Multi-Party Channels: Coinpools & Factories

• Multi-party channels are off-chain constructions that allow multiple participants to jointly fund and transact within a shared structure, reducing liquidity fragmentation.
• They employ leaderless, DAG-based state update protocols to securely coordinate concurrent transactions and efficiently distribute fees among users.
• Capital efficiency is significantly improved as pooled funds minimize on-chain interactions and increase transaction success rates compared to traditional two-party channels.

Multi-party channels—including coinpools and channel factories—are a class of off-chain constructions for decentralized payment systems in which multiple users jointly fund and transact within a shared off-chain structure. These primitives are formalized as collectively funded channels (hyperedges) in payment channel networks (PCNs), supporting highly concurrent, capital-efficient payment flows and improved liquidity management compared to two-party channels. Multi-party channels generalize prior two-party frameworks and, by redesigning state-update and settlement logic, address liquidity fragmentation, channel depletion, and routing inefficiencies inherent to traditional PCNs.

1. Formal Hypergraph Model and Wealth Polytope

Multi-party channels are naturally described using a hypergraph formalism. For a PCN, the off-chain network is represented as a hypergraph $H=(V,E)$, where $V$ is the set of participants and $E$ the set of hyperedges (multi-party channels) (Nainwal et al., 12 Dec 2025). Each hyperedge $e = (P,B)$ consists of a participant set $P = \{u_1,\dots,u_n\}$ and a balance vector $B = [b_1,\dots,b_n]$, tracking each member’s off-chain balance in the channel.

The geometric theory of payment channel networks describes the feasible set of off-chain wealth distributions as a high-dimensional integer polytope $W_G$, defined by liquidity constraints induced by the network topology (Pickhardt, 8 Jan 2026):

$$W_G = \{\,\omega \in \mathbb{N}^n : \sum_v \omega(v) = C,\, \forall S \subset V: \sum_{e\in E[S]} c_e \leq \omega(S) \leq \sum_{e\in E[S]} c_e + C(\delta(S))\,\}$$

where $C$ is the total capacity and $C(\delta(S))$ the sum of channel capacities crossing cut $(S,\bar{S})$. Modeling a $k$-party channel as a $k$-uniform hyperedge widens every cut in expectation, so $W_G$ grows monotonically with $k$, directly increasing every node’s accessible off-chain wealth and the network’s payment throughput.

2. Off-Chain State Update Protocols

H-MPCs (Hypergraph-based Multi-Party Payment Channels) implement a leaderless, fully concurrent state-update mechanism based on proposer-ordered directed acyclic graphs (DAGs) (Nainwal et al., 12 Dec 2025). Each off-chain value transfer is encoded as a "dagleaf": $$\mathrm{leaf} = \langle u_i, u_j, v, f_i, H(r_{\text{prev}}), H(r_{\text{rev}}), r_{\text{prev}}, \sigma_i, \sigma_j \rangle$$ where $u_i \to u_j$ is a value transfer of $v$ with sender fee $f_i$, and the hash structure with revocation secrets ensures both accountability and one-way progression per participant. Leaves are collected by supermajority-signed "dagroots" that checkpoint all valid updates since the prior finalized state.

The symbolic balance update per leaf is: $$\Delta B = [-v-f_i,\; +v,\; f_i/(n-2),\dots,f_i/(n-2)]$$ reflecting the transfer and fee redistribution. Final balances apply only at dagroot finalization: $$B^{(t)} = B^{(t-1)} + \sum_{\mathrm{leaf}\in \mathrm{root}_t}\Delta B_{\mathrm{leaf}}$$ This DAG construction enables multiple parallel state proposals, supports atomic multi-hop and inter-hyperedge payments (via conditional leaves and proofs-of-transfer), and requires no leader or coordinator at runtime.

3. Capital Efficiency and Liquidity Management

Multi-party channels unlock capital efficiency by pooling funds into a single UTXO or smart contract per channel, eliminating per-edge liquidity fragmentation (Xu et al., 29 Apr 2025, Nainwal et al., 12 Dec 2025, Pickhardt, 8 Jan 2026). Within an H-MPC, any participant can pay any other in the same hyperedge without the need for rebalancing. The global conservation law,

$\sum_{i=1}^n b_i^{(t)} = \sum_{i=1}^n b_i^{(0)}$

is enforced at every step.

Empirically, H-MPC implementations demonstrate that with $n=150$ participants, transaction success rates reach 94.69%, with the only cause of failure being insufficient per-user balance at proposal time. The empirical maximum balance skewness metric never exceeds 0.70 (measured as $$S(B^{(t)})=\frac{1}{n}\sum_{i=1}^n\frac{|b_i^{(t)}-\bar b^{(t)}|}{\bar b^{(t)}}$$), well below the theoretical worst-case bound. As $k$, the hyperedge size, increases, the expected accessible wealth per participant scales linearly as $k/n$, and the size of the feasible region $W_G$ strictly increases (Pickhardt, 8 Jan 2026).

