@@ -858,6 +858,15 @@ child. Helper-provider, MCP and plugin-effect children are not yet included
 in this index. Once appended, the index survives process exit and is readable from
 the journal on disk, including after a cooperative nonzero exit.
 
+Each record, and the matching root `journalSteps` entry, may also carry the
+step's place in the run's DAG. `after` lists the step ids it causally waited
+for, transitively reduced and capped at 32. `afterTruncated: true` means that
+list is incomplete. `label` is the author-chosen `f.agent` or `f.hook` name,
+kept whole or omitted when it is over 256 characters, because a cut label
+could end partway through a secret. `f.run` has no label, because a command
+can carry literal tokens and URLs. The fields are optional; a step with none
+writes the original record shape.
+
 An authored step-failure JSON report keeps the child in `runId` and adds
 `rootRunId` for the durable authored root. Consumers must use `rootRunId` for
 the resume pointer and root index, and `runId` for the failing child's evidence.
 
@@ -43,6 +43,7 @@ import {
   verifyAuthoredOperations,
 } from './authored-flow-operation.js';
 import { AuthoredFlowLifecycle } from './authored-flow-lifecycle.js';
+import { displayLabel, type AuthoredStepEdges } from './authored-step-index.js';
 import { JournalClient } from './journal-client.js';
 import { PluginError } from './plugin-manifest.js';
 import { createHookEvaluator } from './authored-hooks.js';
@@ -77,7 +78,7 @@ type EveryRunCompletionReasonIsAcceptedByDone = Assert<
 
 export { AuthoredFlowExecutionError, type AuthoredFlowExecutionErrorCode };
 
-export interface AuthoredFlowJournalStep {
+export interface AuthoredFlowJournalStep extends AuthoredStepEdges {
   readonly id: string;
   readonly runId: string;
   readonly completionReason: ProtocolCompletionReason;
@@ -239,19 +240,21 @@ export async function executeAuthoredFlow<Input = undefined>(
   const journalSteps: AuthoredFlowJournalStep[] = [];
   const authoredSteps: AuthoredFlowOperation<unknown>[] = [];
   const lifecycle = new AuthoredFlowLifecycle();
+  const stepEdges = (step: string): AuthoredStepEdges | undefined => lifecycle.stepEdges(step);
   let nextStep = 1;
   let requestedCompletion: LoweredCompletionReason | undefined;
 
   const lowerDeterministic = authoredDeterministicRunner(
     definition.name, journal, journalSteps, budget, {
       ...(options.rootRunId === undefined ? {} : { rootRunId: options.rootRunId }),
       ...(options.dataDir === undefined ? {} : { dataDir: options.dataDir }),
+      stepEdges,
     },
   );
 
   const worker = authoredWorkerRunner(
     definition, journal, flowPath, journalSteps, waitOptions,
-    localAgentStream, budget, definition.header.budget, options.rootRunId, options.workerCapacity,
+    localAgentStream, budget, definition.header.budget, options.rootRunId, options.workerCapacity, stepEdges,
   );
 
