diff --git a/Cargo.lock b/Cargo.lock
index 4ec9cb8da..b0ff8477c 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -1300,7 +1300,7 @@ version = "1.1.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "40c48f72fd53cd289104fc64099abca73db4166ad86ea0b4341abe65af83dadc"
 dependencies = [
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -1311,7 +1311,7 @@ checksum = "291e6a250ff86cd4a820112fb8898808a366d8f9f58ce16d1f538353ad55747d"
 dependencies = [
  "anstyle",
  "once_cell_polyfill",
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -2710,7 +2710,7 @@ dependencies = [
  "bitflags 2.11.0",
  "cexpr",
  "clang-sys",
- "itertools 0.13.0",
+ "itertools 0.10.5",
  "log",
  "prettyplease",
  "proc-macro2",
@@ -2941,7 +2941,7 @@ dependencies = [
 [[package]]
 name = "bitvm"
 version = "0.1.0"
-source = "git+https://github.com/GOATNetwork/BitVM.git?branch=gc-v2#bab46c2336ad98513bcb8cbaff21b5506a4dcd9a"
+source = "git+https://github.com/GOATNetwork/BitVM.git?branch=committee-force-skip#c24f6cc2fb99d61f38b082202c899cf368abdae6"
 dependencies = [
  "ark-bn254",
  "ark-crypto-primitives",
@@ -2983,7 +2983,7 @@ dependencies = [
  "bincode",
  "bitcoin",
  "bitcoin-script",
- "bitvm 0.1.0 (git+https://github.com/GOATNetwork/BitVM.git?branch=gc-v2)",
+ "bitvm 0.1.0 (git+https://github.com/GOATNetwork/BitVM.git?branch=committee-force-skip)",
  "chacha20poly1305",
  "clap",
  "esplora-client",
@@ -3029,7 +3029,7 @@ dependencies = [
  "bitcoin",
  "bitcoin-light-client-circuit",
  "bitcoin-script",
- "bitvm 0.1.0 (git+https://github.com/GOATNetwork/BitVM.git?branch=gc-v2)",
+ "bitvm 0.1.0 (git+https://github.com/GOATNetwork/BitVM.git?branch=committee-force-skip)",
  "bitvm-gc",
  "blake3",
  "borsh",
@@ -4722,7 +4722,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "39cab71617ae0d63f51a36d69f866391735b51691dbda63cf6f96d042b63efeb"
 dependencies = [
  "libc",
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -5312,7 +5312,7 @@ dependencies = [
 [[package]]
 name = "goat"
 version = "0.1.0"
-source = "git+https://github.com/GOATNetwork/BitVM.git?branch=gc-v2#bab46c2336ad98513bcb8cbaff21b5506a4dcd9a"
+source = "git+https://github.com/GOATNetwork/BitVM.git?branch=committee-force-skip#c24f6cc2fb99d61f38b082202c899cf368abdae6"
 dependencies = [
  "ark-bn254",
  "ark-crypto-primitives",
@@ -5327,7 +5327,7 @@ dependencies = [
  "bitcoin",
  "bitcoin-script",
  "bitcoin-scriptexec",
- "bitvm 0.1.0 (git+https://github.com/GOATNetwork/BitVM.git?branch=gc-v2)",
+ "bitvm 0.1.0 (git+https://github.com/GOATNetwork/BitVM.git?branch=committee-force-skip)",
  "blake3",
  "clap",
  "colored",
@@ -7705,7 +7705,7 @@ version = "0.50.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "7957b9740744892f114936ab4a57b3f487491bbeafaf8083688b16841a4240e5"
 dependencies = [
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -10680,7 +10680,7 @@ dependencies = [
  "errno",
  "libc",
  "linux-raw-sys",
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -10771,7 +10771,7 @@ dependencies = [
  "security-framework 3.7.0",
  "security-framework-sys",
  "webpki-root-certs",
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -11504,7 +11504,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3a766e1110788c36f4fa1c2b71b387a7815aa65f88ce0229841826633d93723e"
 dependencies = [
  "libc",
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -12151,7 +12151,7 @@ dependencies = [
  "getrandom 0.4.2",
  "once_cell",
  "rustix",
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -13451,7 +13451,7 @@ version = "0.1.11"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c2a7b1c03c876122aa43f3020e6c3c3ee5c05081c9a00739faf7503aeba10d22"
 dependencies = [
- "windows-sys 0.61.2",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
diff --git a/Cargo.toml b/Cargo.toml
index 4e7e611c7..b270c52ff 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -29,8 +29,8 @@ members = [
 default-members = ["node"]
 
