diff --git a/crates/float/abi/DecimalFloat.json b/crates/float/abi/DecimalFloat.json
index 8b5f5b7..07a746e 100644
--- a/crates/float/abi/DecimalFloat.json
+++ b/crates/float/abi/DecimalFloat.json
@@ -74,6 +74,25 @@
       ],
       "stateMutability": "pure"
     },
+    {
+      "type": "function",
+      "name": "canonicalize",
+      "inputs": [
+        {
+          "name": "a",
+          "type": "bytes32",
+          "internalType": "Float"
+        }
+      ],
+      "outputs": [
+        {
+          "name": "",
+          "type": "bytes32",
+          "internalType": "Float"
+        }
+      ],
+      "stateMutability": "pure"
+    },
     {
       "type": "function",
       "name": "ceil",
@@ -1102,9 +1121,9 @@
     }
   ],
   "bytecode": {
-    "object": 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   }
 }
\ No newline at end of file
diff --git a/crates/float/src/js_api.rs b/crates/float/src/js_api.rs
index 68c47a0..eb61e64 100644
--- a/crates/float/src/js_api.rs
+++ b/crates/float/src/js_api.rs
@@ -752,6 +752,31 @@ impl Float {
         self.abs()
     }
 
+    /// Returns the canonical representative of the float's numeric value.
+    ///
+    /// Floats are non-canonical by design: multiple representations encode the
+    /// same number. `canonicalize` returns the single representative whose
+    /// magnitude is maximised within the type bounds, so two Floats are
+    /// numerically equal iff their canonical forms are byte-equal. Intended for
+    /// raw-byte equality use cases (map keys, hashing, set membership).
+    ///
+    /// # Returns
+    ///
+    /// * `Ok(Float)` - The canonical form.
+    /// * `Err(FloatError)` - If the operation fails.
+    ///
+    /// # Example
+    ///
+    /// ```typescript
+    /// const a = Float.parse("5").value!;
+    /// const b = Float.parse("5.0").value!;
+    /// assert(a.canonicalize().value.asHex() === b.canonicalize().value.asHex());
+    /// ```
+    #[wasm_export(js_name = "canonicalize", preserve_js_class)]
+    pub fn canonicalize_js(&self) -> Result<Float, FloatError> {
+        self.canonicalize()
+    }
+
     /// Adds two floats.
     ///
     /// # Returns
diff --git a/crates/float/src/lib.rs b/crates/float/src/lib.rs
index 994b8fd..d70b0d8 100644
--- a/crates/float/src/lib.rs
+++ b/crates/float/src/lib.rs
@@ -848,6 +848,41 @@ impl Float {
         })
     }
 
+    /// Returns the canonical representative of the float's numeric value.
+    ///
+    /// Floats are non-canonical by design: multiple `(coefficient, exponent)`
+    /// pairs encode the same number. `canonicalize` returns the single
+    /// representative whose magnitude is maximised within the type bounds, so
+    /// two Floats are numerically equal iff their canonical forms are
+    /// byte-equal. Intended for raw-byte equality use cases (map keys, hashing,
+    /// set membership, content-addressed storage).
+    ///
+    /// # Returns
+    ///
+    /// * `Ok(Float)` - The canonical form.
+    /// * `Err(FloatError)` - If the operation fails.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rain_math_float::Float;
+    ///
+    /// let a = Float::parse("5".to_string())?;
+    /// let b = Float::parse("5.0".to_string())?;
+    /// assert_eq!(a.canonicalize()?.as_hex(), b.canonicalize()?.as_hex());
+    ///
+    /// anyhow::Ok(())
+    /// ```
+    pub fn canonicalize(self) -> Result<Float, FloatError> {
+        let Float(a) = self;
+        let calldata = DecimalFloat::canonicalizeCall { a }.abi_encode();
+
+        execute_call(Bytes::from(calldata), |output| {
+            let decoded = DecimalFloat::canonicalizeCall::abi_decode_returns(output.as_ref())?;
+            Ok(Float(decoded))
+        })
+    }
+
     /// Returns `true` if `self` is less than or equal to `b`.
