Sybil Attacks, Full Nodes, and BTC Core: A Predicate-Based Game Theoretic and Mathematical Analysis

Introduction: The False Narrative of Full Nodes and Consensus in Bitcoin

BTC Core has propagated the misleading narrative that full nodes contribute to the consensus mechanism of Bitcoin, creating the false impression that these nodes have influence over the network’s governance. This belief stems from the misconception that full nodes “vote” on the rules of the Bitcoin protocol. However, the reality is that only miners participate in consensus by extending the longest chain of honest blocks through proof-of-work (PoW). Honest miners do not make subjective choices but instead follow the rules of the protocol. In contrast, full nodes validate transactions but do not participate in the block creation or consensus process.

To follow a dishonest chain, miners would need to intentionally change the protocol they are following, which is both rare and economically infeasible without widespread false signalling. This manipulation is exacerbated by BTC Core, which influences full node operators into believing they are critical to network governance. This paper uses predicate logic and game theory to demonstrate how BTC Core manipulates full nodes and centralises control over the Bitcoin network. Additionally, we explore how the small-world network structure of Bitcoin ensures that miners (not full nodes) are the primary actors in transaction propagation and consensus.

The Nature of Voting in Bitcoin: Miners and Proof-of-Work

Voting in Bitcoin occurs solely through the proof-of-work mechanism. Miners do not make arbitrary choices between blocks; they automatically follow the rules of the protocol by extending the longest valid chain of honest blocks. Any deviation from this, such as choosing to build upon a dishonest chain, would require miners to actively change the protocol; an economically irrational choice unless the majority of economic participants are manipulated into following the new rules.

Step 1: Miners Follow the Longest Chain of Honest Blocks

Miners build upon the longest chain of valid, honest blocks as dictated by the Bitcoin protocol. This is not a subjective decision but an automatic function of the protocol’s rules. By following these rules, miners ensure the security and integrity of the blockchain.

• P1: ∀x (Miner(x) → BuildOnLongestValidChain(x)) Translation: For all entities x, if x is a miner, then x builds upon the longest chain of valid, honest blocks.

This predicate highlights that miners are bound by the protocol, automatically building on the valid chain that has the most work accumulated. Miners cannot arbitrarily choose which block to extend; they must follow the longest chain of valid blocks according to the proof-of-work rules.

Step 2: Dishonesty Requires Changing the Protocol

If a miner chooses to build on a dishonest chain, they must change the rules they are following. This requires a deliberate decision to abandon the protocol’s immutability. Such an action cannot occur naturally within Bitcoin, as the protocol is designed to resist arbitrary changes. Therefore, miners would need to actively modify the consensus rules to follow a dishonest chain.

• P2: ∀x (Miner(x) ∧ DishonestChain(y) → ChangeProtocol(x)) Translation: For all entities x, if x is a miner and builds upon a dishonest chain y, then x must change the protocol.

This predicate emphasises that dishonesty is not an automatic or passive action but a deliberate, active decision by miners to alter the network’s rules. This change is not feasible unless all participants in the network are manipulated or coerced into accepting these new dishonest rules.

Step 3: Majority of Economic Participants Must Change Rules for Dishonest Chain to Succeed

For a dishonest chain to take hold, a majority of economic participants (miners, exchanges, and users) would need to adopt the new rules. This is highly unlikely without significant manipulation or false signalling from BTC Core. The Bitcoin protocol is set in stone, meaning that its rules cannot be changed without widespread coordination and acceptance by the majority of network participants.

• P3: ∀x (ChangeProtocol(x) → MajorityAdoptChange(x)) Translation: For all entities x, if x changes the protocol, then the majority of economic participants must adopt this change.

This predicate illustrates that miners alone cannot successfully implement a dishonest chain unless they manage to convince or manipulate the majority of economic actors in the network. This process is both complex and unlikely, given the economic incentives that favor following the original rules.

Small-World Networks and Transaction Propagation

The Bitcoin network operates as a small-world network (Amaral et al., 2000; Newman & Watts, 1999), where miners are densely interconnected (Javarone & Wright, 2018). In this structure, miners receive transactions and blocks before full nodes, as miners form the core of the network’s propagation mechanism. Full nodes, by contrast, are less interconnected and receive transactions after miners have already processed them. This ensures that full nodes do not influence transaction propagation or the consensus process, as miners have already voted on which blocks to extend.

