refuse an announced tip the header sync cannot link in, reverting to the store tip with a warning

### src/main/java/com/sparrowwallet/sparrow/net/ElectrumServer.java
@@ -1663,6 +1663,22 @@ private void reconcile(HeaderStore store, int tipHeight) throws ServerException,
         }
     }
 
+    /**
+     * The tip of the verified header store, whose header is null while the store holds nothing above the last pin.
+     */
+    static ChainTip getStoreTip() throws ServerException {
+        HeaderStore store = getHeaderStore();
+        try {
+            //The store's monitor, so that a reorg cannot truncate it between reading the tip height and the header at that height
+            synchronized(store) {
+                int tipHeight = store.getTipHeight();
+                return new ChainTip(tipHeight, store.getHeader(tipHeight));
+            }
+        } catch(IOException e) {
+            throw new ServerException("Could not read the block header store", e);
+        }
+    }
+
     /**
      * The header at the given height verified against the compiled-in checkpoints, or null where the connected server cannot substantiate it, which is
      * reported as a refusal. Heights above the last pin are served from the store, and those below it by hash linkage to a pin.
@@ -3407,17 +3423,57 @@ public static class HeaderSyncService extends ScheduledService<Void> {
         //The pair from the event that last restarted this service: the height and the header of one announcement, never of two
         private volatile ChainTip announcedTip;
 
+        //The announcement whose run last failed, so that one still unsubstantiated when its retry fails too is refused rather than retried indefinitely.
+        //Held as the tip rather than a count, since a run cancelled by a later announcement can still fail after it and would spend that one's retry
+        private volatile ChainTip failedTip;
+
         @Override
         protected Task<Void> createTask() {
             return new Task<>() {
                 @Override
                 protected Void call() throws Exception {
-                    syncAnnouncedHeaders(announcedTip);
+                    ChainTip tip = announcedTip;
+                    try {
+                        syncAnnouncedHeaders(tip);
+                    } catch(VerificationException | UnsupportedMethodException e) {
+                        refuseAnnouncedTip(tip, e);
+                    } catch(ServerException | ElectrumServerRpcException e) {
+                        //A failed call says nothing about the chain on its own, but a server answering every request for these headers with an error
+                        //has not substantiated the tip any more than one serving the wrong headers
+                        if(failedTip != tip || !isConnected()) {
+                            failedTip = tip;
+                            throw e;
+                        }
+
+                        refuseAnnouncedTip(tip, e);
+                    }
+
                     return null;
                 }
             };
         }
 
+        /**
+         * Warns of an announced tip the header sync could not substantiate, and sets the chain tip back to the verified store tip where the store holds a
+         * header to set it back to, an empty store leaving only the warning. An announced header need
+         * only meet the target it claims for itself, which at the minimum difficulty costs nothing to produce, so until it links into the chain the height
+         * it arrived with is only the server's claim, as is every confirmation count taken from it.
+         */
+        private void refuseAnnouncedTip(ChainTip tip, Exception e) throws ServerException {
+            ChainTip storeTip = getStoreTip();
+            Platform.runLater(() -> {
+                //A run overtaken by a later announcement has nothing left to correct
+                if(tip != announcedTip) {
+                    return;
+                }
+
+                if(storeTip.header() != null) {
+                    EventManager.get().post(new NewBlockEvent(storeTip.height(), storeTip.header()));
+                }
+                warnInvalidTip("Could not verify the block header chain to the tip announced at height " + tip.height() + ": " + e.getMessage());
+            });
+        }
+
         /**
          * The body of a run, which happens on a background thread: the connection check is therefore the transport level one, since AppServices reads
          * a JavaFX Service and may only be called from the application thread. Without the check a retry firing after the connection closed would
@@ -3434,8 +3490,9 @@ static void syncAnnouncedHeaders(ChainTip tip) throws ServerException {
             } catch(UnsupportedMethodException e) {
                 //Without this call the store can never advance, so verification would refuse every new confirmation for the rest of the session
                 if(isVerificationMandatory()) {
-                    //Leaving the capability on is what lets the next wallet history thread raise this and rotate the server, which this service cannot do
-                    log.warn("Server does not support " + e.getMethod() + ", which is required to verify transactions");
+                    //Leaving the capability on is what lets the next wallet history thread raise this and rotate the server, which this service cannot do.
+                    //Rethrown so the tip is refused: where verification is mandatory, a server without the call has not substantiated the height it announced
+                    throw e;
                 } else {
                     log.warn("Server does not support " + e.getMethod() + ", disabling transaction verification for this session");
                     serverCapability.withMerkleProofs(false);

