diff --git a/packages/sdk/src/authored-budget.ts b/packages/sdk/src/authored-budget.ts
index f934798ec..55a7c1bf4 100644
--- a/packages/sdk/src/authored-budget.ts
+++ b/packages/sdk/src/authored-budget.ts
@@ -21,6 +21,76 @@ interface Charge {
   unmetered: boolean;
 }
 
+type Total = Omit<Charge, 'day'>;
+
+/** `ms` as the budget header writes durations (`45s`, `2h`, `132.9m`), with the value that text denotes. */
+function duration(ms: bigint): {text: string; shown: number} {
+  const n = Number(ms);
+  if (n < 60_000) { const s = Number((n / 1000).toFixed(1)); return {text: `${s}s`, shown: s * 1000}; }
+  if (n % 3_600_000 === 0) return {text: `${n / 3_600_000}h`, shown: n};
+  const m = Number((n / 60_000).toFixed(1));
+  return {text: `${m}m`, shown: m * 60_000};
+}
+
+const usd = (micro: bigint): string => `$${micro / 1_000_000n}.${String(micro % 1_000_000n).padStart(6, '0').replace(/0{1,4}$/, '')}`;
+
+/**
+ * Whether `micro` microdollars exceeds the decimal `limit`, compared exactly at
+ * the limit's own precision (legacy `maxDollars` may carry more than six
+ * decimals, which the kernel compares as written). Undefined if the limit is
+ * not a plain decimal.
+ */
+function dollarsOver(micro: bigint, limit: string): boolean | undefined {
+  const match = /^(\d+)(?:\.(\d+))?$/.exec(limit);
+  if (match === null) return undefined;
+  const scale = Math.max(6, match[2]?.length ?? 0);
+  const limitScaled = BigInt(match[1]! + (match[2] ?? '').padEnd(scale, '0'));
+  return micro * 10n ** BigInt(scale - 6) > limitScaled;
+}
+
+/**
+ * Both durations, exact to the millisecond whenever rounding would make the
+ * overrun invisible: the displayed spend must itself read as over the
+ * displayed limit, compared as quantities so `120m` against `2h` counts too.
+ */
+function durations(used: bigint, limit: bigint): [string, string] {
+  const [u, l] = [duration(used), duration(limit)];
+  return u.shown > l.shown ? [u.text, l.text] : [`${used}ms`, `${limit}ms`];
+}
+
+/**
+ * The kernel refuses admission with only `budget_exceeded`; name which
+ * declared limit the carried spend crossed and by how much, using the same
+ * strict comparisons as `machine/budget.rs`. The kernel stays the authority: a
+ * refusal this accumulator cannot explain keeps the generic wording.
+ */
+export function budgetExceededMessage(limit: KernelBudgetSpec, total: Total, spec?: KernelRunSpec): string {
+  const crossed: string[] = [];
+  if (limit.max_wallclock_ms !== undefined && total.ms > BigInt(limit.max_wallclock_ms)) {
+    const [used, declared] = durations(total.ms, BigInt(limit.max_wallclock_ms));
+    crossed.push(`wallclock ${used} used of ${declared} declared`);
+  }
+  if (limit.max_dollars !== undefined && dollarsOver(total.micro, limit.max_dollars) === true) {
+    const exact = /^(\d+)(?:\.(\d{1,6}))?$/.exec(limit.max_dollars);
+    const declared = exact === null ? `$${limit.max_dollars}`
+      : usd(BigInt(exact[1]!) * 1_000_000n + BigInt((exact[2] ?? '').padEnd(6, '0')));
+    crossed.push(`dollars ${usd(total.micro)}${total.unmetered ? ' metered (some steps unmetered)' : ''} used of ${declared} declared`);
+  }
+  if (limit.max_tokens !== undefined && total.input + total.output > BigInt(limit.max_tokens)) {
