PSCRD: Proof of Success & Reward Distribution

• PSCRD is a unified protocol that uses cryptographic proofs to verify successful actions while ensuring fair, incentive-compatible reward distribution in decentralized systems.
• It formalizes commitment, response, and verification stages with robust cryptographic techniques like collision-resistant hashes and digital signatures to secure multi-agent operations.
• PSCRD employs time-decay reward mechanisms and proportional fee allocation to minimize inequality, enabling dynamic fairness and enhancing decentralization across multi-bridge architectures.

Proof of Success and Reward Distribution (PSCRD) is a unified protocolic and analytical framework integrating cryptographic evidence of successful action ("proof of success") with rigorously fair, resilient, and incentive-compatible reward allocation. Initially developed to address centralization and single-point-of-failure challenges in multi-bridge cross-chain architectures, PSCRD formalizes on-chain event witness, proportional fee allocation, and explicit inequality minimization. The PSCRD design pattern spans domains from cross-chain validation to PoS governance, prediction markets, and evolutionary merit assessment, establishing a general paradigm for trustless coordination and distribution in decentralized systems (Oyinloye et al., 11 Dec 2025).

1. Core System Model and Threat Assumptions

The canonical PSCRD construction operates in a multi-agent, permissioned or permissionless setting with $N$ candidate participants and a task (e.g., cross-chain relay, block validation, governance vote) requiring robust consensus. For cross-chain bridges, a client broadcasts a transfer intent $T$; PSCRD selects a random quorum $\mathcal{Q}$ of size $Q=\frac{R_{\text{total}}}{R_{\min}}$ from the $N$ bridges, where $R_{\min}$ is the minimum per-bridge fee share, and $R_{\text{total}}$ is the user fee for the operation. Each selected bridge attempts the transfer; a threshold-majority (>50%) matching on transaction details is required for finalization. The adversarial model permits control over an arbitrary minority; collusion, misreporting, and non-participation attacks are mitigated by cryptographic guarantees and randomized committee formation. Short-term capture of majority quorums yields only transient economic advantage due to reward decay (Oyinloye et al., 11 Dec 2025).

2. Formal Proof of Success Specification

The PSCRD protocol enforces an auditable event lifecycle:

• Commitment: Each participating agent $b_i \in \mathcal{Q}$ generates a commitment $C_i = H(T \| pk_i \| n_i)$ with $n_i$ a nonce and $pk_i$ a public key, posted as an intent to respond.
• Response: Upon observing task completion (e.g., successful relay on destination chain), each agent emits $R_i = (T, \text{dest\_block}, \sigma_i)$ with a signature $$\sigma_i = \mathrm{Sign}(sk_i, T\|\text{dest\_block})$$.
• Verification: A smart contract or aggregator checks all $\{R_i\}$. If a majority $\mathit{MAJ}$ agree on task outcome, the contract finalizes. The set $(\mathit{MAJ}, \{ \sigma_i \})$ forms a collectively signed "proof of success" for $T$.

This process, reliant on collision-resistant hashes and digital signatures (e.g., BLS in PoS settings), achieves cryptographic accountability. Misbehaving or non-responsive participants are excluded from reward increments (Oyinloye et al., 11 Dec 2025).

3. Reward Distribution and Time-Decay Incentive Mechanisms

Rewards are distributed strictly to majority-contributing agents, governed by "success points" $S_{p,i}$. After each successful task:

• $S_{p,i} \leftarrow S_{p,i} + 1$ for each $b_i \in \mathit{MAJ}$.
• Fee $x$ is distributed proportionally:

$$R_i = \frac{S_{p,i}}{\sum_{j \in \mathit{MAJ}} S_{p,j}} \cdot x$$

To prevent lock-in by early participants, PSCRD uses time-decay. For bridge $i$ with age $A_i > T_w$ and decay coefficient $\lambda \in (0, 1)$:

$S'_{p,i} = \frac{S_{p,i}}{1 + \lambda A_i}$

Reward shares are computed with decayed points $S'_{p,i}$, ensuring that long-term fairness holds dynamically as the network evolves. This decay collapses point inequality, aids in onboarding new agents, and destroys adversarial value if malicious agents disengage or fail to maintain majority repeatedly. Honest participation is incentive-compatible, as only successful contributions increment success points (Oyinloye et al., 11 Dec 2025).

