diff --git a/src/core/relation/RelationUpdates.js b/src/core/relation/RelationUpdates.js
index 277b6ea..2353a00 100644
--- a/src/core/relation/RelationUpdates.js
+++ b/src/core/relation/RelationUpdates.js
@@ -305,7 +305,7 @@ export class RelationUpdates {
       src: srcId,
       rel: relation,
       dst: dstId,
-      possibility: options.possibility !== undefined ? options.possibility : 1.0,
+      possibility: options.possibility !== undefined ? validatePossibility(options.possibility) : 1.0,
       reliability: options.reliability !== undefined ? options.reliability : 1.0,
       value: options.value,
       decayConfig: options.decayConfig,
diff --git a/tests/rigor/tx-rollback-parity.test.js b/tests/rigor/tx-rollback-parity.test.js
new file mode 100644
index 0000000..9bc4943
--- /dev/null
+++ b/tests/rigor/tx-rollback-parity.test.js
@@ -0,0 +1,188 @@
+/**
+ * rigor/tx-rollback-parity.test.js — transactional batch atomicity and
+ * batch+PLTC reachability.
+ *
+ * Contracts pinned:
+ *   - updateRelationsBatchTransactional is ATOMIC: a poison op anywhere in
+ *     the batch (invalid possibility) fails the whole batch and rolls back
+ *     every earlier op; on success every op applies in the given order.
+ *   - batch ADD validates possibility exactly like single adds (an invalid
+ *     possibility must never be stored, even via the batch path).
+ *   - with enableReachabilityCheck, batch adds/removes update the PLTC
+ *     indices: chain checks reflect batch-written edges immediately.
+ */
+import { describe, it } from 'node:test';
+import assert from 'node:assert/strict';
+import { rigor } from '@rigor/core';
+import { Arbiter } from '../../src/index.js';
+
+const DOCS = 3;
+const docKey = (i) => `doc:${i}`;
+const tupleKey = (d) => `u:0|owner|doc:${d}`;
+
+function applyMirror(tuples, ops) {
+  for (const op of ops) {
+    if (op.operation === 'remove') {
+      tuples.delete(tupleKey(op.doc));
+    } else if (op.operation === 'modify' && !tuples.has(tupleKey(op.doc))) {
+      continue; // engine no-op on missing tuple
+    } else {
+      tuples.set(tupleKey(op.doc), op.value);
+    }
+  }
+}
+
+function makeWrapper() {
+  const arbiter = new Arbiter();
+  arbiter.addNode('u:0', 'user');
+  for (let i = 0; i < DOCS; i++) arbiter.addNode(docKey(i), 'doc');
+  arbiter.setRelationConfig('can_read', { type: 'direct', relation: 'owner' });
+  const tuples = new Map();
+  const ops = [];
+
+  const wrapper = {
+    engine: arbiter,
+    tuples,
+    add(doc, value) {
+      arbiter.addRelation('u:0', 'owner', docKey(doc), { possibility: value });
+      tuples.set(tupleKey(doc), value);
+      return { ok: true };
+    },
+    txBatch(batchOps, poisonAt) {
+      const batch = batchOps.map((op, i) => ({
+        operation: op.operation,
+        srcKey: 'u:0',
+        relation: 'owner',
+        dstKey: docKey(op.doc),
+        options: op.operation === 'remove'
+          ? {}
+          : { possibility: i === poisonAt ? 1.5 : op.value }
+      }));
+      const result = arbiter.relationManager.updateRelationsBatchTransactional(batch);
+      if (result.success) {
+        applyMirror(tuples, batchOps);
+      }
+      return { success: result.success, error: result.error };
+    },
+    check(doc) {
+      const result = arbiter.check('u:0', 'can_read', docKey(doc));
+      const expected = tuples.get(tupleKey(doc)) ?? 0;
+      return { engine: result.possibility, expected, reason: result.reason };
+    },
+    clone() {
+      const fresh = makeWrapper();
+      for (const op of ops) {
+        const [name, ...args] = op;
+        fresh[name](...args);
+      }
+      return fresh;
+    }
+  };
+
+  const record = (name, fn) => (...args) => {
+    const res = fn(...args);
+    ops.push([name, ...args]);
+    return res;
+  };
+  wrapper.add = record('add', wrapper.add);
+  wrapper.txBatch = record('txBatch', wrapper.txBatch);
+  wrapper.check = record('check', wrapper.check);
+  return wrapper;
+}
+
+const opGen = rigor.gen.record({
+  operation: rigor.gen.enum(['add', 'modify', 'remove']),
+  doc: rigor.gen.int(0, DOCS - 1),
+  value: rigor.gen.oneOf([0.2, 0.5, 0.8, 0.9])
+});
+
+describe('Transactional batch atomicity and batch+PLTC (rigor)', () => {