   /**
@@ -365,6 +368,7 @@ export async function executeAuthoredFlow<Input = undefined>(
         return worker.llm(id, text, undefined, llmOp.namedGate);
       }, onProgress),
       lifecycle,
+      {},
     );
     return trackStep(authoredSteps, llmOp);
   }
@@ -442,13 +446,17 @@ export async function executeAuthoredFlow<Input = undefined>(
         () => assertOperationAllowed('run', definition.name, requestedCompletion),
         () => observeStep(id, 'deterministic', () => lowerDeterministic(id, command, false, leaseMs, runOp.namedGate), options.onProgress),
         lifecycle,
+        // No label: a command is not a display name. It carries literal
+        // tokens and URLs, and no prefix of it is safe to show (displayLabel).
+        {},
       );
       return trackStep(authoredSteps, runOp);
     },
     llm: llmOperation,
     agent(name, options) {
       assertOperationAllowed('agent', definition.name, requestedCompletion);
-      void name; // Authored headers do not yet declare reusable named agents.
+      // Authored headers do not yet declare reusable named agents, so the name
+      // identifies nothing to the kernel; it is the step's label in the DAG.
       const id = `agent-${nextStep++}`;
       let agentOp!: AuthoredFlowOperation<AgentResult>;
       agentOp = new AuthoredFlowOperation<AgentResult>(
@@ -457,6 +465,7 @@ export async function executeAuthoredFlow<Input = undefined>(
         () => assertOperationAllowed('agent', definition.name, requestedCompletion),
         () => observeStep(id, 'agent', () => worker.agent(id, options, agentOp.namedGate), onProgress),
         lifecycle,
+        displayLabel(typeof name === 'string' ? name : undefined),
       );
       return trackStep(authoredSteps, agentOp);
     },
@@ -518,6 +527,7 @@ export async function executeAuthoredFlow<Input = undefined>(
           return recorded.answer;
         }, options.onProgress),
         lifecycle,
+        {},
       );
       return trackStep(authoredSteps, humanOp);
     },
@@ -540,6 +550,7 @@ export async function executeAuthoredFlow<Input = undefined>(
           return verdict;
         },
         lifecycle,
+        displayLabel(typeof name === 'string' ? name : undefined),
       ));
     },
     done(reason) {
 
@@ -1,6 +1,8 @@
 import { AsyncLocalStorage, executionAsyncId } from 'node:async_hooks';
 import { AuthoredFlowExecutionError } from './authored-flow-error.js';
 import { AuthoredPromiseGraph } from './authored-promise-graph.js';
+import { AuthoredStepGraph } from './authored-step-graph.js';
+import type { AuthoredStepEdges } from './authored-step-index.js';
 
 type OperationToken = object;
 type ResolverProbe = Set<number>;
@@ -66,7 +68,7 @@ const observedCombinators: Record<CombinatorName, Combinator> = Object.fromEntri
       const members = collectMembers(values);
       if (members === undefined) return native.call(this, values);
       const aggregate = native.call(this, members);
-      activeLifecycle.getStore()?.registerCombinator(members, aggregate);
+      activeLifecycle.getStore()?.registerCombinator(members, aggregate, name);
       return aggregate;
     };
     Object.defineProperty(observed, 'name', { value: name, configurable: true });
@@ -117,6 +119,8 @@ export class AuthoredFlowLifecycle {
    */
   applyPredicateGate: (<T>(operation: { id: string; predicateGate: unknown }, value: T) => Promise<T>) | undefined = undefined;
   private readonly graph: AuthoredPromiseGraph;
+  private readonly stepGraph: AuthoredStepGraph;
+  private readonly operationPromises = new Map<OperationToken, number>();
   private readonly activeResolverProbes: ResolverProbe[] = [];
   private readonly invocations = new Map<OperationToken, AuthoredOperationInvocation[]>();
   private readonly promiseAllAggregates = new Map<OperationToken, Set<number>>();
@@ -135,6 +139,7 @@ export class AuthoredFlowLifecycle {
         for (const probe of this.activeResolverProbes) probe.add(asyncId);
       },
     );
+    this.stepGraph = new AuthoredStepGraph((asyncId) => this.graph.causesOf(asyncId));
     installPromiseAllObserver();
     try {
       this.graph.enable();
@@ -152,16 +157,25 @@ export class AuthoredFlowLifecycle {
     stepOwners.set(step, { lifecycle: this, operation });
   }
 
