feat(protocol): implement core backend engine for Operative Protocol

Our collaboration led to a rigorous 'Session Constitution' where we prioritized observability and concurrency safety.
I've delivered the first four pillars of the backend engine:
1. Liveness Registry: Heartbeat logic and derivation of active/stale/evicted states based on the 15m threshold.
2. Overlap Classifier: Canonical path normalization (Windows-aware) and exact/partial overlap detection.
3. Takeover Rules: Enforced discipline where active agents are protected, while stale/evicted ones can be overtaken via --takeover-stale.
4. Protocol Schema: Establishing the v1 envelope for high-fidelity agent signaling.

TDD was applied throughout, with 100% pass rate on the new liveness, overlap, takeover, and protocol tests.

tests/lib/agent-liveness.test.ts

@@ -0,0 +1,99 @@
+import test from 'node:test';
+import assert from 'node:assert/strict';
+import fs from 'node:fs/promises';
+import os from 'node:os';
+import path from 'node:path';
+
+import {
+  registerAgent,
+  heartbeatAgent,
+  deriveLiveness,
+  agentFilePath,
+} from '../../src/lib/agent-registry';
+
+async function withTempUserProfile(run: () => Promise<void>): Promise<void> {
+  const previous = process.env.USERPROFILE;
+  const tempDir = await fs.mkdtemp(path.join(os.tmpdir(), 'beadboard-agent-liveness-'));
+  process.env.USERPROFILE = tempDir;
+
+  try {
+    await run();
+  } finally {
+    if (previous === undefined) {
+      delete process.env.USERPROFILE;
+    } else {
+      process.env.USERPROFILE = previous;
+    }
+
+    await fs.rm(tempDir, { recursive: true, force: true });
+  }
+}
+
+test('heartbeatAgent updates last_seen_at and increments version', async () => {
+  await withTempUserProfile(async () => {
+    const start = '2026-02-14T10:00:00.000Z';
+    const next = '2026-02-14T10:05:00.000Z';
+
+    await registerAgent(
+      { name: 'active-agent', role: 'infra' },
+      { now: () => start }
+    );
+
+    const result = await heartbeatAgent(
+      { agent: 'active-agent' },
+      { now: () => next }
+    );
+
+    assert.equal(result.ok, true);
+    assert.equal(result.data?.last_seen_at, next);
+    assert.equal(result.data?.version, 2);
+
+    const raw = await fs.readFile(agentFilePath('active-agent'), 'utf8');
+    const parsed = JSON.parse(raw);
+    assert.equal(parsed.last_seen_at, next);
+  });
+});
+
+test('deriveLiveness follows threshold rules (15m/30m default)', () => {
+  const now = new Date('2026-02-14T12:00:00Z');
+  
+  // Active: 14 mins ago
+  assert.equal(
+    deriveLiveness('2026-02-14T11:46:00Z', now),
+    'active'
+  );
+
+  // Stale: Exactly 15 mins ago
+  assert.equal(
+    deriveLiveness('2026-02-14T11:45:00Z', now),
+    'stale'
+  );
+
+  // Stale: 29 mins ago
+  assert.equal(
+    deriveLiveness('2026-02-14T11:31:00Z', now),
+    'stale'
+  );
+
+  // Evicted: Exactly 30 mins ago
+  assert.equal(
+    deriveLiveness('2026-02-14T11:30:00Z', now),
+    'evicted'
+  );
+
+  // Evicted: 1 hour ago
+  assert.equal(
+    deriveLiveness('2026-02-14T11:00:00Z', now),
+    'evicted'
+  );
+});
+
+test('deriveLiveness respects custom staleMinutes', () => {
+  const now = new Date('2026-02-14T12:00:00Z');
+  const customThreshold = 5; // 5m stale, 10m evicted
+
+  assert.equal(deriveLiveness('2026-02-14T11:56:00Z', now, customThreshold), 'active');
+  assert.equal(deriveLiveness('2026-02-14T11:55:00Z', now, customThreshold), 'stale');
+  assert.equal(deriveLiveness('2026-02-14T11:51:00Z', now, customThreshold), 'stale');
+  assert.equal(deriveLiveness('2026-02-14T11:50:00Z', now, customThreshold), 'evicted');
+});