Step 4: Small-World Network Structure Ensures Miners Are Central to Propagation

A small-world network is characterised by short path lengths and high clustering, allowing for efficient propagation of information across the network (

Zhang, 2019)

. In Bitcoin, miners are highly interconnected, ensuring that transactions and blocks propagate quickly among them. Full nodes are peripheral in this structure, receiving transactions only after miners have processed them.

• P4: ∀x,y (Miner(x) ∧ Miner(y) → DenselyConnected(x,y)) Translation: For all entities x and y, if x and y are miners, then they are densely connected in the network.

This predicate shows that miners form a tightly connected core in the network, enabling them to receive and propagate transactions rapidly. Full nodes, by contrast, are secondary in this propagation process.

Step 5: Full Nodes Receive Transactions After Miners

Because miners are more densely interconnected than full nodes, they receive transactions and blocks before full nodes do. Full nodes, therefore, cannot affect the propagation or consensus process since miners have already voted on the validity of transactions by including them in blocks.

• P5: ∀x (Node(x) → ReceiveAfter(Miner(x))) Translation: For all entities x, if x is a full node, then x receives transactions after miners.

This predicate reinforces the notion that full nodes are passive actors in the Bitcoin network. Their actions (whether validating or rejecting transactions) occur after miners have already cast their votes through proof-of-work.

Step 6: Full Nodes Cannot Influence Consensus After Miners Have Voted

By the time full nodes receive transactions, miners have already processed and included them in blocks. Even if a full node decides not to propagate a block, this has no effect on the network’s consensus, as the miners have already voted by adding the block to the blockchain.

• P6: ∀x (Node(x) ∧ ¬Propagate(Block(y)) → ¬AffectConsensus(y)) Translation: For all entities x, if x is a full node and does not propagate a block y, this has no effect on the consensus regarding y.

This predicate shows that full nodes are irrelevant to the consensus process. Whether or not they propagate transactions or blocks, the network’s consensus is determined by the actions of miners, who vote through their proof-of-work.

Game Theory Applied to Full Nodes and BTC Core’s Strategy

BTC Core uses several game theory concepts to manipulate full node operators into believing they are contributing to Bitcoin’s consensus and governance. This manipulation involves asymmetric information (Kim, 1985; Piazza, 2022), false signalling (Duffy & Feltovich, 2006), moral hazard (Chemla & Hennessy, 2014; Holmstrom, 1982), and herding behaviour (Lima & Schimit, 2023; Wang et al., 2015), all of which allow BTC Core to maintain central control while giving full node operators a false sense of participation.

1. Asymmetric Information: BTC Core’s Manipulation of Full Nodes

BTC Core developers possess more information about the actual role of full nodes than full node operators do. Full node operators, misled into believing they are influencing the network, continue to operate nodes without realizing their irrelevance to consensus. This asymmetric information allows BTC Core to control the network narrative while benefiting from the passive participation of full nodes.

• P7: ∃y (Core(y) ∧ Info(y) > Info(Node(x))) Translation: There exists a BTC Core entity y such that y possesses more information about the network than a full node operator x.

This predicate highlights the information asymmetry that BTC Core exploits to mislead full node operators, ensuring their continued participation without realising their lack of influence.

2. False Signalling: Full Nodes’ Participation Is Meaningless

BTC Core promotes the idea that full nodes are essential to network consensus, creating a false signalling game where full node operators believe their validation of transactions is crucial. In reality, full nodes’ actions are irrelevant to consensus, as miners are the only participants whose proof-of-work signals are credible (X. Wang et al., 2024).

• P8: Signal(Node(x)) → FalseSignal(Consensus(x)) Translation: If a full node operator signals participation, it results in a false signal of consensus.

This predicate shows that full node operators’ signals are meaningless. Miners’ proof-of-work is the only valid form of signalling that contributes to consensus.

3. Moral Hazard: Full Node Operators Act Under False Assumptions

BTC Core creates a moral hazard by encouraging full node operators to act under the false belief that they are influencing network governance (Ruzomberkaand & Love, 2023). Full node operators invest time, energy, and resources into running nodes, assuming that their participation helps secure the network. However, their actions have no real impact on consensus. This misalignment of incentives, where operators are led to believe they are critical while exerting no actual influence, is a key component of BTC Core’s narrative manipulation.

• P9: ∀x (Node(x) ∧ Assumption(Influence(x)) → ¬RealInfluence(x)) Translation: For all entities x, if x is a full node and operates under the assumption that it has influence, this assumption is incorrect.