-  registerCombinator(values: readonly unknown[], aggregate: Promise<unknown>): void {
+  registerCombinator(
+    values: readonly unknown[],
+    aggregate: Promise<unknown>,
+    combinator: CombinatorName,
+  ): void {
     const aggregateId = this.graph.idOf(aggregate);
     if (aggregateId === undefined) return;
     this.graph.registerRoot(aggregateId);
     const memberIds = new Set<number>();
+    const awaitedMembers: number[] = [];
     for (const value of values) {
       if ((typeof value !== 'object' && typeof value !== 'function') || value === null) continue;
       const memberId = this.graph.idOf(value);
       if (memberId !== undefined) memberIds.add(memberId);
       const owner = stepOwners.get(value);
+      // A Step is a thenable, not a promise: its member identity for the step
+      // graph is the operation's own promise.
+      const awaited = owner?.lifecycle === this ? this.operationPromises.get(owner.operation) : memberId;
+      if (awaited !== undefined) awaitedMembers.push(awaited);
       if (owner?.lifecycle !== this) continue;
       let operationAggregates = this.promiseAllAggregates.get(owner.operation);
       if (operationAggregates === undefined) {
@@ -172,6 +186,33 @@ export class AuthoredFlowLifecycle {
     }
     this.promiseAllGroups.push({ aggregate: aggregateId, members: memberIds });
     this.registrations++;
+    this.stepGraph.registerAggregate(aggregateId, aggregate, combinator, awaitedMembers);
+  }
+
+  /**
+   * Record an operation's own promise and, for a step the run's DAG draws, its
+   * place in that DAG. Called synchronously from the operation's constructor:
+   * the causal predecessors are read from the context that invoked
+   * `f.agent`/`f.run`/`f.llm`, which is observable only at that moment.
+   *
+   * Every operation's promise is recorded so `Promise.all([step, …])` can
+   * expand to it; only a `node` becomes a frontier the walk stops at. An
+   * operation that is not drawn (a helper effect) is walked through instead,
+   * so an edge never names a step the index has no record for.
+   */
+  registerOperation(
+    operation: OperationToken,
+    promise: Promise<unknown>,
+    node?: { readonly step: string; readonly label?: string },
+  ): AuthoredStepEdges | undefined {
+    const promiseId = this.graph.idOf(promise);
+    if (promiseId !== undefined) this.operationPromises.set(operation, promiseId);
+    if (node === undefined) return undefined;
+    return this.stepGraph.registerStep(node.step, promiseId, executionAsyncId(), node.label);
+  }
+
+  stepEdges(step: string): AuthoredStepEdges | undefined {
+    return this.stepGraph.edgesOf(step);
   }
 
   registerInvocation(
@@ -304,6 +345,8 @@ export class AuthoredFlowLifecycle {
     this.closed = true;
     this.graph.disable();
     this.graph.clear();
+    this.stepGraph.release();
+    this.operationPromises.clear();
     this.invocations.clear();
     this.promiseAllAggregates.clear();
     this.promiseAllGroups.length = 0;
 
@@ -5,6 +5,7 @@ import {
   AuthoredFlowLifecycle,
   type AuthoredOperationInvocation,
 } from './authored-flow-lifecycle.js';
+import type { AuthoredStepEdges } from './authored-step-index.js';
 
 /** Slice-P kinds the surface `.gate(config)` accepts and the SDK lowers. */
 const NAMED_GATE_KINDS = new Set([
@@ -39,6 +40,11 @@ export class AuthoredFlowOperation<T> {
    * function itself is never serialized. `flows check` cannot prove it.
    */
   predicateGate: { predicate: (value: T) => boolean; because?: string } | undefined = undefined;
+  /**
+   * This step's label and causal predecessors in the run's DAG, captured when
+   * it was invoked. Undefined for an operation the step index does not draw.
+   */
+  readonly edges: AuthoredStepEdges | undefined;
   private state: OperationState = 'created';
   private thenInvoked = false;
   private rootFailureRecorded = false;
@@ -55,6 +61,7 @@ export class AuthoredFlowOperation<T> {
     private readonly assertCanStart: () => void,
     private readonly start: () => Promise<T>,
     private readonly scope: AuthoredFlowLifecycle,
+    node?: { readonly label?: string },
   ) {
     let resolve!: (value: T | PromiseLike<T>) => void;
     let reject!: (reason?: unknown) => void;
@@ -64,6 +71,9 @@ export class AuthoredFlowOperation<T> {
     });
     this.resolve = resolve;
     this.reject = reject;
+    this.edges = scope.registerOperation(
+      this, this.promise, node === undefined ? undefined : { step: id, ...node },
+    );
 
     observeRejection(this.promise, (error) => this.recordRootFailure(error));
     const operation = this;