diff --git a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.test.ts b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.test.ts
index 2997bcd..d03b75f 100644
--- a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.test.ts
+++ b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.test.ts
@@ -31,7 +31,7 @@ describe('PeggedSwapArgs', () => {
 
   it('should handle maximum uint256 values for reserves and rates', () => {
     const maxUint256 = (1n << 256n) - 1n
-    const maxLinearWidth = 2n * 10n ** 27n
+    const maxLinearWidth = 5000n * 10n ** 27n
     const args = new PeggedSwapArgs(maxUint256, maxUint256, maxLinearWidth, maxUint256, maxUint256)
 
     const encoded = PeggedSwapArgs.CODER.encode(args)
@@ -54,8 +54,8 @@ describe('PeggedSwapArgs', () => {
     expect(() => new PeggedSwapArgs(1n, 1n, 1n, 1n, 0n)).toThrow(/Invalid rateGt/)
   })
 
-  it('should throw when linearWidth exceeds 2e27', () => {
-    const tooLarge = 2n * 10n ** 27n + 1n
+  it('should throw when linearWidth exceeds 5000e27', () => {
+    const tooLarge = 5000n * 10n ** 27n + 1n
     expect(() => new PeggedSwapArgs(1n, 1n, tooLarge, 1n, 1n)).toThrow(/Invalid linearWidth/)
   })
 
diff --git a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.ts b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.ts
index 4667899..b00831c 100644
--- a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.ts
+++ b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-args.ts
@@ -4,6 +4,7 @@ import type { HexString } from '@1inch/sdk-core'
 import { UINT_256_MAX } from '@1inch/byte-utils'
 import assert from 'assert'
 import { PeggedSwapArgsCoder } from './pegged-swap-args-coder'
+import { MAX_LINEAR_WIDTH } from './pegged-swap-math/pegged-swap-math'
 import type { PeggedTokenInfo } from './types'
 import { resolveRate } from './rate-resolver'
 import type { IArgsCoder, IArgsData } from '../types'
@@ -19,7 +20,7 @@ export class PeggedSwapArgs implements IArgsData {
   /**
    * x0 - Initial X reserve (normalization factor) = initial_balance_X * rateLt (or rateGt)
    * y0 - Initial Y reserve (normalization factor) = initial_balance_Y * rateGt (or rateLt)
-   * linearWidth - Linear component coefficient A scaled by 1e27 (e.g., 0.8e27 for A=0.8)
+   * linearWidth - Linear component coefficient A scaled by 1e27 (e.g., 0.8e27 for A=0.8); must be ≤ MAX_LINEAR_WIDTH (A ≤ 5000)
    * rateLt - Rate multiplier for token with LOWER address
    * rateGt - Rate multiplier for token with GREATER address
    * > For equal decimals (e.g., both 18): rateLt = rateGt = 1
@@ -35,7 +36,7 @@ export class PeggedSwapArgs implements IArgsData {
     assert(x0 > 0n && y0 > 0n, 'Reserves cannot be zero')
     assert(x0 <= UINT_256_MAX, `Invalid x0: ${x0}`)
     assert(y0 <= UINT_256_MAX, `Invalid y0: ${y0}`)
-    assert(linearWidth <= 2n * 10n ** 27n, `Invalid linearWidth: ${linearWidth}`)
+    assert(linearWidth <= MAX_LINEAR_WIDTH, `Invalid linearWidth: ${linearWidth}`)
     assert(
       rateLt > 0n && rateLt <= UINT_256_MAX,
       `Invalid rateLt: ${rateLt}. Must be positive and <= UINT_256_MAX`,
diff --git a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.test.ts b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.test.ts
index 654abe2..3a7bf7e 100644
--- a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.test.ts
+++ b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.test.ts
@@ -25,8 +25,13 @@ describe('linearWidthFromSymmetricRangePercent', () => {
     expect(linearWidth).toBe(1460784313725490196078431372n)
   })
 