+    crossed.push(`tokens ${total.input + total.output} used of ${limit.max_tokens} declared`);
+  }
+  if (limit.max_tokens_in !== undefined && total.input > BigInt(limit.max_tokens_in)) {
+    crossed.push(`input tokens ${total.input} used of ${limit.max_tokens_in} declared`);
+  }
+  if (limit.max_tokens_out !== undefined && total.output > BigInt(limit.max_tokens_out)) {
+    crossed.push(`output tokens ${total.output} used of ${limit.max_tokens_out} declared`);
+  }
+  const next = spec?.steps.length === 1 && typeof spec.steps[0]?.id === 'string' ? `step "${spec.steps[0].id}"` : 'the next step';
+  if (crossed.length === 0) return `Flow budget exceeded before ${next}.`;
+  const scope = limit.window === 'day' ? "in today's window of the flow's budget header" : "in the flow's budget header";
+  return `Flow budget exceeded before ${next}: ${crossed.join('; ')} ${scope}.`;
+}
+
 /** Serialized admission for the internal authored runner's separate step runs. */
 export class AuthoredBudget {
   private readonly limit: KernelBudgetSpec | undefined;
@@ -66,7 +136,9 @@ export class AuthoredBudget {
       };
       const outcome = await journal.runStart({ ...spec, budget: { ...this.limit, prior_spend: priorSpend } }, undefined, admissionKey);
       try {
-        if (outcome.completion_reason === 'budget_exceeded') throw new AuthoredFlowExecutionError('step_failed', 'Flow budget exceeded before the next step.', 'budget_exceeded', outcome.run_id);
+        if (outcome.completion_reason === 'budget_exceeded') {
+          throw new AuthoredFlowExecutionError('step_failed', budgetExceededMessage(this.limit!, total, spec), 'budget_exceeded', outcome.run_id);
+        }
         return await consume(outcome);
       } finally {
         let seq = 1;
diff --git a/packages/sdk/tests/budget-attribution.test.ts b/packages/sdk/tests/budget-attribution.test.ts
index cbfd3bc02..7bf18aca6 100644
--- a/packages/sdk/tests/budget-attribution.test.ts
+++ b/packages/sdk/tests/budget-attribution.test.ts
@@ -2,7 +2,7 @@ import { EventEmitter } from 'node:events';
 import { describe, expect, it, vi } from 'vitest';
 import { decodeProviderResult, decodeWrapperResult, requirePricedUsage } from '../src/worker-usage.js';
 import { pricedUsage, MODEL_PRICING } from '../src/model-pricing.js';
-import { AuthoredBudget } from '../src/authored-budget.js';
+import { AuthoredBudget, budgetExceededMessage } from '../src/authored-budget.js';
 import type { JournalClient } from '../src/journal-client.js';
 import type { StepDispatchEvent } from '../src/protocol.js';
 import { LlmWorker } from '../src/llm-worker.js';
@@ -68,3 +68,64 @@ describe('budget attribution', () => {
     expect(calls[1]?.[0].budget.prior_spend).toMatchObject({tokens_in:500, tokens_out:500, dollars:'0.000000', wallclock_ms:5, dollars_unmetered:true});
   });
 });
+
+describe('authored budget refusal names the limit it crossed', () => {
+  const charge = (payload: Record<string, unknown>) => ({seq: 1, entry_type: 'step.completed', at_ms: 0, payload});
+  // The shape of Cloud run f28314ed: 26 steps summed to 132.9 min of step
+  // wallclock under `{ wallclock: "2h", dollars: 25 }`, and the refusal said
+  // only "Flow budget exceeded before the next step." — not which limit.
