diff --git a/packages/cultmesh-ts/test/provider-rudp-transport.test.ts b/packages/cultmesh-ts/test/provider-rudp-transport.test.ts
index e35a42a8..f1dd5d2d 100644
--- a/packages/cultmesh-ts/test/provider-rudp-transport.test.ts
+++ b/packages/cultmesh-ts/test/provider-rudp-transport.test.ts
@@ -360,6 +360,41 @@ test("a client restarted on the same address with the same Connect payload repla
   }
 });
 
+test("the RUDP document server does not acknowledge by name a reliable packet its session did not receive", async () => {
+  const connectionId = 0x43554c55;
+  const server = CultMesh.createRudpDocumentServer("odin-ack-test", connectionId, {
+    bindPort: 0,
+    documents: new CultNetDocumentRegistry(),
+    onError: () => undefined,
+  });
+  await server.start();
+  const socket = createSocket("udp4");
+  const received: CultNetRudpPacket[] = [];
+  socket.on("message", wire => received.push(decodeRudpPacket(wire)));
+  const toServer = (packet: CultNetRudpPacket) =>
+    socket.send(encodeRudpPacket(packet), server.bind.port, "127.0.0.1");
+  try {
+    const client = new CultNetRudpSession({ connectionId, initialSequence: 50_000 });
+    const connect = client.createConnect(Date.now());
+    toServer(connect);
+    await waitFor(() => received.some(packet => packet.packetType === "accept"), "the Accept");
+    received.length = 0;
+
+    // A reliable packet the session ignores (a client does not send an Accept).
+    // The session never received it, so the Ack must not name it.
+    const ignored: CultNetRudpPacket = { ...client.createAck(), packetType: "accept", reliable: true, sequence: connect.sequence + 5 };
+    toServer(ignored);
+    await waitFor(() => received.some(packet => packet.packetType === "ack"), "the acknowledgement");
+    const ack = received.find(packet => packet.packetType === "ack")!;
+    const names = ack.ack === ignored.sequence
+      || Array.from({ length: 32 }, (_, bit) => bit).some(bit => (ack.ackMask & (1 << bit)) !== 0 && ack.ack - bit - 1 === ignored.sequence);
+    assert.equal(names, false, "the server acknowledged by name a packet its session refused");
+  } finally {
+    socket.close();
+    server.close();
+  }
+});
+
 function deferred<T>(): { promise: Promise<T>; resolve(value: T): void } {
   let resolve!: (value: T) => void;
   return { promise: new Promise<T>(done => resolve = done), resolve };
diff --git a/packages/cultnet-ts/src/rudp.ts b/packages/cultnet-ts/src/rudp.ts
index bfe94973..e32bb2d7 100644
--- a/packages/cultnet-ts/src/rudp.ts
+++ b/packages/cultnet-ts/src/rudp.ts
@@ -25,14 +25,11 @@ const RUDP_RECEIVED_SEQUENCE_WINDOW = 4_096;
 /// retransmitting the same sequence would never change its mind.
 const RUDP_CONNECT_ATTEMPT_MS = 3_000;
 
-/// A sequence drawn from a secure source in [floor, 2^31). The Connect's
-/// sequence is what tells a peer whether a Connect repeats one it already
-/// accepted or starts a new session, so two sessions must not share one by
-/// default. A floor above the range draws nothing new: the caller keeps its own
-/// sequence.
-function drawSequence(floor: number): number {
-  const low = Math.max(1, floor);
-  return low >= 2 ** 31 ? low : randomInt(low, 2 ** 31);
+/// A sequence drawn from a secure source in [1, 2^31). The Connect's sequence
+/// is what tells a peer whether a Connect repeats one it already accepted or
+/// starts a new session, so two sessions must not share one by default.
+function drawSequence(): number {
+  return randomInt(1, 2 ** 31);
 }
 
 /// Whether `sequence` is at or before `mark` in serial order, within the
@@ -189,6 +186,9 @@ export class CultNetRudpSession {
   #connectSequence: number | undefined;
   /// A Connect this side sent is unanswered. Only then is an Accept honoured.
   #awaitingAccept = false;
+  /// The payload of the Connect this side sent, kept so a fresh attempt can
+  /// always be built whatever became of the pending packet.
+  #connectPayload = new Uint8Array();
   /// When the unanswered Connect first went out; `dueResends` abandons it for a
   /// fresh attempt once `RUDP_CONNECT_ATTEMPT_MS` has passed.
   #connectStartedAtMs = 0;
@@ -218,7 +218,7 @@ export class CultNetRudpSession {
 