 [workspace.dependencies]
-bitvm = { git = "https://github.com/GOATNetwork/BitVM.git", branch = "gc-v2" }
-goat = { git = "https://github.com/GOATNetwork/BitVM.git", branch = "gc-v2" }
+bitvm = { git = "https://github.com/GOATNetwork/BitVM.git", branch = "committee-force-skip" }
+goat = { git = "https://github.com/GOATNetwork/BitVM.git", branch = "committee-force-skip" }
 
 libp2p = { version = "0.57.1", features = ["tokio", "kad", "noise", "tcp", "yamux", "rsa", "ping"] }
 libp2p-swarm-derive = "0.36.0"
diff --git a/crates/bitvm-gc/src/committee/api.rs b/crates/bitvm-gc/src/committee/api.rs
index 5e8a2d03f..962dadba2 100644
--- a/crates/bitvm-gc/src/committee/api.rs
+++ b/crates/bitvm-gc/src/committee/api.rs
@@ -45,6 +45,12 @@ pub fn operator_challenge_nack_pre_sign_num(watchtower_num: usize) -> usize {
 pub fn operator_commit_timeout_pre_sign_num() -> usize {
     2
 }
+pub fn force_skip_kickoff_pre_sign_num() -> usize {
+    1
+}
+pub fn quick_challenge_pre_sign_num() -> usize {
+    1
+}
 pub fn disprove_pre_sign_num(verifier_num: usize) -> usize {
     verifier_num * 2
 }
@@ -138,6 +144,10 @@ pub struct CommitteeMusig2Data<T> {
     pub operator_challenge_nack: Vec<T>,
     pub operator_commit_timeout: Vec<T>,
     pub disprove: Vec<T>,
+    /// Input 1 (the force-skip connector) of Force-Skip-Kickoff.
+    pub force_skip_kickoff: Vec<T>,
+    /// Input 1 (the force-skip connector) of Quick-Challenge.
+    pub quick_challenge: Vec<T>,
 }
 
 pub type CommitteeSecNonces = CommitteeMusig2Data<SecNonce>;
@@ -170,6 +180,14 @@ impl<T> CommitteeMusig2Data<T> {
             self.disprove.len() == disprove_pre_sign_num(verifier_num),
             "invalid number of disprove"
         );
+        ensure!(
+            self.force_skip_kickoff.len() == force_skip_kickoff_pre_sign_num(),
+            "invalid number of force skip kickoff"
+        );
+        ensure!(
+            self.quick_challenge.len() == quick_challenge_pre_sign_num(),
+            "invalid number of quick challenge"
+        );
         Ok(())
     }
 
@@ -182,6 +200,8 @@ impl<T> CommitteeMusig2Data<T> {
             operator_challenge_nack: vec![],
             operator_commit_timeout: vec![],
             disprove: vec![],
+            force_skip_kickoff: vec![],
+            quick_challenge: vec![],
         }
     }
 }
@@ -287,6 +307,20 @@ pub fn committee_presign_sighash_digest(graph: &BitvmGcGraph) -> Result<[u8; 32]
             TapSighashType::None,
         )?;
     }
+    add_sighash(
+        &mut hasher,
+        b"force_skip_kickoff/1/none",
+        &graph.force_skip_kickoff,
+        1,
+        TapSighashType::None,
+    )?;
+    add_sighash(
+        &mut hasher,
+        b"quick_challenge/1/none",
+        &graph.quick_challenge,
+        1,
+        TapSighashType::None,
+    )?;
     Ok(hasher.finalize().into())
 }
 
@@ -438,6 +472,26 @@ pub fn committee_pre_sign(
         res.disprove = disprove_sigs;
     }
 