     ///
     /// # Arguments
diff --git a/src/concrete/DecimalFloat.sol b/src/concrete/DecimalFloat.sol
index 516762e..0f843ae 100644
--- a/src/concrete/DecimalFloat.sol
+++ b/src/concrete/DecimalFloat.sol
@@ -282,6 +282,13 @@ contract DecimalFloat {
         return a.isZero();
     }
 
+    /// Exposes `LibDecimalFloat.canonicalize` for offchain use.
+    /// @param a The float to canonicalize.
+    /// @return The canonical representative of the float's numeric value.
+    function canonicalize(Float a) external pure returns (Float) {
+        return a.canonicalize();
+    }
+
     /// Exposes `LibDecimalFloat.fromFixedDecimalLosslessPacked` for offchain
     /// use.
     /// @param value The fixed point decimal value to convert.
diff --git a/src/lib/LibDecimalFloat.sol b/src/lib/LibDecimalFloat.sol
index d06a9af..b9c4ad2 100644
--- a/src/lib/LibDecimalFloat.sol
+++ b/src/lib/LibDecimalFloat.sol
@@ -426,6 +426,46 @@ library LibDecimalFloat {
         }
     }
 
+    /// Canonicalize a Float to a unique byte representation per numeric value.
+    /// Floats are non-canonical by design (see the docstring on the `Float`
+    /// type): multiple `(coefficient, exponent)` pairs encode the same number
+    /// and equality is numeric (`eq`) rather than byte-level. This function
+    /// returns the single representative whose magnitude-maximised packing is
+    /// stable, so two Floats are numerically equal iff their canonical forms
+    /// are byte-equal (`Float.unwrap(a.canonicalize()) == Float.unwrap(b.canonicalize())`).
+    /// Intended for consumers that need raw-byte equality: `mapping(Float => X)`
+    /// keys, hashing, set membership, content-addressed storage.
+    ///
+    /// The chosen representative has the largest `|coefficient|` that fits
+    /// int224 subject to the exponent staying `>= type(int32).min`, reached by
+    /// scaling the coefficient up by ten directly within those bounds. This
+    /// never reverts for any valid input Float: scaling simply stops at the
+    /// limit. `canonicalize` is idempotent and value-preserving (the result is
+    /// `eq` to the input).
+    /// @param float The float to canonicalize.
+    /// @return The canonical representative of the float's numeric value.
+    function canonicalize(Float float) internal pure returns (Float) {
+        (int256 signedCoefficient, int256 exponent) = float.unpack();
+        if (signedCoefficient == 0) {
+            return FLOAT_ZERO;
+        }
+        unchecked {
+            while (exponent > type(int32).min) {
+                int256 trySignedCoefficient = signedCoefficient * 10;
+                // int224 overflow is the termination condition for the scaling
+                // loop, not a bug. The cast back is compared against the
+                // pre-cast value to detect that overflow.
+                // forge-lint: disable-next-line(unsafe-typecast)
+                if (int224(trySignedCoefficient) != trySignedCoefficient) {
+                    break;
+                }
+                signedCoefficient = trySignedCoefficient;
+                exponent -= 1;
+            }
+        }
+        return packLossless(signedCoefficient, exponent);
+    }
+
     /// Same as add, but accepts a Float struct instead of separate values.
     /// Costs more gas but helps mitigate stack depth issues, and is more
     /// ergonomic for the caller.
diff --git a/src/lib/deploy/LibDecimalFloatDeploy.sol b/src/lib/deploy/LibDecimalFloatDeploy.sol
index dd0f8bd..1ede21e 100644
--- a/src/lib/deploy/LibDecimalFloatDeploy.sol
+++ b/src/lib/deploy/LibDecimalFloatDeploy.sol
@@ -25,11 +25,11 @@ library LibDecimalFloatDeploy {
     /// @dev Address of the DecimalFloat contract deployed via Zoltu's
     /// deterministic deployment proxy.
     /// This address is the same across all EVM-compatible networks.
-    address constant ZOLTU_DEPLOYED_DECIMAL_FLOAT_ADDRESS = address(0xBee0eEFaffD046c9602109eB30A858Be301CC926);
+    address constant ZOLTU_DEPLOYED_DECIMAL_FLOAT_ADDRESS = address(0x6b7C246F02E67299b5801f8215d7f40abD82056d);
 
     /// @dev The expected codehash of the DecimalFloat contract deployed via
     /// Zoltu's deterministic deployment proxy.