+  it('FIXED MATRIX: poison at every position rolls back everything; batch add validates possibility', () => {
+    const w = makeWrapper();
+    w.add(0, 0.9);
+    w.add(1, 0.7);
+
+    for (const poisonAt of [0, 1, 2]) {
+      const tx = w.txBatch([
+        { operation: 'add', doc: 2, value: 0.4 },
+        { operation: 'modify', doc: 1, value: 0.6 },
+        { operation: 'modify', doc: 0, value: 0.6 }
+      ], poisonAt);
+      assert.equal(tx.success, false, `poison at ${poisonAt} must fail`);
+      assert.equal(w.check(0).engine, 0.9, `poison at ${poisonAt}: doc0 rolled back`);
+      assert.equal(w.check(1).engine, 0.7, `poison at ${poisonAt}: doc1 rolled back`);
+      assert.equal(w.check(2).engine, 0, `poison at ${poisonAt}: doc2 rolled back`);
+    }
+
+    const clean = w.txBatch([
+      { operation: 'add', doc: 2, value: 0.4 },
+      { operation: 'modify', doc: 1, value: 0.6 },
+      { operation: 'modify', doc: 0, value: 0.6 }
+    ], -1);
+    assert.equal(clean.success, true, 'clean tx succeeds');
+    assert.equal(w.check(0).engine, 0.6, 'clean tx: doc0 last-write-wins');
+    assert.equal(w.check(1).engine, 0.6, 'clean tx: doc1 modified');
+    assert.equal(w.check(2).engine, 0.4, 'clean tx: doc2 added');
+
+    assert.throws(
+      () => w.engine.relationManager.updateRelationsBatch([
+        { operation: 'add', srcKey: 'u:0', relation: 'owner', dstKey: 'doc:0', options: { possibility: 7 } }
+      ]),
+      /Invalid possibility/,
+      'batch add must reject invalid possibility'
+    );
+  });
+
+  it('BATCH+PLTC: chain reachability reflects batch writes immediately', () => {
+    const arb = new Arbiter({ enableReachabilityCheck: true });
+    arb.addNode('u:0', 'user');
+    arb.addNode('g:0', 'group');
+    arb.addNode('doc:0', 'doc');
+    arb.setRelationConfig('can_access', {
+      type: 'chain',
+      steps: [
+        { relation: 'member_of', direction: 'out' },
+        { relation: 'reads', direction: 'out' }
+      ]
+    });
+    arb.relationManager.updateRelationsBatch([
+      { operation: 'add', srcKey: 'u:0', relation: 'member_of', dstKey: 'g:0', options: { possibility: 0.8 } },
+      { operation: 'add', srcKey: 'g:0', relation: 'reads', dstKey: 'doc:0', options: { possibility: 0.7 } }
+    ]);
+    assert.equal(arb.check('u:0', 'can_access', 'doc:0').possibility, 0.7, 'chain allow after batch add');
+    arb.relationManager.updateRelationsBatch([
+      { operation: 'remove', srcKey: 'g:0', relation: 'reads', dstKey: 'doc:0', options: {} }
+    ]);
+    assert.equal(arb.check('u:0', 'can_access', 'doc:0').possibility, 0, 'chain deny after batch remove');
+  });
+
+  it('PROPERTY CAMPAIGN: tx atomicity and in-order application hold under fuzzed batches', async () => {
+    const result = await rigor.campaign(
+      [rigor.object('graph', makeWrapper, [
+        rigor.method('add', function (d, v) { return this.add(d, v); }, rigor.args(rigor.gen.int(0, DOCS - 1), rigor.gen.oneOf([0.2, 0.5, 0.8, 0.9]))),
+        rigor.method('txBatch', function (batchOps, poisonAt) { return this.txBatch(batchOps, poisonAt); },
+          rigor.args(rigor.gen.array(opGen, 1, 4), rigor.gen.oneOf([-1, 0, 1, 2, 3]))),
+        rigor.method('check', function (d) { return this.check(d); }, rigor.args(rigor.gen.int(0, DOCS - 1)))
+      ])],
+      rigor.crucible([
+        rigor.invariant('decision parity after every step', (ctx) => {
+          if (ctx.action !== 'graph.check' || ctx.error !== null) return true;
+          return ctx.actual.engine === ctx.actual.expected;
+        }),
+        rigor.invariant('tx returns a boolean success flag', (ctx) => {
+          if (ctx.action !== 'graph.txBatch') return true;
+          return typeof ctx.actual.success === 'boolean';
+        }),
+        rigor.invariant('no action errors', (ctx) => ctx.error === null)
+      ])
+    ).run({ effort: 400, seed: 'tx-rollback-parity', maxTraceLength: 25 });
+
+    const inv = result.crucibleVerdict;
+    assert.equal(inv.passed, true, [
+      `tx atomicity violated in ${inv.failureCount} cases:`,
+      ...result.failures.slice(0, 3).map((f) =>
+        `  [${f.invariant}] action=${f.action} args=${JSON.stringify(f.args)} actual=${JSON.stringify(f.actual)} error=${f.error}`
+      )
+    ].join('\n'));
+  });
+});