+wide entry: changing multiplication operand ownership also changes its storage
+reuse. The measured difference, rather than a source-level clone count, is the
+relevant result. At D=8, for example, wide1024 determinant allocations decrease
+from 2,959 to 2,902, while solve allocations decrease from 4,203 to 4,138. Most
+allocation traffic remains in exact arithmetic.
+
+The allocation-counter 0.8.1 dependency is used only by the separate
+`rational_allocations` test executable. It does not replace the allocator in
+Criterion timing executables or the library. Each measured closure is checked
+three times for identical counts and zero retained allocations/bytes. Counts
+are observations for the pinned dependencies and platform, not public API
+guarantees or fixed cross-version test expectations.
+
+## Timing evidence
+
+The [complete timing CSV](../assets/rational-row-clearing-timings.csv) retains
+all 63 initial comparisons and two repeats, including Criterion mean estimates
+and their marginal 95% confidence intervals in nanoseconds. Percentage change
+is `100 × (borrowed mean / cloned mean - 1)`; negative values mean less time.
+
+| Family | Cases | Median change | Minimum | Maximum |
+|--------|-------|---------------|---------|---------|
+| small | 21 | -0.89% | -6.00% | +3.60% |
+| wide256 | 21 | -1.05% | -7.00% | +3.35% |
+| wide1024 | 21 | -0.36% | -2.97% | +1.01% |
+
+These are descriptive summaries of per-case mean ratios, not a pooled workload
+speedup or a paired confidence interval for the implementation change. Small
+movements on a working desktop can reflect run conditions. The two cases whose
+initial means increased by more than 2% were repeated in reverse implementation
+order (borrowed, then cloned), with identical Criterion settings:
+
+| Case | Initial change | Repeat change |
+|------|----------------|---------------|
+| small D=8 solve | +3.60% | -0.51% |
+| wide256 D=2 determinant | +3.35% | +1.33% |
+
+The initial slowdown magnitudes did not persist. This does not prove identical
+timing, but supplies no stable material regression supporting a production
+change. The allocation reduction is repeatable, while the overall timing
+benefit is modest and workload-dependent. Retain the existing borrowed
+expression; these results do not justify another row-clearing ownership design
+or a general speedup claim.
+
+## Reproduction
+
+Record allocation evidence with:
+
+```bash
+cargo test --locked --release --features bench,exact \
+  --test rational_allocations -- --nocapture --test-threads=1
+```
+
+Each `allocation,...` record contains family, dimension, operation, allocation
+count, and requested bytes. The isolated cloned and borrowed rows are available
+in the same run. For complete public-call comparisons, run once with the
+baseline expression above and once with the existing borrowed expression.
+
+Record focused timings with the counting executable stopped:
+
+```bash
+CRITERION_HOME=target/criterion-issue-233 \
+  cargo bench --locked --features bench,exact --bench exact -- \
+  'rational_input.*/(det_sign|det|solve)_row_cleared_bareiss' \
+  --sample-size 30 --warm-up-time 1 --measurement-time 2 --noplot \
+  --save-baseline issue233-cloned
+```
+
+Repeat the identical command with the borrowed expression and baseline name
+`issue233-borrowed`. Only the expression and output baseline name change.
+`bencher.iter` measures each complete public operation; fixture creation and
+oracle validation remain outside timing. The Gaussian reference timings are
+excluded from this focused comparison. The separate Criterion directory avoids
+overwriting release measurements.
+
+For the two focused repeats, use the filter below with the same settings and
+baseline names `issue233-borrowed-repeat` and `issue233-cloned-repeat`, in that
+order:
+
+```text
+^(rational_input_d8/solve_row_cleared_bareiss|rational_input_wide256_d2/det_row_cleared_bareiss)$
+```
+
+## Environment
+
+The study ran on 2026-09-05 UTC (2026-09-04 PDT), starting from
+`25aa4c02beda16c5efa66f23d1ebfb8b54532ab1`, with the shared harness and allocation
+probe in this patch. Hardware was an Apple M4 Max MacBook Pro, 16 CPU cores
+(12 performance, 4 efficiency), 64 GB memory, running macOS 26.6.2 (25G83).
+Rust was 1.98.0 (`88d9e12ae`, LLVM 22.1.8), targeting aarch64-apple-darwin.
+Cargo's release profile used fat LTO and one codegen unit; no custom Rust flags
+or target override were set. Criterion was 0.8.2, num-bigint 0.4.8, and
+num-rational 0.4.2. Timing runs were sequential, without concurrent builds or
+tests; the desktop environment was not otherwise isolated.