+    {
+        // force skip kickoff
+        let sec_nonces = committee_member_sec_nonce.force_skip_kickoff.try_into().unwrap();
+        let agg_nonces = committee_agg_nonce.force_skip_kickoff.try_into().unwrap();
+        match graph.force_skip_kickoff.pre_sign(&committee_context, &sec_nonces, &agg_nonces) {
+            Ok(v) => res.force_skip_kickoff = v.to_vec(),
+            Err(e) => bail!("fail to pre-sign {}: {e}", graph.force_skip_kickoff.name()),
+        };
+    }
+
+    {
+        // quick challenge
+        let sec_nonces = committee_member_sec_nonce.quick_challenge.try_into().unwrap();
+        let agg_nonces = committee_agg_nonce.quick_challenge.try_into().unwrap();
+        match graph.quick_challenge.pre_sign(&committee_context, &sec_nonces, &agg_nonces) {
+            Ok(v) => res.quick_challenge = v.to_vec(),
+            Err(e) => bail!("fail to pre-sign {}: {e}", graph.quick_challenge.name()),
+        };
+    }
+
     Ok(res)
 }
 
@@ -480,6 +534,8 @@ pub fn nonces_aggregation(pub_nonces_vec: &[CommitteePubNonces]) -> Result<Commi
         operator_challenge_nack: aggregate_field(pub_nonces_vec, |c| &c.operator_challenge_nack)?,
         operator_commit_timeout: aggregate_field(pub_nonces_vec, |c| &c.operator_commit_timeout)?,
         disprove: aggregate_field(pub_nonces_vec, |c| &c.disprove)?,
+        force_skip_kickoff: aggregate_field(pub_nonces_vec, |c| &c.force_skip_kickoff)?,
+        quick_challenge: aggregate_field(pub_nonces_vec, |c| &c.quick_challenge)?,
     })
 }
 
@@ -596,6 +652,32 @@ pub fn signature_aggregation(
     }
     res.disprove = disprove_sigs;
 
+    // force skip kickoff
+    let force_skip_kickoff_agg_nonces = agg_nonces.force_skip_kickoff.clone().try_into().unwrap();
+    let force_skip_kickoff_partial_sigs =
+        [partial_sigs.iter().map(|r| r.force_skip_kickoff[0]).collect()];
+    match graph.force_skip_kickoff.aggregate_pre_sigs(
+        &context,
+        &force_skip_kickoff_partial_sigs,
+        &force_skip_kickoff_agg_nonces,
+    ) {
+        Ok(v) => res.force_skip_kickoff = v.to_vec(),
+        Err(e) => bail!("fail to aggregate pre-sigs {}: {e}", graph.force_skip_kickoff.name()),
+    };
+
+    // quick challenge
+    let quick_challenge_agg_nonces = agg_nonces.quick_challenge.clone().try_into().unwrap();
+    let quick_challenge_partial_sigs =
+        [partial_sigs.iter().map(|r| r.quick_challenge[0]).collect()];
+    match graph.quick_challenge.aggregate_pre_sigs(
+        &context,
+        &quick_challenge_partial_sigs,
+        &quick_challenge_agg_nonces,
+    ) {
+        Ok(v) => res.quick_challenge = v.to_vec(),
+        Err(e) => bail!("fail to aggregate pre-sigs {}: {e}", graph.quick_challenge.name()),
+    };
+
     Ok(res)
 }
 
@@ -905,6 +987,27 @@ pub fn verify_graph_committee_partial_sigs(
         )?;
     }
 
+    verify_pre_signed_input(
+        &graph.force_skip_kickoff,
+        committee_pubkeys,
+        committee_pubkey,
+        &pub_nonces.force_skip_kickoff[0],
+        partial_sigs.force_skip_kickoff[0],
+        &agg_nonces.force_skip_kickoff[0],
+        1,
+        TapSighashType::None,
+    )?;
+    verify_pre_signed_input(
+        &graph.quick_challenge,
+        committee_pubkeys,
+        committee_pubkey,
+        &pub_nonces.quick_challenge[0],
+        partial_sigs.quick_challenge[0],
+        &agg_nonces.quick_challenge[0],
+        1,
+        TapSighashType::None,
+    )?;
+
     Ok(())
 }
 
@@ -950,6 +1053,18 @@ pub fn verify_graph_committee_pre_signatures(graph: &BitvmGcGraph) -> Result<()>
         verify_taproot_pre_signed_input(tx, &committee_pubkey, 0, TapSighashType::None)?;
         verify_taproot_pre_signed_input(tx, &committee_pubkey, 1, TapSighashType::None)?;
     }
+    verify_taproot_pre_signed_input(
+        &graph.force_skip_kickoff,
+        &committee_pubkey,
+        1,
+        TapSighashType::None,
+    )?;
+    verify_taproot_pre_signed_input(
+        &graph.quick_challenge,
+        &committee_pubkey,
+        1,
+        TapSighashType::None,
+    )?;
     Ok(())
 }
 