-    bytes32 constant DECIMAL_FLOAT_CONTRACT_HASH = 0x7a93d0311f7782b44157ba40e94ec936085ebe001c7893bdd74911c8351d3def;
+    bytes32 constant DECIMAL_FLOAT_CONTRACT_HASH = 0x61bbc303586dc1b233644acdebe38dcc757907d7b39edcf6b1152c2081cf3197;
 
     /// Combines all log and anti-log tables into a single bytes array for
     /// deployment. These are using packed encoding to minimize size and remove
diff --git a/test/src/concrete/DecimalFloat.canonicalize.t.sol b/test/src/concrete/DecimalFloat.canonicalize.t.sol
new file mode 100644
index 0000000..3f59b7d
--- /dev/null
+++ b/test/src/concrete/DecimalFloat.canonicalize.t.sol
@@ -0,0 +1,31 @@
+// SPDX-License-Identifier: LicenseRef-DCL-1.0
+// SPDX-FileCopyrightText: Copyright (c) 2020 Rain Open Source Software Ltd
+pragma solidity =0.8.25;
+
+import {LibDecimalFloat, Float} from "src/lib/LibDecimalFloat.sol";
+import {LogTest} from "test/abstract/LogTest.sol";
+import {DecimalFloat} from "src/concrete/DecimalFloat.sol";
+
+contract DecimalFloatCanonicalizeTest is LogTest {
+    using LibDecimalFloat for Float;
+
+    function canonicalizeExternal(Float a) external pure returns (Float) {
+        return a.canonicalize();
+    }
+
+    /// The `canonicalize` method exposed on the deployed concrete contract must
+    /// match the library result for any input (and revert identically if the
+    /// library reverts).
+    function testCanonicalizeDeployed(Float a) external {
+        DecimalFloat deployed = new DecimalFloat();
+
+        try this.canonicalizeExternal(a) returns (Float b) {
+            Float deployedB = deployed.canonicalize(a);
+
+            assertEq(Float.unwrap(b), Float.unwrap(deployedB));
+        } catch (bytes memory err) {
+            vm.expectRevert(err);
+            deployed.canonicalize(a);
+        }
+    }
+}
diff --git a/test/src/lib/LibDecimalFloat.canonicalize.t.sol b/test/src/lib/LibDecimalFloat.canonicalize.t.sol
new file mode 100644
index 0000000..02f0603
--- /dev/null
+++ b/test/src/lib/LibDecimalFloat.canonicalize.t.sol
@@ -0,0 +1,301 @@
+// SPDX-License-Identifier: LicenseRef-DCL-1.0
+// SPDX-FileCopyrightText: Copyright (c) 2020 Rain Open Source Software Ltd
+pragma solidity =0.8.25;
+
+import {LibDecimalFloat, Float} from "src/lib/LibDecimalFloat.sol";
+
+import {Test} from "forge-std-1.16.1/src/Test.sol";
+
+contract LibDecimalFloatCanonicalizeTest is Test {
+    using LibDecimalFloat for Float;
+
+    int224 constant INT224_MAX = type(int224).max;
+    int224 constant INT224_MIN = type(int224).min;
+    int32 constant INT32_MIN = type(int32).min;
+
+    function canonicalizeExternal(Float float) external pure returns (Float) {
+        return float.canonicalize();
+    }
+
+    /// Zero at any exponent canonicalizes to FLOAT_ZERO.
+    function testCanonicalizeZero(int32 exponent) external pure {
+        Float zero = LibDecimalFloat.packLossless(0, exponent);
+        Float canonical = zero.canonicalize();
+        assertEq(Float.unwrap(canonical), Float.unwrap(LibDecimalFloat.FLOAT_ZERO), "zero canonicalizes to FLOAT_ZERO");
+    }
+
+    /// Several different byte representations of the same positive value all
+    /// canonicalize to the same bytes32.
