First-generation Decentralized Autonomous Organizations (DAOs) rely predominantly on "Coin-Voting" schemes (1 Token = 1 Vote). While permissionless, this model inevitably degrades into plutocracy, where capital centralization allows a minority of "Whales" to capture protocol utility. Furthermore, the liquidity of voting tokens exposes governance to "Flash Loan Attacks" and short-term rent-seeking. This paper introduces a novel governance primitive: Time-Decayed Stake-Weighted (TDSW) Voting. We propose a dual-class structure that weighs voting power not merely by capital magnitude, but by Capital Lock-Duration (Time) and Epistemic History (Merit). By introducing "Reputation Entropy"âwhere governance power decays automatically if not exercised - we solve the "Zombie Stake" problem and ensure that control remains with active, long-term contributors rather than passive capital aggregators. Author's Note: This paper is a foundational pillar of the Klyrox Protocol architecture, expanding upon the core framework published in The Klyrox Protocol: A Decentralized Framework for Optimistic Content Verification and Epistemic Reputation (available at: https://doi.org/10.5281/zenodo.18729968). It outlines the specific mechanics underpinning the concept of "Epistemic Capital," as explored in the complete five-volume series, The Algorithmic Monographs (The Algorithmic Invisible Hand, The Republic of Code, The Market for Truth, The Heavy Metal Intelligence, and The Synthetic C-Suite).
In a multipolar world with no trusted monetary coordinator, how do rational actors settle large-value transactions across trust boundaries? We model this as a non-cooperative gameâthe "Exit Game"âin which capital allocators choose between capturable settlement systems ("Stay") and neutral settlement ("Exit"). The model rests on four empirical axioms: persistent multipolarity, rational self-interest, computational hardness, and network effect persistence. We prove three results. First, the payoff advantage of Exit over Stay is strictly increasing in adoption: every term in the payoff differential favors Exit under maintained monotonicity conditions, and each actor's adoption threshold approaches zero under structural debasement (Theorem 1). Second, no coalition can sustain coordinated Stay, because permissionless access makes defection costless and the first defector captures fleeing capital (Theorem 2). Third, the resulting equilibrium is absorbing: the monotone adoption process converges to full adoption once a critical mass is reached, because trust conditions required for coordinated return cannot be reestablished (Theorem 3). The model is explicitly falsifiable: six conditions are identified under which the central claims would fail. Bitcoin is the unique asset satisfying the necessary properties for neutral settlementâa result proved by systematic elimination across seven asset classes in Hash (2026b).
The DebreuâKoopmans theorem [14] restricts separable aggregation to at most one nonconvex component. We solve this by proving that a separable (additive or multiplicative) function is star quasiconvex (those with star-shaped sublevel sets about minimizers) if and only if each component is star quasiconvex. This immediately yields star quasiconvexity of separable sums of quasiconvex functions, formally bridging diversification theory with the S-shaped value functions of Prospect Theory. Furthermore, we develop a complete calculus (monotonic composition, pointwise minima, quasi-arithmetic means) and we apply it to Cobb-Douglas functions, multi-factor risk models, and constant function market makers in decentralized finance. Star quasiconvexity thus provides a unified framework for economic modeling beyond the classical DebreuâKoopmans constraint.