@@ -1040,6 +1155,15 @@ pub fn push_committee_pre_signatures(
         );
     }
 
+    // force skip kickoff and quick challenge
+    let force_skip_connector = graph.parameters.force_skip_connector();
+    graph
+        .force_skip_kickoff
+        .push_pre_sigs(&force_skip_connector, sigs.force_skip_kickoff.clone().try_into().unwrap());
+    graph
+        .quick_challenge
+        .push_pre_sigs(&force_skip_connector, sigs.quick_challenge.clone().try_into().unwrap());
+
     graph.committee_pre_signed = true;
     Ok(())
 }
@@ -1138,6 +1262,28 @@ pub fn generate_nonce_from_seed(
             index += 1;
         }
     }
+    {
+        // force skip kickoff
+        for _ in 0..force_skip_kickoff_pre_sign_num() {
+            let (sec_nonce, pub_nonce, nonce_sig) =
+                generate_nonce(signer_keypair, &graph_seed, index);
+            pub_nonces.force_skip_kickoff.push(pub_nonce);
+            sec_nonces.force_skip_kickoff.push(sec_nonce);
+            nonce_sigs.force_skip_kickoff.push(nonce_sig);
+            index += 1;
+        }
+    }
+    {
+        // quick challenge
+        for _ in 0..quick_challenge_pre_sign_num() {
+            let (sec_nonce, pub_nonce, nonce_sig) =
+                generate_nonce(signer_keypair, &graph_seed, index);
+            pub_nonces.quick_challenge.push(pub_nonce);
+            sec_nonces.quick_challenge.push(sec_nonce);
+            nonce_sigs.quick_challenge.push(nonce_sig);
+            index += 1;
+        }
+    }
     (pub_nonces, sec_nonces, nonce_sigs)
 }
 
@@ -1176,7 +1322,9 @@ pub fn verify_nonce_signatures(
             &pub_nonces.operator_commit_timeout,
             &nonce_sigs.operator_commit_timeout,
         )
-        && verify_vec(pubkey, &pub_nonces.disprove, &nonce_sigs.disprove))
+        && verify_vec(pubkey, &pub_nonces.disprove, &nonce_sigs.disprove)
+        && verify_vec(pubkey, &pub_nonces.force_skip_kickoff, &nonce_sigs.force_skip_kickoff)
+        && verify_vec(pubkey, &pub_nonces.quick_challenge, &nonce_sigs.quick_challenge))
 }
 
 pub(crate) fn generate_nonce(
diff --git a/crates/bitvm-gc/src/operator/api.rs b/crates/bitvm-gc/src/operator/api.rs
index d0ed018b7..de9ffc0dc 100644
--- a/crates/bitvm-gc/src/operator/api.rs
+++ b/crates/bitvm-gc/src/operator/api.rs
@@ -65,7 +65,7 @@ pub fn generate_commit_pubin_wots_key(
 }
 
 pub fn operator_presig_num() -> usize {
-    6
+    4
 }
 
 pub fn generate_bitvm_graph(params: BitvmGcGraphParameters) -> Result<BitvmGcGraph> {
@@ -340,24 +340,15 @@ pub fn operator_pre_sign(
 
     // presign force_skip_kickoff
     let kickoff_connector = graph.parameters.kickoff_connector();
-    let next_force_skip_connector = graph.parameters.force_skip_connector();
-    graph.force_skip_kickoff.pre_sign_and_push(
-        &context,
-        &kickoff_connector,
-        &next_force_skip_connector,
-    );
+    // Input 1 of both penalties spends the force-skip connector and is signed by
+    // the committee.
+    graph.force_skip_kickoff.pre_sign_and_push(&context, &kickoff_connector);
     wits.push(graph.force_skip_kickoff.tx().input[0].witness.clone());
-    wits.push(graph.force_skip_kickoff.tx().input[1].witness.clone());
 
     // presign quick_challenge
     let guardian_connector = graph.guardian_connector();
-    graph.quick_challenge.pre_sign_and_push(
-        &context,
-        &guardian_connector,
-        &next_force_skip_connector,
-    );
+    graph.quick_challenge.pre_sign_and_push(&context, &guardian_connector);
     wits.push(graph.quick_challenge.tx().input[0].witness.clone());
-    wits.push(graph.quick_challenge.tx().input[1].witness.clone());
 