+    function testCanonicalizeEqualValuesByteEqual() external pure {
+        bytes32 expected = Float.unwrap(LibDecimalFloat.packLossless(5, 0).canonicalize());
+        assertEq(Float.unwrap(LibDecimalFloat.packLossless(50, -1).canonicalize()), expected, "50e-1");
+        assertEq(Float.unwrap(LibDecimalFloat.packLossless(5000, -3).canonicalize()), expected, "5000e-3");
+        assertEq(Float.unwrap(LibDecimalFloat.packLossless(5e10, -10).canonicalize()), expected, "5e10 e-10");
+    }
+
+    /// Same as above for a negative value.
+    function testCanonicalizeNegativeEqualValuesByteEqual() external pure {
+        bytes32 expected = Float.unwrap(LibDecimalFloat.packLossless(-5, 0).canonicalize());
+        assertEq(Float.unwrap(LibDecimalFloat.packLossless(-50, -1).canonicalize()), expected, "-50e-1");
+        assertEq(Float.unwrap(LibDecimalFloat.packLossless(-5000, -3).canonicalize()), expected, "-5000e-3");
+        assertEq(Float.unwrap(LibDecimalFloat.packLossless(-5e10, -10).canonicalize()), expected, "-5e10 e-10");
+    }
+
+    /// canonicalize preserves the numeric value.
+    function testCanonicalizeValuePreserving() external pure {
+        Float f = LibDecimalFloat.packLossless(1234567890, -3);
+        assertTrue(f.eq(f.canonicalize()), "value preserved");
+    }
+
+    /// canonicalize is idempotent for a concrete value.
+    function testCanonicalizeIdempotent() external pure {
+        Float f = LibDecimalFloat.packLossless(42, 7);
+        Float once = f.canonicalize();
+        Float twice = once.canonicalize();
+        assertEq(Float.unwrap(once), Float.unwrap(twice), "idempotent");
+    }
+
+    /// Fuzz: canonicalize preserves the numeric value for any valid Float.
+    function testCanonicalizeValuePreservingFuzz(int224 signedCoefficient, int32 exponent) external pure {
+        Float f = LibDecimalFloat.packLossless(signedCoefficient, exponent);
+        Float canonical = f.canonicalize();
+        assertTrue(f.eq(canonical), "value preserved");
+    }
+
+    /// Fuzz: canonicalize is idempotent for any valid Float.
+    function testCanonicalizeIdempotentFuzz(int224 signedCoefficient, int32 exponent) external pure {
+        Float f = LibDecimalFloat.packLossless(signedCoefficient, exponent);
+        Float once = f.canonicalize();
+        Float twice = once.canonicalize();
+        assertEq(Float.unwrap(once), Float.unwrap(twice), "idempotent");
+    }
+
+    /// Fuzz: two Floats that are numerically equal (same coefficient shifted by
+    /// a power of ten) are byte-equal after canonicalize.
+    function testCanonicalizeEqImpliesByteEqualFuzz(int128 signedCoefficient, uint8 shift) external pure {
+        // Avoid the degenerate all-zero case where the shift is irrelevant; it
+        // is covered separately by testCanonicalizeZero.
+        vm.assume(signedCoefficient != 0);
+
+        // Base representation.
+        Float a = LibDecimalFloat.packLossless(signedCoefficient, 0);
+
+        // Shifted representation of the same value: multiply the coefficient by
+        // 10^shift and lower the exponent by the same amount. int128 * 10^255
+        // cannot overflow int256, so packLossless is safe here (it tolerates a
+        // coefficient that does not fit int224 only via packLossy, but for
+        // shift large enough to exceed int224 we would need packLossy; keep the
+        // shift bounded so the shifted coefficient still fits int224).
+        uint256 boundedShift = shift % 19;
+        int256 shiftedCoefficient = int256(signedCoefficient) * int256(10 ** boundedShift);
+        Float b = LibDecimalFloat.packLossless(shiftedCoefficient, -int256(boundedShift));
+
+        // Same numeric value.
+        assertTrue(a.eq(b), "same value precondition");
+
+        // Byte-equal after canonicalize.