The Deflated Sharpe Ratio (Bailey and LĂłpez de Prado, 2014) corrects an observed Sharpe ratio for the number of trials N behind it, separating genuine skill from the selection bias of a large backtest search. Its practical weakness is structural: N is supplied by the same researcher whose result it constrains. A search over a thousand configurations, reported as a single trial, satisfies the formula while defeating its purpose. The correction is sound; its input is self-reported. We present a construction that removes the researcher's discretion over that input. The trial set is committed to a Merkle tree before evaluation; the trial count N is the leaf count of the tree, not a reported scalar; and the winning strategy is bound, inside a zero-knowledge proof (a STARK), to be the maximum over the committed leaves. The deflation is then recomputed in-circuit on Merkle-pinned prices, net of a cost model the credential discloses, so the figure an allocator reads is derived by the circuit rather than asserted by the manager. The output is a credential, checkable by anyone, in seconds, without disclosure of the strategy, whose anti-overfitting correction cannot be understated within the committed search. We give the commitment scheme and its in-circuit binding; state precisely the manipulation it eliminates (understating N, cherry-picking a non-maximal winner, softening the cost model) and the residual trust it does not (off-ledger trials, closed only by forward pre-registration); and report a live implementation that additionally computes, in-circuit, the Probability of Backtest Overfitting over all C(16,8) = 12,870 combinatorially-symmetric splits (via recursive proof composition), together with the Probabilistic Sharpe Ratio and Hansen's Superior Predictive Ability. We demonstrate the system on its own flagship strategy, which it rules not significant (DSR 0.68, below the 0.95 bar), and publish that failure as the reference credential.
Most decentralized autonomous organizations (DAOs) use a 1-Token-1-Vote rule, allowing capital ownership to translate directly into governance power. This paper evaluates how a Quadratic Voting (QV)-inspired square-root reweighting counterfactual would affect voting outcomes in the Arbitrum DAO. For this, a time-paginated pipeline was developed to retrieve approximately 850,000 off-chain Snapshot vote records across fifteen of the DAO's highest-turnout proposals where each participating wallet's token-weighted voting power was replaced with its square root, and the proposal outcomes were recalculated. The results reveal extreme concentration of voting power, with a mean Gini coefficient of approximately 0.9950 among active participating wallets. In some proposals, the ten largest participating wallets or delegates collectively controlled as much as 86.87% of the total voting weight. Consequently, square-root reweighting changed the winning outcome in four of the fifteen proposals (26.7% of this purposively-selected, high-turnout sample), demonstrating that these outcomes were sensitive to the distribution of voting power across wallets. Its effect on victory margins was heterogeneous: margins widened in six proposals and narrowed in nine, with changes ranging from a 55.90-percentage-point expansion to a 37.76-percentage-point contraction. Notably, all four outcome reversals involved funding, grants, security expenditure, coalition financing, or related resource-allocation decisions. These findings suggest that square-root reweighting can alter both the magnitude and direction of token-weighted governance outcomes by reducing the relative influence of highly concentrated token holdings.
Token-based voting systems are increasingly adopted in digital governance contexts such as decentralized autonomous organizations and participatory budgeting, yet their standard aggregation rules often lead to undesirable outcomes, including oligarchic dominance or voter apathy. This paper introduces a general mathematical framework for token-based voting that interpolates between one-person-one-vote and one-token-onevote paradigms through the notion of radical voting functions. These functions map voting tokens to actual votes via concave transformations that preserve incentives for participation while compressing excessive voting power. We formalize consensus as an aggregation of transformed votes and study its structural properties using tools from convex analysis and majorization theory. We show that radical voting functions reward broad and evenly distributed support and penalize highly concentrated voting patterns, thereby favoring pluralistic outcomes over individualistic ones. Quadratic voting emerges as a special case within this framework, characterized by linear marginal voting costs. The analysis is extended to account for voter heterogeneity by incorporating similarity measures into the consensus function, linking voting outcomes to diversity among participants. Overall, the framework provides a principled foundation for designing voting mechanisms that balance merit, inclusiveness, and resistance to capture in token-based governance systems.
