diff --git a/packages/kernel/codec/blocks.js b/packages/kernel/codec/blocks.js
index d38a471..93974b0 100644
--- a/packages/kernel/codec/blocks.js
+++ b/packages/kernel/codec/blocks.js
@@ -227,6 +227,7 @@ export class BlockEngine {
       i === 0 ? NULL_TXID : this.codec.wtxid(tx));
     const root = hexToBytes(this.codec.merkleRoot(wtxids)).reverse();
     const reserved = hexToBytes(block.transactions[0].witness?.[0]?.[0] ?? '00'.repeat(32));
+    if (reserved.length !== 32) return null; // malformed reserved value can never match the commitment
     const cat = new Uint8Array(64);
     cat.set(root); cat.set(reserved, 32);
     return bytesToHex(dsha256(cat));
diff --git a/packages/kernel/codec/codec.js b/packages/kernel/codec/codec.js
index ff0b666..28fd457 100644
--- a/packages/kernel/codec/codec.js
+++ b/packages/kernel/codec/codec.js
@@ -80,6 +80,10 @@ class Writer {
 export class Codec {
   constructor(...schemas) {
     this.types = new Map();
+    // Network proof-of-work ceiling, as a BigInt. Null until chain params are
+    // supplied; checkProofOfWork skips only the network-specific bound while
+    // it is unset, never the universal range checks.
+    this.powLimit = null;
     for (const schema of schemas) {
       for (const node of schema['@graph'] ?? []) {
         if (node['@type'] === 'ConsensusStruct') this.types.set(shortId(node['@id']), node);
@@ -87,6 +91,14 @@ export class Codec {
     }
   }
 
+  // Supply the network parameters the consensus checks need. Called by
+  // createKernel and by HeaderEngine.fromSchemas; safe to call directly when
+  // constructing a Codec by hand.
+  setChainParams(params) {
+    if (params?.powLimit != null) this.powLimit = BigInt('0x' + params.powLimit);
+    return this;
+  }
+
   def(typeName) {
     const def = this.types.get(typeName);
     if (!def) throw new Error(`unknown type: ${typeName}`);
@@ -275,7 +287,34 @@ export class Codec {
     return exponent <= 3 ? mantissa >> (8n * BigInt(3 - exponent)) : mantissa << (8n * BigInt(exponent - 3));
   }
 
-  checkProofOfWork(header) {
-    return BigInt('0x' + this.blockHash(header)) <= this.expandCompact(header.bits);
+  // The target plus the two flags Bitcoin Core's arith_uint256::SetCompact
+  // reports. `negative` is the sign bit the mantissa mask discards; `overflow`
+  // marks an nBits whose target cannot fit in 256 bits. Both make a header
+  // invalid regardless of network.
+  expandCompactChecked(bits) {
+    const size = bits >>> 24;
+    const word = bits & 0x007fffff;
+    return {
+      target: this.expandCompact(bits),
+      negative: word !== 0 && (bits & 0x00800000) !== 0,
+      overflow: word !== 0 && (size > 34
+        || (word > 0xff && size > 33)
+        || (word > 0xffff && size > 32)),
+    };
+  }
+
+  // Core's CheckProofOfWork: the target must be in range *before* the hash is
+  // compared against it. Without the range checks any nBits claiming an easier
+  // target than the network permits is accepted, which makes a proof of work
+  // free to forge.
+  //
+  // `powLimit` defaults to the value set on this codec (see `setChainParams`);
+  // when neither is available the network-specific bound cannot be applied, but
+  // the negative, zero and overflow checks always are.
+  checkProofOfWork(header, powLimit = this.powLimit) {
+    const { target, negative, overflow } = this.expandCompactChecked(header.bits);
+    if (negative || overflow || target === 0n) return false;
+    if (powLimit != null && target > powLimit) return false;
+    return BigInt('0x' + this.blockHash(header)) <= target;
   }
 }
diff --git a/packages/kernel/codec/headers.js b/packages/kernel/codec/headers.js
index 5184454..02f3c96 100644
--- a/packages/kernel/codec/headers.js
+++ b/packages/kernel/codec/headers.js
@@ -57,6 +57,9 @@ export class HeaderEngine {
   static fromSchemas(codec, chainSchema, validateSchema, network = 'btc:mainnet') {
     const params = chainSchema['@graph'].find((n) => n['@id'] === network);
     const ruleSet = validateSchema['@graph'].find((n) => n['@type'] === 'RuleSet' && n.phase === 'header');
+    // The SPV ruleset has no difficulty rule, so btc:rule-spv-pow is the only
+    // work check there; the codec needs the ceiling to enforce it.
+    codec.setChainParams(params);
     return new HeaderEngine(codec, params, ruleSet);
   }
 
diff --git a/packages/kernel/index.js b/packages/kernel/index.js
index 3504904..41054a3 100644
--- a/packages/kernel/index.js
+++ b/packages/kernel/index.js
@@ -17,13 +17,14 @@ export * from './codec/hash.js';
 export * from './codec/secp256k1.js';
 export const schemas = { core, proof, script, chain, validate };
 