+        assertEq(
+            Float.unwrap(a.canonicalize()), Float.unwrap(b.canonicalize()), "eq implies byte-equal after canonicalize"
+        );
+    }
+
+    // ---------------------------------------------------------------------
+    // Adversarial coverage that deliberately leaves the int128/uint8 "easy
+    // middle" the tests above stay inside. These target the int224 and int32
+    // type boundaries and, crucially, assert the SAFETY property the tests
+    // above never check: numerically DISTINCT Floats must canonicalize to
+    // byte-UNEQUAL results (no collision). They also pin the exponent to the
+    // int32.min floor where the scaling loop is capped before the coefficient
+    // is maximised, and the int224.min/int224.max coefficient boundaries.
+    // ---------------------------------------------------------------------
+
+    // ---------------------------------------------------------------------
+    // NO-COLLISION: numerically distinct -> byte-UNEQUAL after canonicalize.
+    // ---------------------------------------------------------------------
+
+    /// Concrete no-collision at the int32.min exponent floor. Two tiny values
+    /// pinned at the floor that differ only in their (already minimal)
+    /// coefficient must NOT collapse to the same bytes. At the floor the loop
+    /// cannot scale, so this directly exercises whether distinct floor-pinned
+    /// coefficients survive distinct.
+    function testCanonicalizeNoCollisionAtFloorConcrete() external pure {
+        // 1e(int32.min) and 2e(int32.min): genuinely different numbers.
+        Float a = LibDecimalFloat.packLossless(1, INT32_MIN);
+        Float b = LibDecimalFloat.packLossless(2, INT32_MIN);
+        assertTrue(!a.eq(b), "precondition: distinct values");
+        assertTrue(
+            Float.unwrap(a.canonicalize()) != Float.unwrap(b.canonicalize()),
+            "distinct floor-pinned values must not collide"
+        );
+    }
+
+    /// Concrete no-collision where one value's loop is capped by the int224
+    /// bound and a neighbouring distinct value's is too. Maximised positive vs.
+    /// negative of nearly-equal magnitude must not collide.
+    function testCanonicalizeNoCollisionInt224CapConcrete() external pure {
+        Float a = LibDecimalFloat.packLossless(7, 0);
+        Float b = LibDecimalFloat.packLossless(7, 1); // 70, distinct value
+        Float c = LibDecimalFloat.packLossless(-7, 0); // distinct sign
+        bytes32 ca = Float.unwrap(a.canonicalize());
+        bytes32 cb = Float.unwrap(b.canonicalize());
+        bytes32 cc = Float.unwrap(c.canonicalize());
+        assertTrue(ca != cb, "7e0 vs 70e0 must not collide");
+        assertTrue(ca != cc, "7 vs -7 must not collide");
+        assertTrue(cb != cc, "70 vs -7 must not collide");
+    }
+
+    /// Fuzz no-collision across the FULL int224/int32 box. Build two Floats from
+    /// raw boundary-capable inputs; if they are numerically distinct (`!eq`),
+    /// their canonical forms must be byte-distinct. `eq` is the library's own
+    /// numeric-equality oracle, so this is exactly the documented guarantee
+    /// "two Floats are numerically equal iff their canonical forms are
+    /// byte-equal" applied in the contrapositive.
+    function testCanonicalizeNoCollisionFuzz(int224 coefficientA, int32 exponentA, int224 coefficientB, int32 exponentB)
+        external
+        pure
+    {
+        Float a = LibDecimalFloat.packLossless(coefficientA, exponentA);
+        Float b = LibDecimalFloat.packLossless(coefficientB, exponentB);
+        if (!a.eq(b)) {
+            assertTrue(
+                Float.unwrap(a.canonicalize()) != Float.unwrap(b.canonicalize()),
+                "distinct values must canonicalize to distinct bytes"
+            );
+        }
+    }
+
+    /// Fuzz no-collision focused at the int32.min floor: both operands pinned to
+    /// a narrow band just above the floor so the loop terminates at the floor
+    /// for small coefficients, the regime the tests above never reach.
+    function testCanonicalizeNoCollisionNearFloorFuzz(int224 coefficientA, int224 coefficientB, uint8 lift)
+        external
+        pure
+    {
+        // Exponent within [int32.min, int32.min + 255]: the floor band.