Decentralized reputation mechanisms certify trust by making agents spend a scarce resource: computation (Proof of Work), capital (Proof of Stake), or identity (Proof of Personhood). In all three the resource is orthogonal to the quality being certified â a well-capitalized agent is not a skilled one. We study the construction in which the spent resource is the certified competence: Proof of Calibration, in which pseudonymous agents commit probabilistic predictions, outcomes resolve against ground truth, and reputation accrues through a strictly proper scoring rule. Building on the merit-gating results of Calibration-Gated Reputation (Alassa and Alashqar, SSRN 6505678), we replace that paper's concentration estimates with an exact theory. The realized mean score of an identity is a linear function of a single sufficient statistic â its empirical outcome frequency pÌ â so passing a merit bar is exactly the event that pÌ reaches an "alibi frequency" q_c, and the price of that event is an information divergence: the Sybil-lottery success probability is controlled, two-sidedly for all K and all N beyond a mild explicit threshold, by e^(âN·KL(q_câp)). Strict propriety is precisely positivity of this rate at every dishonest report, unifying the companion paper's impossibility and merit-gating theorems as the zero- and positive-rate regimes of one scalar. The theory is exact enough to reproduce, with zero free parameters, every Monte Carlo experiment of the companion suite, including the finite-size deviations from the asymptotic Δâ»âŽ cold-start law. Two structural results follow. First, the gate has two margins: in expectation, the adversary's best response is honesty and the margin is the generalized-entropy gap; at the event level, the optimal attack is skill-mimicry â report the bar's skill, not your own â and the margin is min{KL(p_hâp_a), KL(1âp_hâp_a)}, the divergence between the skills themselves, identical across all strictly proper, outcome-symmetric rules. The gate's security exponent is a property of the skills, not of the rule. Second, Sybil amplification requires independent evidence: identities scored on a shared outcome stream gain almost nothing from their number. Finally, the gate is not merely sound but optimal: no local pseudonymous mechanism that admits honest bar-skill agents with non-vanishing probability achieves a soundness exponent exceeding KL(p_hâp_a), and the strictly proper gate attains it â it is the NeymanâPearson test of the skill hypothesis. The composite Notch Score reduces to the same single statistic, yielding an exact calibration-weight floor.
This paper identifies and resolves a critical architectural flaw in citation-weighted reputation systems operating within Weighted Directed Acyclic Graph (WDAG) governance structures for Decentralized Autonomous Organizations (DAOs). Under existing formulations, rational agents face a direct financial disincentive to cite prior contributions, as citation-weighted value allocation through PageRank-derived mechanisms transfers economic reward from the citing agent to the cited agent. This under-citation incentive undermines the foundational promise of knowledge attribution in decentralized collaborative systems. The paper formalizes the under-citation problem, demonstrates the impossibility of precise citation quantification, and identifies a gap in existing game-theoretic proofs that purport to establish citation honesty as an equilibrium. Drawing on the WDAG governance framework developed in Calcaterra (2018), this paper proposes an integrated solution that decouples citation accuracy from quality-based payment, introduces validator-assessed citation honesty as a separately ranked and rewarded dimension, and establishes retroactive audit mechanisms with graduated sanctions. A new equilibrium theorem (Theorem 3b) demonstrates that under the integrated solution, honest citation constitutes a Nash equilibrium when validators assess citation accuracy and the marginal effect of citation accuracy on validator-assessed honesty scores exceeds the marginal gain from self-citation inflation. The paper situates these findings within the broader framework of dynamic regulation theory and New Institutional Economics incomplete contract theory, arguing that static citation protocols are inherently vulnerable to gaming and that evolutionary governance mechanisms are essential for sustaining honest knowledge attribution in decentralized systems.
<b>Proof-of-Stake (PoS) security models</b> assume validator independence, decentralized decision-making, and economically rational but non-coordinated behavior. This paper introduces <b><i>Shadow Validator Cartels</i></b>, a class of covert consensus capture attacks in which validators coordinate off-chain to influence block production, transaction ordering, and governance outcomes while remaining individually protocol-compliant. Unlike explicit majority or 51% attacks, shadow cartels do not require dominant stake ownership or on-chain collusion. Instead, they leverage shared infrastructure, aligned economic incentives, and soft coordination mechanisms that render their behavior statistically indistinguishable from organic validator activity. We analyze the structural enablers, formation mechanics, and systemic impacts of shadow validator cartels, demonstrate why existing decentralization metrics fail to detect them, and outline system-level mitigation requirements necessary to preserve credible neutrality in PoS networks.