     // presign challenge_incomplete_kickoff
     let next_prekickoff_connector = graph.parameters.prekickoff_connector();
@@ -385,11 +376,9 @@ pub fn push_operator_pre_signature(
     };
 
     graph.force_skip_kickoff.tx_mut().input[0].witness = signed_witness[0].clone();
-    graph.force_skip_kickoff.tx_mut().input[1].witness = signed_witness[1].clone();
-    graph.quick_challenge.tx_mut().input[0].witness = signed_witness[2].clone();
-    graph.quick_challenge.tx_mut().input[1].witness = signed_witness[3].clone();
-    graph.challenge_incomplete_kickoff.tx_mut().input[0].witness = signed_witness[4].clone();
-    graph.challenge_incomplete_kickoff.tx_mut().input[1].witness = signed_witness[5].clone();
+    graph.quick_challenge.tx_mut().input[0].witness = signed_witness[1].clone();
+    graph.challenge_incomplete_kickoff.tx_mut().input[0].witness = signed_witness[2].clone();
+    graph.challenge_incomplete_kickoff.tx_mut().input[1].witness = signed_witness[3].clone();
 
     graph.operator_pre_signed = true;
     Ok(())
@@ -407,24 +396,12 @@ pub fn verify_graph_operator_pre_signatures(graph: &BitvmGcGraph) -> Result<()>
         0,
         TapSighashType::None,
     )?;
-    verify_taproot_pre_signed_input(
-        &graph.force_skip_kickoff,
-        &operator_pubkey,
-        1,
-        TapSighashType::None,
-    )?;
     verify_taproot_pre_signed_input(
         &graph.quick_challenge,
         &operator_pubkey,
         0,
         TapSighashType::None,
     )?;
-    verify_taproot_pre_signed_input(
-        &graph.quick_challenge,
-        &operator_pubkey,
-        1,
-        TapSighashType::None,
-    )?;
     verify_taproot_pre_signed_input(
         &graph.challenge_incomplete_kickoff,
         &operator_pubkey,
diff --git a/crates/bitvm-gc/src/types.rs b/crates/bitvm-gc/src/types.rs
index 829725b7d..dadecdfcf 100644
--- a/crates/bitvm-gc/src/types.rs
+++ b/crates/bitvm-gc/src/types.rs
@@ -387,8 +387,10 @@ impl BitvmGcGraphParameters {
         PrekickoffConnector::new(self.network(), &self.operator_taproot_public_key())
     }
 
+    /// Output 0 of the next Pre-Kickoff. It is locked to this graph's committee,
+    /// which pre-signs its spend in Quick-Challenge and Force-Skip-Kickoff.
     pub fn force_skip_connector(&self) -> ForceSkipConnector {
-        ForceSkipConnector::new(self.network(), &self.operator_taproot_public_key())
+        ForceSkipConnector::new(self.network(), &self.n_of_n_taproot_public_key())
     }
 
