[codex] Add run liveness continuations (#4083)

## Thinking Path

> - Paperclip orchestrates AI agents for zero-human companies.
> - Heartbeat runs are the control-plane record of each agent execution
window.
> - Long-running local agents can exhaust context or stop while still
holding useful next-step state.
> - Operators need that stop reason, next action, and continuation path
to be durable and visible.
> - This pull request adds run liveness metadata, continuation
summaries, and UI surfaces for issue run ledgers.
> - The benefit is that interrupted or long-running work can resume with
clearer context instead of losing the agent's last useful handoff.

## What Changed

- Added heartbeat-run liveness fields, continuation attempt tracking,
and an idempotent `0058` migration.
- Added server services and tests for run liveness, continuation
summaries, stop metadata, and activity backfill.
- Wired local and HTTP adapters to surface continuation/liveness context
through shared adapter utilities.
- Added shared constants, validators, and heartbeat types for liveness
continuation state.
- Added issue-detail UI surfaces for continuation handoffs and the run
ledger, with component tests.
- Updated agent runtime docs, heartbeat protocol docs, prompt guidance,
onboarding assets, and skills instructions to explain continuation
behavior.
- Addressed Greptile feedback by scoping document evidence by run,
excluding system continuation-summary documents from liveness evidence,
importing shared liveness types, surfacing hidden ledger run counts,
documenting bounded retry behavior, and moving run-ledger liveness
backfill off the request path.

## Verification

- `pnpm exec vitest run packages/adapter-utils/src/server-utils.test.ts
server/src/__tests__/run-continuations.test.ts
server/src/__tests__/run-liveness.test.ts
server/src/__tests__/activity-service.test.ts
server/src/__tests__/documents-service.test.ts
server/src/__tests__/issue-continuation-summary.test.ts
server/src/services/heartbeat-stop-metadata.test.ts
ui/src/components/IssueRunLedger.test.tsx
ui/src/components/IssueContinuationHandoff.test.tsx
ui/src/components/IssueDocumentsSection.test.tsx`
- `pnpm --filter @paperclipai/db build`
- `pnpm exec vitest run server/src/__tests__/activity-service.test.ts
ui/src/components/IssueRunLedger.test.tsx`
- `pnpm --filter @paperclipai/ui typecheck`
- `pnpm --filter @paperclipai/server typecheck`
- `pnpm exec vitest run server/src/__tests__/activity-service.test.ts
server/src/__tests__/run-continuations.test.ts
ui/src/components/IssueRunLedger.test.tsx`
- `pnpm exec vitest run
server/src/__tests__/heartbeat-process-recovery.test.ts -t "treats a
plan document update"`
- `pnpm exec vitest run server/src/__tests__/activity-service.test.ts
server/src/__tests__/heartbeat-process-recovery.test.ts -t "activity
service|treats a plan document update"`
- Remote PR checks on head `e53b1a1d`: `verify`, `e2e`, `policy`, and
Snyk all passed.
- Confirmed `public-gh/master` is an ancestor of this branch after
fetching `public-gh master`.
- Confirmed `pnpm-lock.yaml` is not included in the branch diff.
- Confirmed migration `0058_wealthy_starbolt.sql` is ordered after
`0057` and uses `IF NOT EXISTS` guards for repeat application.
- Greptile inline review threads are resolved.

## Risks

- Medium risk: this touches heartbeat execution, liveness recovery,
activity rendering, issue routes, shared contracts, docs, and UI.
- Migration risk is mitigated by additive columns/indexes and idempotent
guards.
- Run-ledger liveness backfill is now asynchronous, so the first ledger
response can briefly show historical missing liveness until the
background backfill completes.
- UI screenshot coverage is not included in this packaging pass;
validation is currently through focused component tests.

> 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-5.4, local tool-use coding agent with terminal, git,
GitHub connector, GitHub CLI, and Paperclip API access.

## 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

Screenshot note: no before/after screenshots were captured in this PR
packaging pass; the UI changes are covered by focused component tests
listed above.

---------

Co-authored-by: Paperclip <noreply@paperclip.ing>

packages/db/src/migrations/0058_wealthy_starbolt.sql

@@ -0,0 +1,6 @@
+ALTER TABLE "heartbeat_runs" ADD COLUMN IF NOT EXISTS "liveness_state" text;--> statement-breakpoint
+ALTER TABLE "heartbeat_runs" ADD COLUMN IF NOT EXISTS "liveness_reason" text;--> statement-breakpoint
+ALTER TABLE "heartbeat_runs" ADD COLUMN IF NOT EXISTS "continuation_attempt" integer DEFAULT 0 NOT NULL;--> statement-breakpoint
+ALTER TABLE "heartbeat_runs" ADD COLUMN IF NOT EXISTS "last_useful_action_at" timestamp with time zone;--> statement-breakpoint
+ALTER TABLE "heartbeat_runs" ADD COLUMN IF NOT EXISTS "next_action" text;--> statement-breakpoint
+CREATE INDEX IF NOT EXISTS "heartbeat_runs_company_liveness_idx" ON "heartbeat_runs" USING btree ("company_id","liveness_state","created_at");

packages/db/src/migrations/meta/_journal.json

@@ -407,6 +407,13 @@
       "when": 1776309613598,
       "tag": "0057_tidy_join_requests",
       "breakpoints": true
+    },
+    {
+      "idx": 58,
+      "version": "7",
+      "when": 1776542245004,
+      "tag": "0058_wealthy_starbolt",
+      "breakpoints": true
     }
   ]
-}
+}

packages/db/src/schema/heartbeat_runs.ts

@@ -41,6 +41,11 @@ export const heartbeatRuns = pgTable(
     issueCommentStatus: text("issue_comment_status").notNull().default("not_applicable"),
     issueCommentSatisfiedByCommentId: uuid("issue_comment_satisfied_by_comment_id"),
     issueCommentRetryQueuedAt: timestamp("issue_comment_retry_queued_at", { withTimezone: true }),
+    livenessState: text("liveness_state"),
+    livenessReason: text("liveness_reason"),
+    continuationAttempt: integer("continuation_attempt").notNull().default(0),
+    lastUsefulActionAt: timestamp("last_useful_action_at", { withTimezone: true }),
+    nextAction: text("next_action"),
     contextSnapshot: jsonb("context_snapshot").$type<Record<string, unknown>>(),
     createdAt: timestamp("created_at", { withTimezone: true }).notNull().defaultNow(),
     updatedAt: timestamp("updated_at", { withTimezone: true }).notNull().defaultNow(),
@@ -51,5 +56,10 @@ export const heartbeatRuns = pgTable(
       table.agentId,
       table.startedAt,
     ),
+    companyLivenessIdx: index("heartbeat_runs_company_liveness_idx").on(
+      table.companyId,
+      table.livenessState,
+      table.createdAt,
+    ),
   }),
 );