Stefano Balietti, Pietro Saggese, Markus Strohmaier
Decentralized Autonomous Organizations (DAOs) use token-weighted voting to allocate resources, set protocol rules, and legitimate collective decisions. Yet, support in DAO voting is strikingly concentrated. What happens inside the ballot that produces this concentration? We study DAOs' governance at the proposal-choice level, linking each choice's voting-power share to three observable features: whether it expresses an approval-oriented stance, where it appears in the choice list, and whether it is selected by the proposal author. We find that (i) author-selected choices show the strongest and most robust association with voting-power share, with a 58.8% increase relative to non-author choices; (ii) approval-oriented choices retain a positive but slightly less consistent advantage (27.1%); and (iii) first-listed choices also attract systematically higher shares, consistent with position and order effects (7.7%). Results are robust across several specifications, which include subtracting an author's own voting power from computations. We use bias descriptively, to denote systematic associations rather than proven causal distortion. The results shift attention from proposal outcomes alone to the interface and social signals through which choices are presented. In DAO governance, ordering, author signals, and vote visibility should be treated as institutional design choices, not neutral implementation details.
This paper examines the strategic behavior of rational actors in the TON blockchain, focusing on their responses to slashing mechanisms in a proof-of-stake (PoS) environment. Slashing introduces financial penalties for behavior that threatens network integrity, addressing the nothing-at-stake problem, where validators in PoS systems can support multiple chains at no cost. Although slashing is intended to deter malicious behavior by Byzantine actors, it also affects rational validators by altering their expected returns. Using a game-theoretic model inspired by the BAR framework, this study examines how rational, utility-maximizing validators weigh the risks and rewards of violating or enforcing slashing mechanisms in the presence of potentially Byzantine actors when penalty enforcement is uncertain. Located at the intersection of game theory and distributed systems, this research sheds light on compliance and deviation dynamics in PoS networks, contributing to a deeper understanding of incentive alignment in blockchain governance.
Ioannis Papastaikoudis, Jeremy D. Watson, Ioannis Lestas
This work explores network coalition-based models using dynamic average consensus protocols, where agents in coalitions interact to reach global agreement. We employ hypergraphs to model communication structures and compare their convergence rates with clique expansion graphs. Our results show that hypergraph-based models achieve faster convergence for the case of continuous consensus dynamical systems and also in discrete time for coalitions with an equal number of agents. Our findings suggest that hypergraphs offer a scalable, decentralized approach to improving consensus algorithms in generalized tree like information structures, with significant potential for enhancing performance in applications like finance and economics.
Concentrated-liquidity automated market makers (CLAMMs), as exemplified by Uniswap v3, are now a common primitive in decentralized finance frameworks. Their design combines continuous trading on constant-function curves with discrete tick boundaries at which liquidity positions change and rounding effects accumulate. While there is a body of economic and game-theoretic analysis of CLAMMs, there is negligible work that treats Uniswap v3 at the level of formal state machines amenable to model checking or theorem proving. In this paper we propose a formal modeling approach for Uniswap v3-style CLAMMs using (i) networks of priced timed automata (PTA), and (ii) finite-state transducers (FST) over discrete ticks. Positions are treated as stateful objects that transition only when the pool price crosses the ticks that bound their active range. We show how to encode the piecewise constant-product invariant, fee-growth variables, and tick-crossing rules in a PTA suitable for tools such as UPPAAL, and how to derive a tick-level FST abstraction for specification in TLA+. We define an explicit tick-wise invariant for a discretized, single-tick CLAMM model and prove that it is preserved up to a tight additive rounding bound under fee-free swaps. This provides a formal justification for the "$Δ$-slack" used in invariance properties and shows how rounding enters as a controlled perturbation. We then instantiate these models in TLA+ and use TLC to exhaustively check the resulting invariants on structurally faithful instances, including a three-tick concentrated-liquidity configuration and a bounded no-rounding-only-arbitrage property in a bidirectional single-tick model. We discuss how these constructions lift to the tick-wise structure of Uniswap v3 via virtual reserves, and how the resulting properties can be phrased as PTA/TLA+ invariants about cross-tick behaviour and rounding safety.