+  it('reports wallclock used against the declared header on refusal', async () => {
+    const budget = new AuthoredBudget({wallclock: '2h', dollars: 25});
+    let started = 0;
+    const client = {
+      runStart: vi.fn(async () => ({run_id: `r${++started}`, status: started === 1 ? 'completed' : 'failed',
+        completion_reason: started === 1 ? 'success' : 'budget_exceeded', completed_steps: started === 1 ? 1 : 0})),
+      journalRead: vi.fn(async (run: string, seq: number) => ({entries: run === 'r1' && seq === 1
+        ? [charge({budget: {tokens_in: 878, tokens_out: 257687, dollars: '6.446600'}, spend: {wallclock_ms: 7_974_000}})] : []})),
+    };
+    const step = (id: string) => ({version: '0.1.0', steps: [{id}]}) as never;
+    await budget.execute(client as unknown as JournalClient, step('agent-26'), async () => 'ok');
+    const refused = budget.execute(client as unknown as JournalClient, step('run-27'), async () => 'unreachable');
+    await expect(refused).rejects.toMatchObject({
+      message: 'step_failed: Flow budget exceeded before step "run-27": wallclock 132.9m used of 2h declared in the flow\'s budget header.',
+      code: 'step_failed', completionReason: 'budget_exceeded',
+    });
+  });
+  it('names every crossed dimension, marks unmetered dollars, and scopes a day window', () => {
+    const total = {input: 900n, output: 300n, micro: 25_500_000n, ms: 30_000n, unmetered: true};
+    expect(budgetExceededMessage({max_dollars: '25', max_tokens: 1000, max_wallclock_ms: 60_000, window: 'day'}, total))
+      .toBe("Flow budget exceeded before the next step: dollars $25.50 metered (some steps unmetered) used of $25.00 declared; tokens 1200 used of 1000 declared in today's window of the flow's budget header.");
+    expect(budgetExceededMessage({max_tokens_in: 800, max_tokens_out: 300}, total))
+      .toBe("Flow budget exceeded before the next step: input tokens 900 used of 800 declared in the flow's budget header.");
+  });
+  it('prints exact milliseconds when rounding would show a strict overrun as equal (PR #594 review)', () => {
+    const zero = {input: 0n, output: 0n, micro: 0n, unmetered: false};
+    expect(budgetExceededMessage({max_wallclock_ms: 120_000}, {...zero, ms: 120_001n}))
+      .toBe("Flow budget exceeded before the next step: wallclock 120001ms used of 120000ms declared in the flow's budget header.");
+    expect(budgetExceededMessage({max_wallclock_ms: 60_000}, {...zero, ms: 60_001n}))
+      .toBe("Flow budget exceeded before the next step: wallclock 60001ms used of 60000ms declared in the flow's budget header.");
+    // Mixed units: the limit renders in hours, the spend in rounded minutes.
+    expect(budgetExceededMessage({max_wallclock_ms: 7_200_000}, {...zero, ms: 7_200_001n}))
+      .toBe("Flow budget exceeded before the next step: wallclock 7200001ms used of 7200000ms declared in the flow's budget header.");
+    expect(budgetExceededMessage({max_wallclock_ms: 7_200_000}, {...zero, ms: 7_206_000n}))
+      .toBe("Flow budget exceeded before the next step: wallclock 120.1m used of 2h declared in the flow's budget header.");
+    expect(budgetExceededMessage({max_wallclock_ms: 10}, {...zero, ms: 20n}))
+      .toBe("Flow budget exceeded before the next step: wallclock 20ms used of 10ms declared in the flow's budget header.");
+  });
+  it('names a legacy sub-microdollar dollar limit, compared at its own precision (PR #594 review)', () => {
+    const spent = {input: 0n, output: 0n, micro: 1n, ms: 0n, unmetered: false};
+    expect(budgetExceededMessage({max_dollars: '0.0000005'}, spent))
+      .toBe("Flow budget exceeded before the next step: dollars $0.000001 used of $0.0000005 declared in the flow's budget header.");
+    // Redundant trailing zeros are still the same limit, and equal is not over.
+    expect(budgetExceededMessage({max_dollars: '0.0000010000'}, spent)).toBe('Flow budget exceeded before the next step.');
+    expect(budgetExceededMessage({max_dollars: '0.0000009999'}, spent))
+      .toBe("Flow budget exceeded before the next step: dollars $0.000001 used of $0.0000009999 declared in the flow's budget header.");
+  });
+  it('keeps the generic wording when the carried totals do not explain the kernel refusal', () => {
+    // Equal is not over: the kernel compares strictly, so this total alone
+    // did not trip it and the accumulator must not invent a reason.
+    expect(budgetExceededMessage({max_wallclock_ms: 60_000, max_dollars: '1'}, {input: 0n, output: 0n, micro: 1_000_000n, ms: 60_000n, unmetered: false}))
+      .toBe('Flow budget exceeded before the next step.');
+  });
+});
+