[codex] Detect issue graph liveness deadlocks (#4209)

## Thinking Path

> - Paperclip orchestrates AI agents for zero-human companies.
> - The heartbeat harness is responsible for waking agents, reconciling
issue state, and keeping execution moving.
> - Some dependency graphs can become live-locks when a blocked issue
depends on an unassigned, cancelled, or otherwise uninvokable issue.
> - Review and approval stages can also stall when the recorded
participant can no longer be resolved.
> - This pull request adds issue graph liveness classification plus
heartbeat reconciliation that creates durable escalation work for those
cases.
> - The benefit is that harness-level deadlocks become visible,
assigned, logged, and recoverable instead of silently leaving task
sequences blocked.

## What Changed

- Added an issue graph liveness classifier for blocked dependency and
invalid review participant states.
- Added heartbeat reconciliation that creates one stable escalation
issue per liveness incident, links it as a blocker, comments on the
affected issue, wakes the recommended owner, and logs activity.
- Wired startup and periodic server reconciliation for issue graph
liveness incidents.
- Added focused tests for classifier behavior, heartbeat escalation
creation/deduplication, and queued dependency wake promotion.
- Fixed queued issue wakes so a coalesced wake re-runs queue selection,
allowing dependency-unblocked work to start immediately.

## Verification

- `pnpm exec vitest run
server/src/__tests__/heartbeat-dependency-scheduling.test.ts
server/src/__tests__/issue-liveness.test.ts
server/src/__tests__/heartbeat-issue-liveness-escalation.test.ts`
- Passed locally: `server/src/__tests__/issue-liveness.test.ts` (5
tests)
- Skipped locally: embedded Postgres suites because optional package
`@embedded-postgres/darwin-x64` is not installed on this host
- `pnpm --filter @paperclipai/server typecheck`
- `git diff --check`
- Greptile review loop: ran 3 times as requested; the final
Greptile-reviewed head `0a864eab` had 0 comments and all Greptile
threads were resolved. Later commits are CI/test-stability fixes after
the requested max Greptile pass count.
- GitHub PR checks on head `87493ed4`: `policy`, `verify`, `e2e`, and
`security/snyk (cryppadotta)` all passed.

## Risks

- Moderate operational risk: the reconciler creates escalation issues
automatically, so incorrect classification could create noise. Stable
incident keys and deduplication limit repeated escalation.
- Low schema risk: this uses existing issue, relation, comment, wake,
and activity log tables with no migration.
- No UI screenshots included because this change is server-side harness
behavior only.

> For core feature work, check [`ROADMAP.md`](ROADMAP.md) first and
discuss it in `#dev` before opening the PR. Feature PRs that overlap
with planned core work may need to be redirected — check the roadmap
first. See `CONTRIBUTING.md`.

## Model Used

- OpenAI Codex, GPT-5-based coding agent. Exact runtime model ID and
context window were not exposed in this session. Used tool execution for
git, tests, typecheck, Greptile review handling, and GitHub CLI
operations.

## Checklist

- [x] I have included a thinking path that traces from project context
to this change
- [x] I have specified the model used (with version and capability
details)
- [x] I have checked ROADMAP.md and confirmed this PR does not duplicate
planned core work
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [x] If this change affects the UI, I have included before/after
screenshots
- [x] I have updated relevant documentation to reflect my changes
- [x] I have considered and documented any risks above
- [x] I will address all Greptile and reviewer comments before
requesting merge

