Tasks: a pull request appears once on the board

Phase 3 of 3. Small, verifiable tasks; each _Test:_ names a row of testing-plan.md.

Task list

• [x] 1. One notion of a treeless loop

  • ui/src/api/model.ts: extract treeless(record) over TREELESS_LOOPS; sessionTree calls it instead of reading record.graph?.loop inline.
  • Depends on: none
  • Requirements: R4.2
  • Test: T9 — the existing sessionTree cases stay green

• [x] 2. The claim

  • ui/src/api/model.ts: pullRequestClaims(sessions, recordByRef) — treeless owners do not claim, self-claims are ignored, a claim by a claimed ref is discarded. buildWorkItemViews skips a claimed ref.
  • Security-relevant (abuse case A1): the last two rules are the mitigation.
  • Depends on: 1
  • Requirements: R1.1, R1.2, R1.3, R1.4
  • Test: T1, T11 — bun run test -- src/api/model.test.ts

• [x] 3. The fold

  • ui/src/api/model.ts: PullRequestView gains record, attention, question, lastActivity; buildPullRequests takes the record and attention maps and the awaiting map; sessionTree reads pr.lastActivity.
  • Depends on: 2
  • Requirements: R2.1
  • Test: T2 — bun run test -- src/api/model.test.ts

• [x] 4. The fold reaches the inbox and the row

  • ui/src/api/model.ts: collapseByKind extracted from attentionEntries; attentionEntries emits a PR's question and collapsed attention against the owner's ref with the PR's short ref, suffixed · PR; rowFlag raises needs input for a PR's open question and nothing else.
  • Depends on: 3
  • Requirements: R2.2, R2.3, R2.4
  • Test: T2 — bun run test -- src/api/model.test.ts

• [x] 5. A nested endpoint is a session

  • cli/the_loop/core/attention.py: the liveness map includes each record's nested pullRequests, a ref's own record still winning.
  • Depends on: none
  • Requirements: R3.1, R3.2
  • Test: T4, T11 — uv run pytest tests/test_core_attention.py

• [x] 6. Tests

  • ui/src/api/model.test.ts: the T1 and T2 cases.
  • ui/src/App.test.tsx: the sidebar draws the PR once (T3, T8).
  • cli/tests/test_core_attention.py: the T4 cases.
  • Depends on: 4, 5
  • Requirements: all
  • Test: T1, T2, T3, T4, T8

• [x] 7. Verification and evidence

  • Both suites, both linters, typecheck and production build; a Chromium screenshot of the sidebar against a fixture holding both identities. Results in evidence/verification.md.
  • Depends on: 6
  • Requirements: R4.1
  • Test: T7, T10

• [x] 8. Docs in the same PR

  • docs/capabilities/control-plane.md: the reconciliation and a history row.
  • Depends on: 7
  • Requirements: —
  • Test: markdownlint