   constructor(options: CultNetRudpSessionOptions) {
     this.connectionId = toUint32(options.connectionId, "connectionId");
-    this.#nextSequence = toUint32(options.initialSequence ?? drawSequence(1), "initialSequence");
+    this.#nextSequence = toUint32(options.initialSequence ?? drawSequence(), "initialSequence");
     if (this.#nextSequence === 0xffff_ffff) {
       throw new Error("RUDP initialSequence must leave room for a reliable packet.");
     }
@@ -317,6 +317,7 @@ export class CultNetRudpSession {
     this.#connectSequence = packet.sequence;
     this.#awaitingAccept = true;
     this.#connectStartedAtMs = nowMs;
+    this.#connectPayload = new Uint8Array(payload);
     this.#trackReliable(packet, nowMs);
     return packet;
   }
@@ -489,7 +490,12 @@ export class CultNetRudpSession {
     if (packet.packetType === "accept" && !honoursAccept) {
       return { delivered: [], readyToSend: [] };
     }
-    this.#applyAcknowledgements(packet);
+    // While this side's Connect awaits its Accept, only the Accept it honours
+    // retires it: an Ack that names the Connect (a server's reply to a repeat or
+    // a stale copy) says the server did not start a session.
+    if (honoursAccept || !this.#awaitingAccept) {
+      this.#applyAcknowledgements(packet);
+    }
     const readyToSend = this.#promoteQueuedReliable(nowMs);
     this.#lastReceivedAtMs = nowMs;
 
@@ -666,24 +672,24 @@ export class CultNetRudpSession {
   }
 
   /// A Connect unanswered for `RUDP_CONNECT_ATTEMPT_MS` is replaced, not
-  /// retransmitted further, by a Connect with a newly drawn sequence and the
-  /// same payload. Nothing was ever sent in an unanswered generation, so no
-  /// sequence issued so far is owed; the draw stays above them, so a frame the
-  /// peer still remembers from an earlier generation of this session stays at or
-  /// before the new Connect.
+  /// retransmitted further, by a Connect with the same payload and the
+  /// abandoned sequence plus the receive window less one. Nothing was ever sent
+  /// in an unanswered generation, so no sequence issued so far is owed. The jump
+  /// keeps a late copy of the abandoned Connect inside the new one's stale
+  /// window, so a server that took the new Connect answers the copy with an Ack
+  /// instead of restarting; and it leaves the stale window of whatever
+  /// generation the server holds, unless that generation sits exactly at the
+  /// jump, and then the next attempt leaves it. The first Connect of a session
+  /// is the only one drawn at random.
   #abandonUnansweredConnect(nowMs: number): CultNetRudpPacket | undefined {
     if (!this.#awaitingAccept || nowMs - this.#connectStartedAtMs < RUDP_CONNECT_ATTEMPT_MS) {
       return undefined;
     }
-    const pending = this.#connectSequence === undefined
-      ? undefined
-      : this.#pendingReliable.get(this.#connectSequence);
-    if (!pending) {
+    if (this.#connectSequence === undefined) {
       return undefined;
     }
-    const payload = new Uint8Array(pending.packet.payload ?? []);
-    this.#nextSequence = drawSequence(this.#nextSequence);
-    return this.createConnect(nowMs, payload);
+    this.#nextSequence = Math.min(this.#connectSequence + RUDP_RECEIVED_SEQUENCE_WINDOW - 1, 0xffff_fffe);
+    return this.createConnect(nowMs, this.#connectPayload);
   }
 