server/src/__tests__/issue-liveness.test.ts

@@ -0,0 +1,185 @@
+import { describe, expect, it } from "vitest";
+import { classifyIssueGraphLiveness } from "../services/issue-liveness.ts";
+
+const companyId = "company-1";
+const managerId = "manager-1";
+const coderId = "coder-1";
+const blockerId = "blocker-1";
+const blockedId = "blocked-1";
+
+function issue(overrides: Record<string, unknown> = {}) {
+  return {
+    id: blockedId,
+    companyId,
+    identifier: "PAP-1703",
+    title: "Parent work",
+    status: "blocked",
+    assigneeAgentId: coderId,
+    assigneeUserId: null,
+    createdByAgentId: null,
+    createdByUserId: null,
+    executionState: null,
+    ...overrides,
+  };
+}
+
+function agent(overrides: Record<string, unknown> = {}) {
+  return {
+    id: coderId,
+    companyId,
+    name: "Coder",
+    role: "engineer",
+    title: null,
+    status: "idle",
+    reportsTo: managerId,
+    ...overrides,
+  };
+}
+
+const manager = agent({
+  id: managerId,
+  name: "CTO",
+  role: "cto",
+  reportsTo: null,
+});
+
+const blocks = [{ companyId, blockerIssueId: blockerId, blockedIssueId: blockedId }];
+
+describe("issue graph liveness classifier", () => {
+  it("detects a PAP-1703-style blocked chain with an unassigned blocker and stable incident key", () => {
+    const findings = classifyIssueGraphLiveness({
+      issues: [
+        issue(),
+        issue({
+          id: blockerId,
+          identifier: "PAP-1704",
+          title: "Missing unblock work",
+          status: "todo",
+          assigneeAgentId: null,
+        }),
+      ],
+      relations: blocks,
+      agents: [agent(), manager],
+    });
+
+    expect(findings).toHaveLength(1);
+    expect(findings[0]).toMatchObject({
+      issueId: blockedId,
+      identifier: "PAP-1703",
+      state: "blocked_by_unassigned_issue",
+      recommendedOwnerAgentId: managerId,
+      dependencyPath: [
+        expect.objectContaining({ issueId: blockedId }),
+        expect.objectContaining({ issueId: blockerId }),
+      ],
+      incidentKey: `harness_liveness:${companyId}:${blockedId}:blocked_by_unassigned_issue:${blockerId}`,
+    });
+  });
+
+  it("does not flag a live blocked chain with an active assignee and wake path", () => {
+    const findings = classifyIssueGraphLiveness({
+      issues: [
+        issue(),
+        issue({
+          id: blockerId,
+          identifier: "PAP-1704",
+          title: "Live unblock work",
+          status: "todo",
+          assigneeAgentId: "blocker-agent",
+        }),
+      ],
+      relations: blocks,
+      agents: [
+        agent(),
+        manager,
+        agent({ id: "blocker-agent", name: "Blocker Agent", reportsTo: managerId }),
+      ],
+      queuedWakeRequests: [{ companyId, issueId: blockerId, agentId: "blocker-agent", status: "queued" }],
+    });
+
+    expect(findings).toEqual([]);
+  });
+
+  it("does not flag an unassigned blocker that already has an active execution path", () => {
+    const findings = classifyIssueGraphLiveness({
+      issues: [
+        issue(),
+        issue({
+          id: blockerId,
+          identifier: "PAP-1704",
+          title: "Unassigned but already running",
+          status: "todo",
+          assigneeAgentId: null,
+        }),
+      ],
+      relations: blocks,
+      agents: [agent(), manager],
+      activeRuns: [{ companyId, issueId: blockerId, agentId: coderId, status: "running" }],
+    });
+
+    expect(findings).toEqual([]);
+  });
+
+  it("detects cancelled blockers and uninvokable blocker assignees deterministically", () => {
+    const cancelled = classifyIssueGraphLiveness({
+      issues: [
+        issue(),
+        issue({
+          id: blockerId,
+          identifier: "PAP-1704",
+          title: "Cancelled unblock work",
+          status: "cancelled",
+          assigneeAgentId: "blocker-agent",
+        }),
+      ],
+      relations: blocks,
+      agents: [agent(), manager, agent({ id: "blocker-agent", name: "Paused", status: "paused" })],
+    });
+    expect(cancelled[0]?.state).toBe("blocked_by_cancelled_issue");
+
+    const paused = classifyIssueGraphLiveness({
+      issues: [
+        issue(),
+        issue({
+          id: blockerId,
+          identifier: "PAP-1704",
+          title: "Paused unblock work",
+          status: "todo",
+          assigneeAgentId: "blocker-agent",
+        }),
+      ],
+      relations: blocks,
+      agents: [agent(), manager, agent({ id: "blocker-agent", name: "Paused", status: "paused" })],
+    });
+    expect(paused[0]?.state).toBe("blocked_by_uninvokable_assignee");
+  });
+
+  it("detects invalid in_review execution participant", () => {
+    const findings = classifyIssueGraphLiveness({
+      issues: [
+        issue({
+          status: "in_review",
+          executionState: {
+            status: "pending",
+            currentStageId: "stage-1",
+            currentStageIndex: 0,
+            currentStageType: "review",
+            currentParticipant: { type: "agent", agentId: "missing-agent" },
+            returnAssignee: { type: "agent", agentId: coderId },
+            completedStageIds: [],
+            lastDecisionId: null,
+            lastDecisionOutcome: null,
+          },
+        }),
+      ],
+      relations: [],
+      agents: [agent(), manager],
+    });
+
+    expect(findings).toHaveLength(1);
+    expect(findings[0]).toMatchObject({
+      state: "invalid_review_participant",
+      incidentKey: `harness_liveness:${companyId}:${blockedId}:invalid_review_participant:missing-agent`,
+    });
+  });
+});