+
+SHA-256 identities of the measured source and executables:
+
+```text
+Cargo.toml
+353e511917fbde3e73f6a10bdd05ca4a6a44cf94a91995689868a1a9714913db
+Cargo.lock
+f07e3a6a4366712f5a96d1b806e5c1562542e9af2087b58b00b800d8f02080ee
+benches/exact.rs
+8302e233df39f4ed5931afd94f5e774f30e7224912619bc7e426b4624f9c3c70
+benches/common/rational.rs
+fb835a8c859f48d16f612165ff5ab18ca5313b968c36dcc0f8399109ca6c548c
+tests/rational_allocations.rs
+6bb87fd3b7e90ed3c42a7ebf0354d88f2f76d2b232314a85cc53aafd1d867239
+src/rational.rs (cloned experiment)
+af0aeb30059a61922b1ef78662a9ad45e12447f6eedf40fa8f84ea25dedff93c
+src/rational.rs (existing borrowed implementation)
+c707a22ab9abae32d92a9a781563ddfd22d9ec6b2cba77666c0bc7c85160df2d
+exact benchmark executable (cloned experiment)
+59b6f1bd13398276c57a744450e42b22be95163958c4fe89e6860ada45b0bb51
+exact benchmark executable (borrowed implementation)
+41f7337ba4ee2245d226901b690a13f7401fd2b40159fb2b40ff8527fcebccfd
+```
+
+## Validation
+
+- `just test-exact`: 753 tests passed, both before the experiment and on the
+  restored production implementation.
+- The standalone allocation command: 10 tests passed for each implementation;
+  the final borrowed run reproduced all 189 recorded allocation rows exactly.
+- Focused Criterion runs: 63 cases per implementation, plus the two reverse-order
+  repeats. All measured fixtures passed their independent checks.
+- `just ci`: passed, including 824 Rust tests, 612 Python tests, default and
+  exact-feature doctests, static checks, example execution, and benchmark
+  compilation.
+- Both CSVs were checked for complete row counts, valid timing intervals and
+  ratios, and equality between public-call allocation reductions and the
+  isolated scaling reductions. The production `src/` tree has no final diff.
diff --git a/justfile b/justfile
index 679e5e1..95838df 100644
--- a/justfile
+++ b/justfile
@@ -26,7 +26,7 @@ clippy_sarif_version := "0.8.0"
 dprint_version := "0.57.1"
 git_cliff_version := "2.14.1"
 just_version := "1.58.0"
-rumdl_version := "0.2.64"
+rumdl_version := "0.2.65"
 sarif_fmt_version := "0.8.0"
 taplo_version := "0.10.0"
 typos_version := "1.50.1"
diff --git a/pyproject.toml b/pyproject.toml
index aa5295f..fee3c26 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -155,7 +155,7 @@ dev = [
     "actionlint-py==1.7.12.24",
     "pytest==9.1.1",
     "ruff==0.16.6",
-    "semgrep==1.176.0",
+    "semgrep==1.176.1",
     "shellcheck-py==0.11.0.1",
     "shfmt-py==4.1.0",
     "ty==0.0.78",
diff --git a/tests/rational_allocations.rs b/tests/rational_allocations.rs
new file mode 100644
index 0000000..df57291
--- /dev/null
+++ b/tests/rational_allocations.rs
@@ -0,0 +1,138 @@
+//! Allocation evidence for canonical rational row clearing (issue #233).
+//!
+//! The counting allocator is linked only into this test executable; Criterion
+//! timing executables retain their normal allocator. All fixture construction,
+//! row scales, and exact oracle checks precede the measured closures.
+
+#![cfg(all(feature = "bench", feature = "exact"))]
+#![forbid(unsafe_code)]
+
+#[path = "../benches/common/bench_utils.rs"]
+mod bench_utils;
+#[path = "../benches/common/rational.rs"]
+pub mod rational_bench;
+
+use std::{array::from_fn, hint::black_box};
+
+use allocation_counter::{AllocationInfo, measure};
+use la_stack::{BigInt, BigRational};
+use pastey::paste;
+use rational_bench::{RationalInputKind, rational_input};
+
+/// Reproduce the positive-canonical branch before a62e72a removed its clones.
+fn scaled_cloned(value: &BigRational, scale: &BigInt) -> BigInt {
+    let denominator = value.denom().clone();
+    let multiplier = scale / denominator;
+    let numerator = value.numer().clone();
+    numerator * multiplier
+}
+
+/// Model the expression used by the private production `integer_at_scale`.
+fn scaled_borrowed(value: &BigRational, scale: &BigInt) -> BigInt {
+    value.numer() * (scale / value.denom())
+}
+
+/// Compute LCM via rational reduction, independently of production's GCD loop.