   #createPacket(packet: {
diff --git a/packages/cultnet-ts/test/rudp-connect-generation.test.ts b/packages/cultnet-ts/test/rudp-connect-generation.test.ts
index 47455165..cea61a6d 100644
--- a/packages/cultnet-ts/test/rudp-connect-generation.test.ts
+++ b/packages/cultnet-ts/test/rudp-connect-generation.test.ts
@@ -416,3 +416,120 @@ test("an accepted peer that goes silent times out", () => {
   server.acceptConnect(session(10).createConnect(0), 0);
   assert.equal(server.checkTimeout(100_000, 1_000), true);
 });
+
+// Ack Cut 1d, batch 2: the connect-attempt timeout.
+
+test("an Ack naming the pending Connect does not retire it", () => {
+  const server = session(500);
+  const old = session(1);
+  const oldAccept = server.acceptConnect(old.createConnect(0), 0);
+  old.receive(oldAccept, 0);
+  server.receive(old.createAckForReceived(oldAccept.sequence), 0);
+
+  const restarted = session(1);
+  const first = restarted.createConnect(0, enc("join"));
+  const reply = server.acceptConnect(first, 1);
+  assert.equal(reply.packetType, "ack");
+  assert.ok(namesSequence(reply, first.sequence), "the Ack must name the pending Connect for this test to bite");
+  restarted.receive(reply, 1);
+  assert.equal(restarted.connected, false);
+  assert.deepEqual(restarted.pendingReliableSequences, [first.sequence], "an Ack retired the Connect");
+
+  const fresh = restarted.dueResends(3_000);
+  assert.equal(fresh.length, 1, "the client waits for ever with nothing to resend");
+  assert.equal(dec(fresh[0]!.payload ?? new Uint8Array()), "join");
+  const accept = server.acceptConnect(fresh[0]!, 3_000);
+  assert.equal(accept.packetType, "accept");
+  restarted.receive(accept, 3_000);
+  assert.ok(restarted.connected);
+});
+
+test("a late copy of an abandoned Connect is stale once its replacement is accepted", () => {
+  const server = session(500);
+  const client = session(10);
+  const abandoned = client.createConnect(0);
+  const fresh = client.dueResends(3_000);
+  assert.equal(fresh.length, 1);
+  assert.equal(fresh[0]!.sequence, abandoned.sequence + 4_095);
+  const accept = server.acceptConnect(fresh[0]!, 3_001);
+  client.receive(accept, 3_002);
+  server.receive(client.createAckForReceived(accept.sequence), 3_002);
+  assert.ok(client.connected);
+  const a = send(client, "a");
+  assert.deepEqual(names(server.receive(a, 3_003)), ["a"]);
+  client.receive(server.createAckForReceived(a.sequence), 3_003);
+
+  assert.equal(server.connectRepeats(abandoned), true, "the late copy would restart the server");
+  const reply = server.acceptConnect(abandoned, 3_004);
+  assert.equal(reply.packetType, "ack");
+  client.receive(reply, 3_005);
+  assert.ok(client.connected);
+  assert.deepEqual(names(server.receive(send(client, "b"), 3_006)), ["b"]);
+});
+
+test("a server sitting at the jump is left by the next attempt", () => {
+  const server = session(500);
+  const old = session(5_095);
+  const oldAccept = server.acceptConnect(old.createConnect(0), 0);
+  old.receive(oldAccept, 0);
+  server.receive(old.createAckForReceived(oldAccept.sequence), 0);
+
+  const restarted = session(1_000);
+  const first = restarted.createConnect(0, enc("join"));
+  restarted.receive(server.acceptConnect(first, 1), 1);
+  assert.equal(restarted.connected, false);
+
+  const second = restarted.dueResends(3_000)[0]!;
+  assert.equal(second.sequence, 5_095, "the jump lands on the server's generation");
+  const reply = server.acceptConnect(second, 3_001);
+  assert.equal(reply.packetType, "ack");
+  restarted.receive(reply, 3_001);
+  assert.equal(restarted.connected, false);
+
+  const third = restarted.dueResends(6_000)[0]!;
+  assert.equal(third.sequence, 5_095 + 4_095);
+  const accept = server.acceptConnect(third, 6_001);
+  assert.equal(accept.packetType, "accept");
+  restarted.receive(accept, 6_001);
+  assert.ok(restarted.connected);
+});
+
+test("server mode admits a pinned client that restarts on the same address", async () => {
+  const serverSocket = await bind();
+  const peer = await bind();
+  const server = new CultNetRudpSocketTransportConnection({
+    runtimeId: "srv", socket: serverSocket, mode: "server", connectionId, resendPollMs: 20, resendDelayMs: 20,
+  });
+  const port = (serverSocket.address() as { port: number }).port;
+  const received: CultNetRudpPacket[] = [];
+  peer.on("message", (wire) => received.push(decodeRudpPacket(wire)));
+  const take = async (type: string) => {
+    for (let index = 0; index < 50; index += 1) {
+      const found = received.findIndex((packet) => packet.packetType === type);
+      if (found >= 0) return received.splice(found, 1)[0]!;
+      await sleep(10);
+    }
+    throw new Error(`no ${type} arrived`);
+  };
+  try {
+    const first = session(1);
+    peer.send(encodeRudpPacket(first.createConnect(0, enc("join"))), port, "127.0.0.1");
+    const accept = await take("accept");
+    first.receive(accept, 0);
+    peer.send(encodeRudpPacket(first.createAckForReceived(accept.sequence)), port, "127.0.0.1");
+    await sleep(50);
+    received.length = 0;
+
+    const restarted = session(1);
+    peer.send(encodeRudpPacket(restarted.createConnect(0, enc("join"))), port, "127.0.0.1");
+    restarted.receive(await take("ack"), 1);
+    assert.equal(restarted.connected, false);
+
+    peer.send(encodeRudpPacket(restarted.dueResends(3_000)[0]!), port, "127.0.0.1");
+    restarted.receive(await take("accept"), 3_001);
+    assert.ok(restarted.connected, "the restarted pinned client was never admitted");
+  } finally {
+    server.close();
+    peer.close();
+  }
+});