-export function createKernel() {
+export function createKernel(network = 'btc:mainnet') {
   const codec = new Codec(core, proof);
-  const scriptEngine = ScriptEngine.fromSchemas(script, chain);
+  codec.setChainParams(chain['@graph'].find((n) => n['@id'] === network));
+  const scriptEngine = ScriptEngine.fromSchemas(script, chain, network);
   const limits = script['@graph'].find((n) => n['@id'] === 'btc:scriptLimits');
   const interpreter = new ScriptInterpreter(codec, scriptEngine, limits);
-  const headers = HeaderEngine.fromSchemas(codec, chain, validate);
-  const blocks = BlockEngine.fromSchemas(codec, chain, validate, script);
+  const headers = HeaderEngine.fromSchemas(codec, chain, validate, network);
+  const blocks = BlockEngine.fromSchemas(codec, chain, validate, script, network);
   const spv = SpvEngine.fromSchemas(codec, validate);
   return { codec, script: scriptEngine, interpreter, headers, blocks, spv, schemas };
 }
diff --git a/tools/sync-kernel.mjs b/tools/sync-kernel.mjs
index f37cd2e..c89d35f 100644
--- a/tools/sync-kernel.mjs
+++ b/tools/sync-kernel.mjs
@@ -3,7 +3,8 @@
 // step: re-run this, review the diff, commit. The engine's canonical dev home
 // stays bitcoin-desktop/schema; this is a vendored copy.
 //
-//   PIN: bitcoin-desktop/schema @ b213128 (Fix #70 OP_CODESEPARATOR, PR #71)
+//   PIN: bitcoin-desktop/schema @ PENDING (PoW target range checks + witness
+//        reserved-value guard, PR #72) — update to the merge SHA before landing.
 //
 // Sources (override via env for non-default checkouts):
 //   SCHEMA_DIR  — the schema repo (codec/ + schema/*.jsonld)
@@ -32,8 +33,17 @@ for (const k of SCHEMAS) {
 // wasm: copy, and make the loader fetch the wasm co-located with the MODULE
 // (import.meta.url) so it works served from any URL / the CDN.
 await copyFile(new URL('secp256k1.wasm', WASM), new URL('wasm/secp256k1.wasm', OUT));
-const loader = (await readFile(new URL('secp-wasm.js', WASM), 'utf8'))
-  .replace(/loadSecpWasm\(url = [^)]*\)/, "loadSecpWasm(url = new URL('./secp256k1.wasm', import.meta.url).href)");
+const WASM_DEFAULT_URL = "loadSecpWasm(url = new URL('./secp256k1.wasm', import.meta.url).href)";
+let loader = await readFile(new URL('secp-wasm.js', WASM), 'utf8');
+// Idempotent: the replacement text contains a ')', so [^)]* matches this
+// rewrite's own output and would corrupt it on a second pass. That happens
+// whenever WASM_DIR points at a previously generated copy.
+if (!loader.includes(WASM_DEFAULT_URL)) {
+  if (!/loadSecpWasm\(url = [^)]*\)/.test(loader)) {
+    throw new Error('secp-wasm.js: no loadSecpWasm(url = ...) default to rewrite');
+  }
+  loader = loader.replace(/loadSecpWasm\(url = [^)]*\)/, WASM_DEFAULT_URL);
+}
 await writeFile(new URL('wasm/secp-wasm.js', OUT), loader);
 
 // barrel + package.json
@@ -56,13 +66,14 @@ export * from './codec/hash.js';
 export * from './codec/secp256k1.js';
 export const schemas = { core, proof, script, chain, validate };
 
-export function createKernel() {
+export function createKernel(network = 'btc:mainnet') {
   const codec = new Codec(core, proof);
-  const scriptEngine = ScriptEngine.fromSchemas(script, chain);
+  codec.setChainParams(chain['@graph'].find((n) => n['@id'] === network));
+  const scriptEngine = ScriptEngine.fromSchemas(script, chain, network);
   const limits = script['@graph'].find((n) => n['@id'] === 'btc:scriptLimits');
   const interpreter = new ScriptInterpreter(codec, scriptEngine, limits);
-  const headers = HeaderEngine.fromSchemas(codec, chain, validate);
-  const blocks = BlockEngine.fromSchemas(codec, chain, validate, script);
+  const headers = HeaderEngine.fromSchemas(codec, chain, validate, network);
+  const blocks = BlockEngine.fromSchemas(codec, chain, validate, script, network);
   const spv = SpvEngine.fromSchemas(codec, validate);
   return { codec, script: scriptEngine, interpreter, headers, blocks, spv, schemas };
 }