+fn row_scale<'a>(values: impl Iterator<Item = &'a BigRational>) -> BigInt {
+    values.fold(BigInt::from(1), |scale, value| {
+        let reduced = BigRational::new(scale, value.denom().clone());
+        reduced.numer() * value.denom()
+    })
+}
+
+fn record<const D: usize>(kind: RationalInputKind, operation: &str, run: impl Fn()) {
+    let counts = measure(&run);
+    // Counts must be repeatable, and each complete call drops its outputs.
+    assert_eq!(counts.count_current, 0);
+    assert_eq!(counts.bytes_current, 0);
+    for _ in 0..2 {
+        assert_eq!(measure(&run), counts);
+    }
+    let AllocationInfo {
+        count_total,
+        bytes_total,
+        ..
+    } = counts;
+    println!(
+        "allocation,{},{D},{operation},{count_total},{bytes_total}",
+        kind.name()
+    );
+}
+
+fn rational_allocation_evidence<const D: usize>() {
+    for kind in RationalInputKind::ALL {
+        let input = rational_input::<D>(kind);
+        let matrix = input.matrix();
+        let rhs = input.rhs();
+        record::<D>(kind, "det", || {
+            black_box(black_box(matrix).det());
+        });
+        record::<D>(kind, "det_sign", || {
+            let _ = black_box(black_box(matrix).det_sign());
+        });
+        record::<D>(kind, "solve", || {
+            let _ = black_box(black_box(matrix).solve(black_box(rhs)).unwrap());
+        });
+
+        for augmented in [false, true] {
+            let values_in_row = |row: usize| {
+                matrix.as_rows()[row]
+                    .iter()
+                    .chain(augmented.then_some(&rhs.as_array()[row]))
+            };
+            let scales: [BigInt; D] = from_fn(|row| row_scale(values_in_row(row)));
+            let entries: Vec<_> = scales
+                .iter()
+                .enumerate()
+                .flat_map(|(row, scale)| values_in_row(row).map(move |value| (value, scale)))
+                .collect();
+            for &(value, scale) in &entries {
+                let expected = value * BigRational::from_integer(scale.clone());
+                assert_eq!(
+                    BigRational::from_integer(scaled_cloned(value, scale)),
+                    expected
+                );
+                assert_eq!(
+                    BigRational::from_integer(scaled_borrowed(value, scale)),
+                    expected
+                );
+            }
+
+            let prefix = if augmented { "augmented" } else { "matrix" };
+            record::<D>(kind, &format!("{prefix}_component_clones"), || {
+                for &(value, _) in black_box(&entries) {
+                    black_box((value.numer().clone(), value.denom().clone()));
+                }
+            });
+            record::<D>(kind, &format!("{prefix}_scaled_cloned"), || {
+                for &(value, scale) in black_box(&entries) {
+                    black_box(scaled_cloned(value, scale));
+                }
+            });
+            record::<D>(kind, &format!("{prefix}_scaled_borrowed"), || {
+                for &(value, scale) in black_box(&entries) {
+                    black_box(scaled_borrowed(value, scale));
+                }
+            });
+        }
+    }
+}
+
+macro_rules! gen_rational_allocation_tests {
+    ($d:literal) => {
+        paste! {
+            #[test]
+            fn [<rational_allocation_evidence_ $d d>]() {
+                rational_allocation_evidence::<$d>();
+            }
+        }
+    };
+}
+
+gen_rational_allocation_tests!(2);
+gen_rational_allocation_tests!(3);
+gen_rational_allocation_tests!(4);
+gen_rational_allocation_tests!(5);
+gen_rational_allocation_tests!(6);
+gen_rational_allocation_tests!(7);
+gen_rational_allocation_tests!(8);
diff --git a/uv.lock b/uv.lock
index 09bd9e8..d4efedb 100644
--- a/uv.lock
+++ b/uv.lock
@@ -476,7 +476,7 @@ dev = [
     { name = "actionlint-py", specifier = "==1.7.12.24" },
     { name = "pytest", specifier = "==9.1.1" },
     { name = "ruff", specifier = "==0.16.6" },
-    { name = "semgrep", specifier = "==1.176.0" },
+    { name = "semgrep", specifier = "==1.176.1" },
     { name = "shellcheck-py", specifier = "==0.11.0.1" },
     { name = "shfmt-py", specifier = "==4.1.0" },
     { name = "ty", specifier = "==0.0.78" },
@@ -1057,7 +1057,7 @@ wheels = [
 
 [[package]]
 name = "semgrep"
-version = "1.176.0"
+version = "1.176.1"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
     { name = "attrs" },
@@ -1088,15 +1088,15 @@ dependencies = [
     { name = "urllib3" },
     { name = "wcmatch" },
 ]
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 ]
 
 [[package]]