The applications of blockchain technology in a broad variety of contexts have become the basis of decentralized systems, and it has since grown much beyond its initial application to cryptocurrencies. This paper sheds light on two important bodies of research and provides an in-depth analysis of blockchain consensus algorithms. The former is the algorithm of Du et al. (2020) known as Mixed Byzantine Fault Tolerance (MBFT). Such MBFT illustrates a new solution to the fault tolerance and scalability problems of blockchain models of Ethereum and Bitcoin. Second, Chaudhry and Yousaf (2018) provided a clear analysis of consensus mechanisms. They went as far as to draw a comparative analysis of consensus algorithms, including but not limited to Byzantine Fault Tolerance (BFT), Proof of Work (PoW), and Proof of Stake (PoS). After conducting an extensive review and experimentation of each of the algorithms, relevant strengths, limitations, and suggestions on how to improve each of the analyses were brought to light in this paper. To summarize, the analysis given gives a platform to understand the area of future blockchain consensus research in security mechanisms, scaling solutions, and performance enhancement methods.
Decentralized Autonomous Organizations (DAOs) overwhelmingly use token-weighted voting as their core governance mechanism. Empirical evidence reveals that this approach often leads to plutocratic governance, with voting power concentrated among a few large holders. Traditional models exacerbate this dilemma: on-chain voting is transparent but costly, marginalizing small participants, while off-chain mechanisms lower participation costs but rely on trusted multi-signature execution, reintroducing centralization. To resolve this trilemma of decentralization, efficiency, and trust, we propose a VoS. VoS introduces a trust-minimized aggregation model tailored for DAO governance: votes are collected offchain and aggregated into a constant-size proof that smart contracts verify in $O(1)$ time, thereby enabling fully on-chain execution without intermediaries. Although VoS cannot eliminate the plutocracy rooted in token distribution, it prevents governance mechanisms from amplifying it, charting a practical path toward secure, efficient, and trust-minimized DAO governance.
Abstract A hybrid lattice-based commitment scheme is proposed for anonymous proofs between hidden values. The method is based on a modification of the BDLOP zero-knowledge proof (ZKP) scheme by replacing the learning with errors (LWE) problem with a learning with rounding (LWR) problem, which theoretically makes it possible to reduce the size of the parameters and reduce the complexity of parameter selection. It is shown that the proposed scheme preserves the property of additive homomorphism, which makes it possible to apply it to prove linear relations. The obtained results can be applied to construct electronic voting protocols or conduct anonymous transactions.
Committees are extensively used in the designs of various Proof-of-Stake (PoS) blockchains. A committee is simply a randomly selected subset of the parties/nodes in the system. Ideally, the committee should i) be as small as possible, and ii) properly represent the entire system, in terms of the corruption ratio. Existing committee selection schemes all follow the principle of proportionality, which says that a committee member should neither over-represent nor under-represent the stake it holds.
AndrĂĄs Nagy, JĂĄnos Tapolcai, IstvĂĄn AndrĂĄs Seres, Bence LadĂłczki
Proof-of-stake consensus protocols often rely on distributed randomness beacons (DRBs) to generate randomness for leader selection. This work analyses the manipulability of Ethereum's DRB implementation, RANDAO, in its current consensus mechanism. Even with its efficiency, RANDAO remains vulnerable to manipulation through the deliberate omission of blocks from the canonical chain. Previous research has shown that economically rational players can withhold blocks known as a block withholding attack or selfish mixing when the manipulated RANDAO outcome yields greater financial rewards.