1.2 OmniPact Solution: FSM + Game Theory

This section will elaborate on how OmniPact addresses this challenge through a Hybrid Architecture. We integrate deterministic computer science (state machines) with probabilistic crypto-economics (game theory) to construct a decentralized trust system that is mathematically rigorous and economically robust.

---

To enable complex business collaboration in a trustless blockchain environment, OmniPact proposes a Dual-Layer Consensus Architecture. This architecture decouples the transaction execution process into two orthogonal dimensions: the certainty of fund flow and the social consensus in dispute adjudication.

1.2.1 The Deterministic Layer: OES-FSM

At the bottom layer of the protocol, OES (Omni Escrow System) is designed as a strict deterministic finite state machine (DFSM).

Unlike the flexibility of general-purpose programming languages, OES contracts enforce transactions to follow a predefined, linear lifecycle. This design eliminates the arbitrariness of human operations and ensures the Atomicity and Immutability of fund states.

mathematical model

We define each guaranteed transaction $T$ as a 5-tuple automaton:

$$M = (Q, \Sigma, \delta, q_0, F)$$

Among them:

• is a finite set of states

• is a collection of input events (such as Deposit, SubmitProof, RaiseDispute）。

• is a state transition function, which strictly specifies the legal flow paths. For example, the system does not have a transition from Jump directly to path must pass through or the input of an external arbitration signal.

• It is the initial state.

• is the set of termination states (funds have been settled).

Institutional advantages

• Deadlock Prevention: Through built-in Timelocks and timeout rollback logic, FSM ensures that funds will never be permanently stuck in the contract regardless of any accidents (such as the loss of one party's private key).

• Formal Verification Friendly: Due to the limited and closed state space, OES logic can be easily verified through formal methods, thereby eliminating logical vulnerabilities and reentrancy attack risks at the mathematical level.

---

1.2.2 The Probabilistic Layer: DAN & Game Theory

When the FSM enters DisputedIn a (dispute) state, pure code logic can no longer handle it, the system then suspends, and control is transferred to DAN (Decentralized Arbitration Network).

DAN is not seeking "absolute truth" (which is philosophically difficult to define), but rather a Schelling Point through mechanism design——that is, a Focal Equilibrium in non-cooperative games that people tend to choose when they cannot communicate.

Schelling Point Consensus

OmniPact Hypothesis: In a network composed of diverse, anonymous, and economically rational arbitrators, the "truth" in the eyes of the majority is the consensus.

To encourage arbitrators to vote honestly, we have introduced a reward and punishment matrix based on the Nash Equilibrium:

1. Voting Consistency (Coherence): Arbitrators cannot communicate with each other (to prevent collusion). The system rewards arbitrators whose votes are consistent with the majority (Majority) and punishes those whose votes are inconsistent with the majority.

2. Expected Value Analysis (EV Analysis):

   For a rational arbitrator J, if he attempts to lie (by voting for the false party), he must bet that "the majority of other arbitrators will also decide to lie." However, without collusion, this is a high-risk strategy.

   Conversely, voting for the obvious truth (for example: seeing an obviously fake delivery screenshot) is the safest strategy for all rational participants. Therefore, "truth" becomes the only Schelling point.

Economic incentive formula

The arbitrator's profit function $R$ can be expressed as:

$$R_i = \begin{cases} \beta \cdot F_{arb} + \frac{\sum S_{lost}}{N_{win}} & \text{if } V_i = V_{consensus} \\ -S_{stake} & \text{if } V_i \neq V_{consensus} \end{cases}$$

Among them, $S_{stake}$ is the $PACT token staked by arbitrators. This means that malicious behavior not only yields no benefits but also faces the risk of principal confiscation (Slashing). This asymmetric risk-return ratio constructs a strong cryptoeconomic security barrier for the protocol (Cryptoeconomic Security).

---

1.2.3 Architecture Overview: A Closed Loop from Code to Consensus

The innovation of OmniPact lies in successfully bridging these two worlds:

1. Under normal circumstances: Transactions mainly run on the OES-FSM layer. This is an efficient and low-cost automated layer that handles 99% of normal transactions. Code is Law.

2. Under abnormal circumstances: once a dispute arises, the game theory layer intervenes. This is a social layer with high security and high judgment. At this time, social consensus is law (Consensus is Law).

Through this hybrid design of "FSM for Efficiency, Game Theory for Truth" (Finite State Machine ensures efficiency, Game Theory ensures truthfulness), OmniPact has successfully transformed any non-standardized business interaction into credible on-chain settlement, completely solving the "commercial oracle problem".