### src/test/java/com/sparrowwallet/sparrow/net/HeaderSyncTest.java
@@ -13,6 +13,7 @@
 import com.sparrowwallet.sparrow.EventManager;
 import com.sparrowwallet.sparrow.SparrowWallet;
 import com.sparrowwallet.sparrow.event.ChainReorgEvent;
+import com.sparrowwallet.sparrow.io.Config;
 import com.sparrowwallet.sparrow.io.Storage;
 import com.google.common.eventbus.Subscribe;
 import org.junit.jupiter.api.AfterAll;
@@ -38,6 +39,7 @@
 import java.util.stream.Stream;
 
 import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertFalse;
 import static org.junit.jupiter.api.Assertions.assertNull;
 import static org.junit.jupiter.api.Assertions.assertThrows;
 import static org.junit.jupiter.api.Assertions.assertTrue;
@@ -741,6 +743,55 @@ public void doesNotSyncOnceTheConnectionHasGone() throws Exception {
         assertEquals(0, fake.getChunkRequests());
     }
 
+    /**
+     * An announced header need only meet the target it claims for itself, which at the minimum difficulty costs nothing to produce, so a server can
+     * announce a height the chain has not reached. The sync refuses such a tip, and the store tip it leaves behind - holding the honest headers the
+     * server did serve - is the verified height the chain tip is set back to. An empty store has no header to set it back to.
+     */
+    @Test
+    public void refusesAnAnnouncedTipAboveTheChainTheServerServes() throws Exception {
+        List<BlockHeader> chain = mineChain(Network.REGTEST.getGenesisHeader(), 12, CHAIN_TIME);
+        BlockHeader unlinked = mineChain(Network.REGTEST.getGenesisHeader(), 1, BRANCH_TIME).getFirst();
+        assertNull(ElectrumServer.getStoreTip().header());
+
+        seedStore(chain, 10);
+        serve(chain);
+        assertThrows(VerificationException.class, () -> ElectrumServer.HeaderSyncService.syncAnnouncedHeaders(new ChainTip(5000, unlinked)));
+
+        ChainTip storeTip = ElectrumServer.getStoreTip();
+        assertEquals(12, storeTip.height());
+        assertEquals(chain.getLast().getHash(), storeTip.header().getHash());
+    }
+
+    /**
+     * Where verification is mandatory, a server answering that it has no block.headers has not substantiated the tip it announced, so the failure must
+     * reach the service as itself for the tip to be refused - with the capability still on, which is what lets a history pass rotate the server. A
+     * private server answering the same has verification turned off for the session instead, and is never refused.
+     */
+    @Test
+    public void refusesATipFromAMandatoryServerWithoutTheHeadersCall() throws Exception {
+        Network.set(Network.MAINNET);
+        ServerCapability previousCapability = ElectrumServer.serverCapability;
+        ServerType previousServerType = Config.get().getServerType();
+        try {
+            FakeElectrumServerRpc fake = serve(List.of());
+            fake.setFailure(new UnsupportedMethodException("blockchain.block.headers", new IllegalStateException()));
+            ChainTip tip = new ChainTip(Network.MAINNET.getHeaderCheckpoints().getMaxHeight() + 10, Network.MAINNET.getGenesisHeader());
+
+            ElectrumServer.serverCapability = new ServerCapability(false, false, false);
+            Config.get().setServerType(ServerType.PUBLIC_ELECTRUM_SERVER);
+            assertThrows(UnsupportedMethodException.class, () -> ElectrumServer.HeaderSyncService.syncAnnouncedHeaders(tip));
+            assertTrue(ElectrumServer.serverCapability.supportsMerkleProofs());
+
+            Config.get().setServerType(ServerType.ELECTRUM_SERVER);
+            ElectrumServer.HeaderSyncService.syncAnnouncedHeaders(tip);
+            assertFalse(ElectrumServer.serverCapability.supportsMerkleProofs());
+        } finally {
+            Config.get().setServerType(previousServerType);
+            ElectrumServer.serverCapability = previousCapability;
+        }
+    }
+
     private static void runOffThread(Callable<Void> task) throws Exception {
         ExecutorService executorService = Executors.newSingleThreadExecutor();
         try {