Techniques such as the Starfish protocol efficiently aggregate and rebalance liquidity in star-shaped or merged channel topologies, achieving $O(N)$ on-chain setup and teardown, and providing full utilization of the collective deposit for off-chain payments (Xu et al., 29 Apr 2025).

4. Security and Fault Tolerance

H-MPCs and related protocols enforce strong integrity and fault tolerance via cryptographic means (Nainwal et al., 12 Dec 2025, Ye et al., 2020):

• Dual signatures authenticate every off-chain transfer.
• Threshold signatures ($>2n/3$) on dagroots ensure that a Byzantine minority cannot finalize invalid states.
• Revocation chains (or per-epoch separation in Garou) prevent double-spending and unauthorized state divergence.
• On-chain dispute contracts allow any honest party to submit valid signed states for enforcement and challenge conflicting or stale updates.

In protocols such as Garou, additional liveness protection is obtained by rotating the leader role per epoch, batching off-chain payments, and guaranteeing progress through on-chain dispute escalation. Security proofs are provided in the UC framework for selected protocols (Xu et al., 29 Apr 2025).

5. On-Chain Interactions: Funding and Settlement

Multi-party channels require collective funding via an n-party m-of-n multisignature or smart contract. On-chain interactions are minimized: a single FundingTx collects deposits, and standard withdrawal logic distributes final balances on cooperative or unilateral close (Nainwal et al., 12 Dec 2025, Xu et al., 29 Apr 2025, Ye et al., 2020). In the event of disputes or participant exits, mechanisms such as unilateral escape and hyperedge reconstruction ensure continued operation for non-leaving parties.

Starfish, Garou, and H-MPCs all focus on minimizing on-chain overhead per payment. For example, Starfish achieves only $O(N)$ on-chain operations for merge/close on $N$ links, and Garou’s design further reduces frequent on-chain dependence by ensuring all off-chain activity is self-enforcing unless a dispute arises.

6. Performance and Comparative Evaluation

Performance evaluations demonstrate the superiority of multi-party channels over both two-party networks and centralized hubs. H-MPCs achieve 94.69% transaction success on 150-node topologies, compared to 50–80% for Lightning, 60–90% for SpeedyMurmurs, and 80–95% for Spider (Nainwal et al., 12 Dec 2025). Garou achieves up to 7,782 tps (20× improvement over contemporaries) due to its batch settlement and concurrency design (Ye et al., 2020). Starfish increases payment success by 20–25 percentage points in Lightning-style topologies relative to no-rebalance baselines (Xu et al., 29 Apr 2025).

The throughput law from (Pickhardt, 8 Jan 2026): $S = \zeta / \rho$ where $S$ is sustainable off-chain throughput, $\zeta$ is on-chain settle bandwidth, and $\rho$ is the failure rate due to infeasible payments, implies that expanding the feasible region $W_G$ via larger multi-party channels reduces $\rho$ and hence increases off-chain capacity.

Protocol	Success Rate	Primary Failure Modes
Lightning	50–80%	HTLC expiry, path liquidity
SpeedyMurmurs	60–90%	Path-finding, partial info
Spider	80–95%	Queueing, multi-path imbalance
H-MPC	94.69%	Only insufficient balance

7. Extensions, Applications, and Theoretical Insights

The extension of star-shaped rebalancing protocols (Starfish) and hub-based designs (Garou) to coinpools and channel factories is supported by the underlying merge and atomic broadcast logic (Xu et al., 29 Apr 2025). Coinpools generalize the on-chain "hub" to a fully shared pool with versioned balances for each participant, supporting atomic reallocations via off-chain coordination. Channel factories generalize further, enabling the creation of many two-party and multi-party subchannels from a single joint deposit, amortizing on-chain setup cost and maximizing liquidity flexibility.

The geometric lens provided by Pickhardt (Pickhardt, 8 Jan 2026) establishes that multi-party channels monotonically enlarge the feasible-wealth polytope, providing a protocol-theoretic justification for their capital efficiency and resilience to channel depletion. Fee design (symmetry, convexity, coordination) and periodic coordinated replenishment are essential tools for maintaining high throughput and minimizing depletion.

Altogether, multi-party channel constructions—including coinpools and channel factories—represent a protocol-level scaling lever that overcomes the structural limitations of two-party meshes by enabling full liquidity utilization, robust concurrency, and strong enforceability within non-custodial payment networks.