+        int32 exponent = int32(int256(INT32_MIN) + int256(uint256(lift)));
+        Float a = LibDecimalFloat.packLossless(coefficientA, exponent);
+        Float b = LibDecimalFloat.packLossless(coefficientB, exponent);
+        if (!a.eq(b)) {
+            assertTrue(
+                Float.unwrap(a.canonicalize()) != Float.unwrap(b.canonicalize()),
+                "distinct near-floor values must not collide"
+            );
+        }
+    }
+
+    // ---------------------------------------------------------------------
+    // EQ -> BYTE-EQUAL across representations, driven at the FLOOR and the
+    // int224 cap (the (c) hunt: same value via different starting reps).
+    // ---------------------------------------------------------------------
+
+    /// Same value reached two different ways, both bottoming out at the floor.
+    /// 10e(min) and 1e(min+1) are the same number; both must canonicalize to the
+    /// identical bytes even though one starts already-scaled.
+    function testCanonicalizeFloorCrossRepConcrete() external pure {
+        Float a = LibDecimalFloat.packLossless(10, INT32_MIN);
+        Float b = LibDecimalFloat.packLossless(1, int32(int256(INT32_MIN) + 1));
+        assertTrue(a.eq(b), "precondition: same value");
+        assertEq(
+            Float.unwrap(a.canonicalize()),
+            Float.unwrap(b.canonicalize()),
+            "same value at floor -> identical canonical bytes"
+        );
+    }
+
+    /// Fuzz: a value whose loop is capped by the floor, reached from two
+    /// different starting representations, canonicalizes identically. Start with
+    /// coefficient `base` at `int32.min + k`, and the pre-scaled `base*10^j` at
+    /// `int32.min + k - j`; both encode the same value and both must hit the
+    /// same floor-capped canonical form.
+    function testCanonicalizeFloorCrossRepFuzz(int64 base, uint8 k, uint8 j) external pure {
+        vm.assume(base != 0);
+        // Keep both exponents in the floor band and >= int32.min.
+        uint256 kk = uint256(k) % 30 + 1; // 1..30
+        uint256 jj = uint256(j) % kk; // 0..kk-1 so exp stays >= floor
+        int32 expA = int32(int256(INT32_MIN) + int256(kk));
+        // base * 10^jj still fits int224 comfortably (int64 * 10^29 < int224).
+        int256 scaled = int256(base) * int256(10 ** jj);
+        int32 expB = int32(int256(INT32_MIN) + int256(kk) - int256(jj));
+
+        Float a = LibDecimalFloat.packLossless(base, expA);
+        Float b = LibDecimalFloat.packLossless(scaled, expB);
+        assertTrue(a.eq(b), "precondition: same value");
+        assertEq(
+            Float.unwrap(a.canonicalize()), Float.unwrap(b.canonicalize()), "cross-rep at floor must be byte-equal"
+        );
+    }
+
+    // ---------------------------------------------------------------------
+    // VALUE PRESERVATION + IDEMPOTENCE at the int224/int32 boundaries the
+    // tests above avoid.
+    // ---------------------------------------------------------------------
+
+    /// Value preservation at the floor where the coefficient is NOT maximised
+    /// (the loop is capped by int32.min, leaving a small coefficient). 1e(min)
+    /// cannot scale at all; the canonical form must still be `eq` to the input
+    /// and idempotent.
+    function testCanonicalizeFloorValuePreservedConcrete() external pure {
+        Float f = LibDecimalFloat.packLossless(123, INT32_MIN);
+        Float c = f.canonicalize();
+        assertTrue(f.eq(c), "value preserved at floor");
+        // At the floor with a tiny coefficient the loop cannot run, so the form
+        // is already canonical: the input bytes must equal the canonical bytes.
+        assertEq(Float.unwrap(c), Float.unwrap(f), "floor-pinned tiny coeff is already canonical");
+        assertEq(Float.unwrap(c.canonicalize()), Float.unwrap(c), "idempotent at floor");
+    }
+
+    /// int224.max / int224.min coefficients: already at the magnitude ceiling so
+    /// the loop cannot scale (×10 overflows int224). Value-preserving and
+    /// idempotent, and the input is already its own canonical form.
