feat(ai): flow-authoring agent should emit the ADR-0044 revise-loop shape (revise + type:'back') #2274

Context

ADR-0044 (approval send-back-for-revision) is implemented engine-side, and the Studio designer authoring is now done in objectui — authors can draw a revise branch, mark an edge type: 'back', see un-declared cycles flagged, and one-click an "add revision loop" (objectstack-ai/objectui#1954, #1955, #1958).

The remaining gap is the AI Build path. When the flow-authoring agent generates an approval flow with a send-back, it must emit the full revise-loop shape — otherwise the result is rejected at registration. This is the AI-authoring follow-up flagged in #1770 ("designer support … AI flow authoring all need the same reduced-graph rule").

Problem — the failure chain

The canonical revise loop is:

approval ──approve──▶ …
         ──reject───▶ …
         ──revise───▶ wait (signal)
                        └──resubmit──[type:'back']──▶ approval   (round N+1)

registerFlow validates graph-minus-declared-back-edges must be a DAG. So if the agent generates the revise → wait → resubmit loop but forgets to mark the closing edge type: 'back', registerFlow hard-rejects it as an un-declared cycle. The generated flow won't save — the user gets an error instead of a working loop.

The shape knowledge exists in schemas the agent may consume (FlowEdgeSchema.type describes back; ApprovalNodeConfigSchema.maxRevisions is documented), but schema-visibility ≠ reliable generation. We need a deterministic safety net, not just prompt adherence.

Proposed work (prioritized by reliability)

1. Deterministic guardrail in packages/cli/src/utils/lint-flow-patterns.ts (its stated purpose: "guide the author — very often an AI generating templates — toward the robust pattern"). Add a revise-loop rule that detects an approval node sitting on a cycle whose closing edge is not type: 'back', and either:
   • auto-repair: mark the closing edge type: 'back' (turn a hard registerFlow rejection into a working flow), or
   • structured feedback: surface the precise fix so the agent self-corrects on the next turn.
     Auto-repair is preferred — it doesn't depend on the model "remembering."
2. Agent prompt + few-shot — add the revise-loop shape to the flow-authoring guidance and point at the canonical examples/app-showcase/src/flows/index.ts → showcase_budget_approval. Also nudge maxRevisions when a revise edge is emitted.
3. Spec completeness — packages/spec/src/studio/flow-builder.zod.ts edge visual registry currently covers normal/default/fault but not back; add a back edge style so every flow-builder-protocol consumer (not just objectui's hand-rolled canvas) renders the return arc.
4. Eval — a small eval set: given prompts that imply send-back/rework, assert the generated flow (a) registers cleanly and (b) contains a revise out-edge + a type:'back' closing edge. Guards against regressions in the agent's adherence.

Acceptance criteria

• An AI-generated approval flow with a send-back registers cleanly (no un-declared-cycle rejection) — verified by the guardrail + eval.
• lint-flow-patterns covers the revise-loop anti-pattern (unit-tested, like the existing [P2] Provide a declarative time-relative trigger (avoid fragile date-equality on record-change) #1874 rule).
• The flow-builder spec describes the back edge style.
• Eval demonstrates reliable generation of the revise + type:'back' shape.

References

• Parent: feat(studio): flow designer authoring for the approval revise loop (ADR-0044) #1770 (designer authoring — objectui side done)
• objectui PRs: feat(studio): author the approval revise loop in the flow designer (ADR-0044) objectui#1954 (authoring), refactor(audit): retire service-feed; sys_comment canonical (ADR-0052 §5) #1955 (simulate decisions), fix(spec): object.tenancy.tenantField is live (sql-driver), not dead — deletion paused #1958 (inline cycle surfacing)
• packages/cli/src/utils/lint-flow-patterns.ts — flow anti-pattern linter (guardrail home)
• packages/spec/src/studio/flow-builder.zod.ts — flow-builder protocol (edge styles)
• packages/spec/src/automation/flow.zod.ts — FlowEdgeSchema.type ('back'); registerFlow DAG-modulo-back-edges rule
• packages/spec/src/automation/approval.zod.ts — APPROVAL_BRANCH_LABELS (revise), maxRevisions
• examples/app-showcase/src/flows/index.ts — showcase_budget_approval (canonical shape)