-  it('allows linearWidth at the on-chain maximum (20% symmetric range)', () => {
-    expect(linearWidthFromSymmetricRangePercent(20)).toBe(MAX_LINEAR_WIDTH)
+  it('maps a 20% symmetric range to A = 2', () => {
+    expect(linearWidthFromSymmetricRangePercent(20)).toBe(2n * PEGGED_SWAP_ONE)
+  })
+
+  it('allows narrow peg bands up to the on-chain maximum (A ≈ 5000 at the 0.01% floor)', () => {
+    // X = 0.0001 → A = (1 - X) / (2X) = 4999.5 → 4999.5e27 ≤ MAX_LINEAR_WIDTH (5000e27).
+    expect(linearWidthFromSymmetricRangePercent(0.01)).toBe(49995n * 10n ** 26n)
   })
 
   it('rejects zero and 100% symmetric range', () => {
@@ -34,8 +39,8 @@ describe('linearWidthFromSymmetricRangePercent', () => {
     expect(() => linearWidthFromSymmetricRangePercent(100)).toThrow(/less than 100%/)
   })
 
-  it('rejects narrow peg bands whose A exceeds 2', () => {
-    expect(() => linearWidthFromSymmetricRangePercent(0.2)).toThrow(/exceeds maximum/)
+  it('rejects peg bands tighter than the A ≤ 5000 floor', () => {
+    expect(() => linearWidthFromSymmetricRangePercent(0.001)).toThrow(/exceeds maximum/)
   })
 })
 
@@ -44,8 +49,12 @@ describe('symmetricRangePercentFromLinearWidth', () => {
     expect(symmetricRangePercentFromLinearWidth(15n * 10n ** 26n)).toBe(25)
   })
 
-  it('returns 20% at the on-chain maximum linearWidth', () => {
-    expect(symmetricRangePercentFromLinearWidth(MAX_LINEAR_WIDTH)).toBe(20)
+  it('returns 20% at A = 2', () => {
+    expect(symmetricRangePercentFromLinearWidth(2n * PEGGED_SWAP_ONE)).toBe(20)
+  })
+
+  it('returns ≈0.009999% at the on-chain maximum linearWidth (A = 5000)', () => {
+    expect(symmetricRangePercentFromLinearWidth(MAX_LINEAR_WIDTH)).toBeCloseTo(100 / 10001, 6)
   })
 
   it('returns 100% when linearWidth is zero', () => {
@@ -63,7 +72,7 @@ describe('symmetricRangePercentFromLinearWidth', () => {
   })
 
   it('round-trips percent -> linearWidth -> percent', () => {
-    for (const percent of [20, 25, 25.5, 33.33, 50, 99]) {
+    for (const percent of [0.01, 0.1, 1, 20, 25, 25.5, 33.33, 50, 99]) {
       const linearWidth = linearWidthFromSymmetricRangePercent(percent)
       expect(symmetricRangePercentFromLinearWidth(linearWidth)).toBeCloseTo(percent, 10)
     }
@@ -75,7 +84,7 @@ describe('symmetricRangePercentFromLinearWidth', () => {
       5n * 10n ** 26n,
       10n ** 27n,
       15n * 10n ** 26n,
-      MAX_LINEAR_WIDTH,
+      2n * PEGGED_SWAP_ONE,
     ]) {
       const percent = symmetricRangePercentFromLinearWidth(linearWidth)
       const recovered = linearWidthFromSymmetricRangePercent(percent)
@@ -86,7 +95,7 @@ describe('symmetricRangePercentFromLinearWidth', () => {
   })
 
   it('round-trips exactly for clean percents', () => {
-    for (const percent of [20, 25, 50]) {
+    for (const percent of [0.01, 0.1, 20, 25, 50]) {
       const linearWidth = linearWidthFromSymmetricRangePercent(percent)
       expect(symmetricRangePercentFromLinearWidth(linearWidth)).toBe(percent)
     }
diff --git a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.ts b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.ts
index db98ad4..2c70e7d 100644
--- a/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.ts
+++ b/typescript/swap-vm/src/swap-vm/instructions/pegged-swap/pegged-swap-math/pegged-swap-math.ts
@@ -6,8 +6,8 @@ import { bigintSqrt } from '../../utils'
 /** Matches `PeggedSwapMath.ONE` in swap-vm. */
 export const PEGGED_SWAP_ONE: bigint = 10n ** 27n
 
-/** Maximum on-chain `linearWidth` (`A` ≤ 2). */
-export const MAX_LINEAR_WIDTH: bigint = 2n * PEGGED_SWAP_ONE
+/** Maximum on-chain `linearWidth` (`A` ≤ 5000). */
+export const MAX_LINEAR_WIDTH: bigint = 5000n * PEGGED_SWAP_ONE
 
 const MARGINAL_PRICE_ONE = 10n ** 18n