     pub fn kickoff_connector(&self) -> KickoffConnector {
@@ -712,9 +714,7 @@ impl BitvmGcGraph {
         let operator_pre_sigs = if self.operator_pre_signed {
             Some(vec![
                 self.force_skip_kickoff.tx().input[0].witness.clone(),
-                self.force_skip_kickoff.tx().input[1].witness.clone(),
                 self.quick_challenge.tx().input[0].witness.clone(),
-                self.quick_challenge.tx().input[1].witness.clone(),
                 self.challenge_incomplete_kickoff.tx().input[0].witness.clone(),
                 self.challenge_incomplete_kickoff.tx().input[1].witness.clone(),
             ])
@@ -747,6 +747,10 @@ impl BitvmGcGraph {
                 disprove.push(extract_sig_from_witness(&disprove_tx.tx().input[0].witness)?);
                 disprove.push(extract_sig_from_witness(&disprove_tx.tx().input[1].witness)?);
             }
+            let force_skip_kickoff =
+                vec![extract_sig_from_witness(&self.force_skip_kickoff.tx().input[1].witness)?];
+            let quick_challenge =
+                vec![extract_sig_from_witness(&self.quick_challenge.tx().input[1].witness)?];
             Some(CommitteeSignatures {
                 take1,
                 take2,
@@ -755,6 +759,8 @@ impl BitvmGcGraph {
                 operator_challenge_nack,
                 operator_commit_timeout,
                 disprove,
+                force_skip_kickoff,
+                quick_challenge,
             })
         } else {
             None
diff --git a/crates/bitvm-gc/src/verifier/api.rs b/crates/bitvm-gc/src/verifier/api.rs
index 8cb87467d..20c01a873 100644
--- a/crates/bitvm-gc/src/verifier/api.rs
+++ b/crates/bitvm-gc/src/verifier/api.rs
@@ -79,6 +79,10 @@ pub fn build_force_skip_kickoff_tx(
     if !graph.operator_pre_signed() {
         bail!("missing pre-signatures from operator")
     };
+    // Input 1 spends the force-skip connector, which only the committee signs.
+    if !graph.committee_pre_signed() {
+        bail!("missing pre-signatures from committee")
+    };
     let mut tx = graph.force_skip_kickoff.tx().clone();
     let total_input_amount = graph.force_skip_kickoff.prev_outs().iter().map(|o| o.value).sum();
     let anchor_added = add_change_or_anchor_output(
@@ -100,6 +104,10 @@ pub fn build_quick_challenge_tx(
     if !graph.operator_pre_signed() {
         bail!("missing pre-signatures from operator")
     };
+    // Input 1 spends the force-skip connector, which only the committee signs.
+    if !graph.committee_pre_signed() {
+        bail!("missing pre-signatures from committee")
+    };
     let mut tx = graph.quick_challenge.tx().clone();
     let total_input_amount = graph.quick_challenge.prev_outs().iter().map(|o| o.value).sum();
     let anchor_added = add_change_or_anchor_output(
diff --git a/crates/bitvm-gc/tests/transaction_graph_invariants.rs b/crates/bitvm-gc/tests/transaction_graph_invariants.rs
index 205a12149..144a428d3 100644
--- a/crates/bitvm-gc/tests/transaction_graph_invariants.rs
+++ b/crates/bitvm-gc/tests/transaction_graph_invariants.rs
@@ -196,6 +196,66 @@ fn csv_inputs_and_scripts_match_network_parameters() {
     }
 }
 