4. Formal Analysis of Fairness, Decentralization, and Robustness

PSCRD is analyzed under standard inequality and decentralization metrics:

• Gini index: $$G = \frac{1}{nS} \sum_{i=1}^n (2i - n - 1) S_{p(i)}$$, with $S_{p(i)}$ sorted, decreasing under decay (i.e., $G' < G$).
• Nakamoto coefficient: For points ranked $S_{p[1]} \geq \cdots \geq S_{p[n]}$, $K$ is the minimum $k$ s.t. $\sum_{i=1}^k S_{p[i]} \geq 0.5S$. Time-decay increases $K$, i.e., improves decentralization ($K' > K$).
• Empirical results: In simulations with 50 bridges and three join groups, the Gini index converges toward $0.1$ and Nakamoto grows from $\approx 10$ to $\approx 21$. Parameter sweeps for decay factors/times ($\lambda \in \{0.01,0.05,0.1\}, T_w \in \{1,5,10\}$) confirm robustness: Gini $\in [0.1,0.15]$, $K \in [20,22]$. This demonstrates stable, fair, and decentralized reward allocation (Oyinloye et al., 11 Dec 2025).

5. PSCRD in Proof-of-Stake Governance and Consensus

The PSCRD principle extends to PoS governance and validator economics. In delegated PoS with a ground-truth binary outcome, DReps (delegation representatives) exert effort $x_i$, attracting proportional voting/stake weight $w_i = x_i / \sum x_j$. Reward schemes (proportional vs. threshold $k$-rewarding) demonstrate:

• Proportional sharing leads to exponentially diminishing effort as committee size grows, inducing minimal effort in large groups.
• Threshold-based PSCRD ($k$-top performers, equal fixed reward $B/k$) yields symmetric Nash equilibria with exactly $k$ active DReps at effort level $x$ solving $k c(x) = B$, maximizing collective probability of success. For convex/concave cost functions, optimal $k$ is typically small—threshold PSCRD ensures high individual effort, near-optimal group outcome, and budget-efficient reward (Birmpas et al., 15 Jun 2024).
• Empirical studies of Ethereum 2.0 validator reward distributions confirm low Gini ($G \lesssim 0.2$), high Nakamoto coefficients, and incentive-compatibility: >97% maximum available rewards are captured by honest, online participants and missed-duty rates remain $<5\%$ (Cortes-Goicoechea et al., 2023, Yan et al., 17 Feb 2024).

6. Broader Applications and Extensions

PSCRD has been adapted for prediction markets and dynamic group learning. In the "self-governing prediction reward" paradigm, rewards combine accuracy (proper scoring deviation), adversarial weightings (variance in prediction confidence), and consensus (mean group agreement), forming:

$$r_{i,j} = (s_j^{\text{Big}} - s_{i,j}) \Delta s_j |V_j|$$

with $s_{i,j}$ surprisal, $\Delta s_j$ peer-variance, and $|V_j|$ consensus. Monte Carlo studies establish that, for low group bias and adequate reward-influence, the system drives agents collectively to correct beliefs (Gonzalez-Hernandez et al., 2023).

A general reward allocation algorithm further synthesizes raw output, risk-adjusted metrics (e.g., Sharpe ratio), and forward-looking merit into a normalized, weighted composite, distributing rewards proportionally while mitigating the confusion of luck vs. skill (Sornette et al., 2019).

7. Security, Latency, and Cost Trade-Off Analysis

PSCRD achieves high security: random quorums minimize the probability of adversarial majority; even under 51% adversary control, long-term malicious reward capture is capped (e.g., to $\approx 49.7\%$ in simulated bridge networks). Latency remains low, matching that of single-bridge or parallelized relay, as all bridges attest in parallel and require only simple majority for finalization. Critically, user-facing cost is flat and decoupled from the number of participating validators; no additional relay or multi-signature costs are imposed. On-chain logic for commit/reveal, signature aggregation, reward update, and decay operates efficiently and at minimal amortized gas cost (Oyinloye et al., 11 Dec 2025).

---

PSCRD systematically integrates cryptographic proof, parametric reward allocation, and explicit fairness/decentralization analysis. It provides a compositional template for the design of trustless coordination protocols in cross-chain, consensus, governance, and forecasting domains, balancing security, scalability, and sustained economic participation across heterogeneous agent populations (Oyinloye et al., 11 Dec 2025, Birmpas et al., 15 Jun 2024, Cortes-Goicoechea et al., 2023, Gonzalez-Hernandez et al., 2023, Yan et al., 17 Feb 2024, Sornette et al., 2019).