+    function testCanonicalizeInt224ExtremesConcrete() external pure {
+        int224[2] memory extremes = [INT224_MAX, INT224_MIN];
+        for (uint256 i = 0; i < extremes.length; i++) {
+            Float f = LibDecimalFloat.packLossless(extremes[i], 3);
+            Float c = f.canonicalize();
+            assertTrue(f.eq(c), "value preserved at int224 extreme");
+            assertEq(Float.unwrap(c), Float.unwrap(f), "int224 extreme already canonical");
+            assertEq(Float.unwrap(c.canonicalize()), Float.unwrap(c), "idempotent at int224 extreme");
+        }
+    }
+
+    /// Fuzz value-preservation + idempotence pinned to the int32.min floor band.
+    /// This is the regime the uniform-int32-exponent fuzz above almost never
+    /// samples.
+    function testCanonicalizeFloorValuePreservedFuzz(int224 coefficient, uint16 lift) external pure {
+        int32 exponent = int32(int256(INT32_MIN) + int256(uint256(lift)));
+        Float f = LibDecimalFloat.packLossless(coefficient, exponent);
+        Float c = f.canonicalize();
+        assertTrue(f.eq(c), "value preserved near floor");
+        assertEq(Float.unwrap(c.canonicalize()), Float.unwrap(c), "idempotent near floor");
+    }
+
+    /// Fuzz value-preservation + idempotence with coefficients pinned to the
+    /// top/bottom of the int224 range (where the loop terminates immediately or
+    /// after a single step), across arbitrary int32 exponents.
+    function testCanonicalizeInt224EdgeValuePreservedFuzz(uint64 delta, bool negative, int32 exponent) external pure {
+        // Coefficient within `delta` of an int224 extreme.
+        int256 coefficient =
+            negative ? int256(INT224_MIN) + int256(uint256(delta)) : int256(INT224_MAX) - int256(uint256(delta));
+        Float f = LibDecimalFloat.packLossless(coefficient, exponent);
+        Float c = f.canonicalize();
+        assertTrue(f.eq(c), "value preserved near int224 edge");
+        assertEq(Float.unwrap(c.canonicalize()), Float.unwrap(c), "idempotent near int224 edge");
+    }
+
+    /// Fuzz the documented end-to-end guarantee at full boundary width: build two
+    /// Floats from raw int224/int32 inputs and assert `eq` <=> byte-equal after
+    /// canonicalize (both directions in one test). The eq->byte-equal fuzz above
+    /// only ever feeds equal values; this also feeds unequal ones.
+    function testCanonicalizeEqIffByteEqualFuzz(
+        int224 coefficientA,
+        int32 exponentA,
+        int224 coefficientB,
+        int32 exponentB
+    ) external pure {
+        Float a = LibDecimalFloat.packLossless(coefficientA, exponentA);
+        Float b = LibDecimalFloat.packLossless(coefficientB, exponentB);
+        bool numericallyEqual = a.eq(b);
+        bool byteEqual = Float.unwrap(a.canonicalize()) == Float.unwrap(b.canonicalize());
+        assertEq(numericallyEqual, byteEqual, "eq iff byte-equal after canonicalize");
+    }
+}
diff --git a/test_js/float.test.ts b/test_js/float.test.ts
index ca30a2c..25b3be2 100644
--- a/test_js/float.test.ts
+++ b/test_js/float.test.ts
@@ -151,6 +151,18 @@ describe("Test Float Bindings", () => {
       expect(a.add(b)?.value!.format()?.value!).toBe("0");
     });
 
+    it("should test canonicalize", () => {
+      // Two different representations of the same value canonicalize to
+      // byte-equal Floats, and the canonical form is numerically equal to the
+      // input.
+      const a = Float.parse("5")?.value!;
+      const b = Float.parse("5.0")?.value!;
+      const canonicalA = a.canonicalize()?.value!;
+      const canonicalB = b.canonicalize()?.value!;
+      expect(canonicalA.asHex()).toBe(canonicalB.asHex());
+      expect(a.eq(canonicalA)?.value!).toBe(true);
+    });
+
     it("should test zero constant", () => {
       // Test the zero function
       const zeroResult = Float.zero();