+#[test]
+fn committee_signs_both_spends_of_the_force_skip_connector() {
+    use bitcoin::{
+        TapSighashType, XOnlyPublicKey,
+        key::Keypair,
+        secp256k1::{SECP256K1, SecretKey},
+    };
+    use bitvm_lib::{committee::*, connectors::base::TaprootConnector, operator::*};
+
+    let mut graph = generate_bitvm_graph(graph_parameters(Network::Regtest, 1, 1)).unwrap();
+    let mut seed = [0u8; 32];
+    seed[28..].copy_from_slice(&1u32.to_be_bytes());
+    let keypair = Keypair::from_secret_key(SECP256K1, &SecretKey::from_slice(&seed).unwrap());
+    let committee_pubkeys = graph.parameters.instance_parameters.committee_pubkeys.clone();
+
+    let force_skip = graph.parameters.force_skip_connector();
+    assert_eq!(force_skip.n_of_n_taproot_public_key, graph.parameters.n_of_n_taproot_public_key());
+    assert_eq!(
+        graph.next_prekickoff.tx().output[0].script_pubkey,
+        force_skip.generate_taproot_address().script_pubkey()
+    );
+
+    let witnesses = operator_pre_sign(keypair, &mut graph).unwrap();
+    assert_eq!(witnesses.len(), operator_presig_num());
+    verify_graph_operator_pre_signatures(&graph).unwrap();
+
+    let (pub_nonces, sec_nonces, _) = generate_nonce_from_seed("seed".into(), 0, keypair, 1, 1);
+    let agg_nonces = nonces_aggregation(std::slice::from_ref(&pub_nonces)).unwrap();
+    let partial = committee_pre_sign(keypair, sec_nonces, agg_nonces.clone(), &mut graph).unwrap();
+    verify_graph_committee_partial_sigs(
+        &graph,
+        &committee_pubkeys,
+        &committee_pubkeys[0],
+        &pub_nonces,
+        &agg_nonces,
+        &partial,
+    )
+    .unwrap();
+    let sigs = signature_aggregation(&vec![partial], &agg_nonces, &graph).unwrap();
+    push_committee_pre_signatures(&mut graph, &sigs).unwrap();
+    verify_graph_committee_pre_signatures(&graph).unwrap();
+
+    // The operator's key cannot spend the connector.
+    let operator = XOnlyPublicKey::from(graph.parameters.operator_pubkey);
+    for tx in [graph.quick_challenge.tx(), graph.force_skip_kickoff.tx()] {
+        assert_eq!(tx.input[1].witness.len(), 3);
+    }
+    assert!(
+        verify_taproot_pre_signed_input(&graph.quick_challenge, &operator, 1, TapSighashType::None)
+            .is_err()
+    );
+
+    let restored =
+        bitvm_lib::types::BitvmGcGraph::from_simplified(&graph.to_simplified().unwrap()).unwrap();
+    verify_graph_operator_pre_signatures(&restored).unwrap();
+    verify_graph_committee_pre_signatures(&restored).unwrap();
+    assert_eq!(restored.quick_challenge.tx(), graph.quick_challenge.tx());
+    assert_eq!(restored.force_skip_kickoff.tx(), graph.force_skip_kickoff.tx());
+}
+
 fn graph_parameters(
     network: bitcoin::Network,
     watchtowers: usize,
diff --git a/node/src/aggregates/graph_pegout_jobs.rs b/node/src/aggregates/graph_pegout_jobs.rs
index 5bfef22de..b7a424799 100644
--- a/node/src/aggregates/graph_pegout_jobs.rs
+++ b/node/src/aggregates/graph_pegout_jobs.rs
@@ -523,6 +523,13 @@ async fn enforce_previous_slot(deps: &JobDeps, graph: &BitvmGcGraph) -> Result<S
     if !tx_confirmed(btc, &prekickoff_txid).await? {
         return after_blocks(deps, "pre-kickoff is not confirmed yet", 1);
     }
+    // Quick-Challenge and Force-Skip-Kickoff both spend this Pre-Kickoff's
+    // force-skip connector, so a spent connector means one of them already ran.
+    let force_skip_connector = output_topology::prekickoff::force_skip_connector() as u64;
+    let spend = spend_of(btc, &prekickoff_txid, force_skip_connector).await?;
+    if let Some(step) = settled_by(deps, &spend, "force-skip connector") {
+        return step;
+    }
     let operator_pubkey = graph.parameters.operator_pubkey.to_string();
     let previous_slot = graph_nonce - 1;
     let previous_id = deps
@@ -582,6 +589,9 @@ async fn enforce_previous_slot(deps: &JobDeps, graph: &BitvmGcGraph) -> Result<S
         if let Some(step) = settled_by(deps, &spend, "previous slot's kickoff connector") {
             return step;
         }
+        if !previous.committee_pre_signed() {
+            return Step::retry("previous graph has no committee pre-signatures", 600);
+        }
         let txid = verifier_force_skip_kickoff(btc, &previous).await?;
         info!(event = "graph_punish", graph_id = %previous_row.graph_id, txid = %txid, "Force-Skip-Kickoff broadcast");
         return broadcast_pending(deps, &format!("Force-Skip-Kickoff {txid}"));
@@ -594,6 +604,9 @@ async fn enforce_previous_slot(deps: &JobDeps, graph: &BitvmGcGraph) -> Result<S
     if let Some(step) = settled_by(deps, &spend, "previous slot's guardian connector") {
         return step;
     }
+    if !previous.committee_pre_signed() {
+        return Step::retry("previous graph has no committee pre-signatures", 600);
+    }
     let txid = verifier_quick_challenge(btc, &previous).await?;
     info!(event = "graph_punish", graph_id = %previous_row.graph_id, txid = %txid, "Quick-Challenge broadcast");
     broadcast_pending(deps, &format!("Quick-Challenge {txid}"))
diff --git a/node/src/utils/graph_tx.rs b/node/src/utils/graph_tx.rs
index 47e24b944..9c0b6d41b 100644
--- a/node/src/utils/graph_tx.rs
+++ b/node/src/utils/graph_tx.rs
@@ -109,6 +109,8 @@ pub async fn build_genesis_prekickoff_tx(
     let node_keypair = operator_master_key.master_keypair();
     let operator_taproot_public_key = node_keypair.x_only_public_key().0;
     let cur_prekickoff_connector = PrekickoffConnector::new(network, &operator_taproot_public_key);
+    // No graph precedes the genesis Pre-Kickoff, so no committee guards its
+    // force-skip connector and nothing pre-signs a spend of it.
     let next_force_skip_connector = ForceSkipConnector::new(network, &operator_taproot_public_key);
     let next_kickoff_connector = KickoffConnector::new(network, &operator_taproot_public_key);
     let next_prekickoff_connector = PrekickoffConnector::new(network, &operator_taproot_public_key);