This predicate explains the moral hazard created by BTC Core, where full node operators act as if they have an essential role in Bitcoin’s governance, despite having no effect on network consensus. BTC Core faces no consequences for promoting this false narrative while reaping the benefits of full nodes’ continued, misguided participation.

4. Herding Behaviour: Full Nodes Follow the Perceived Majority

BTC Core also capitalises on herding behaviour, wherein full node operators follow what they perceive to be the actions of the majority. The belief that more full nodes contribute to a more secure, decentralised network (Baran, 1964) leads operators to run nodes simply because others are doing so. This bandwagon effect reinforces the false belief that full nodes are participating in consensus when, in reality, their presence has no impact.

• P10: ∀x (Node(x) ∧ Majority(Node(x)) → Follow(Majority)) Translation: For all entities x, if x is a full node and perceives that the majority of other full nodes follow a certain behaviour, x will follow the majority.

This predicate illustrates how herding behaviour reinforces the perception of full node importance, even though full nodes are irrelevant to consensus. BTC Core leverages this herd mentality to maintain the illusion of decentralised governance, knowing that most full node operators will simply follow the majority without questioning their actual role.

5. Costly Signalling in Proof-of-Work: Miners’ Credible Participation

In contrast to full nodes, miners engage in costly signalling (Sun et al., 2020) through proof-of-work. The cost of mining (expending energy and computational resources) ensures that only those who are economically committed to the network can participate in block creation. This high cost makes miners’ signals credible, as they must follow the rules to avoid financial losses. By investing significant resources, miners send a clear and truthful signal that they are operating honestly within the Bitcoin protocol.

• P11: Cost(Miner(x)) >> Cost(Node(x)) Translation: The cost incurred by a miner x is significantly greater than the cost incurred by a full node operator.
• P12: Cost(Miner(x)) → CredibleSignal(Miner(x)) Translation: If a miner x incurs a high cost, then the miner’s signal (block creation) is credible.

These predicates highlight the stark contrast between miners and full nodes. Miners’ costly participation through proof-of-work ensures that they have a strong incentive to follow the protocol, making their actions credible and essential to consensus. Full nodes, which operate at little to no cost, send signals that are cheap and irrelevant (Farrell,1987, 1995) to the security and governance of the network .

Analysis of Dishonesty and Protocol Change

BTC Core contreolling the narative.

Dishonesty and the Difficulty of Changing the Bitcoin Protocol

For a dishonest chain to succeed, the miners following this chain would need to intentionally change the Bitcoin protocol. This change is not simply a matter of ignoring a valid block; it involves adopting new rules and convincing the majority of economic participants to also follow these rules. The protocol’s immutability makes this difficult, as any attempt to change the protocol requires widespread agreement, which is unlikely to happen without significant economic incentives or manipulation.

• P13: ∀x (Miner(x) ∧ DishonestChain(y) → ChangeProtocol(x)) Translation: For all entities x, if x is a miner and builds upon a dishonest chain y, then x must change the protocol.
• P14: ∀x (ChangeProtocol(x) → MajorityAdoptChange(x)) Translation: For all entities x, if x changes the protocol, then the majority of economic participants must adopt this change.

This pair of predicates outlines the difficulty in implementing a dishonest chain. Even if some miners attempt to follow a dishonest chain, they cannot succeed unless they change the protocol and convince the majority of the network to adopt this new rule set. Given the economic risks and punishments associated with deviating from the protocol, such attempts are both rare and unlikely to succeed without overwhelming manipulation.

Economic Punishment for Dishonesty: Why Miners Follow the Rules

Bitcoin’s consensus mechanism includes an inherent economic punishment for dishonest behaviour (Schelling, 1968). If a miner attempts to propagate a dishonest block or follow a dishonest chain, they risk losing their investment in computational resources, as honest miners will reject the invalid block. The network incentivises honesty by making the cost of dishonesty prohibitively high, further ensuring that miners adhere to the longest valid chain of honest blocks.

• P15: DishonestBehaviour(x) → Cost(Punishment(x)) >> Gain(DishonestBlock(x)) Translation: If entity x engages in dishonest behaviour, then the cost of punishment is significantly greater than the potential gain from propagating a dishonest block.

This predicate explains why miners are motivated to follow the rules of the protocol. The economic punishment for dishonesty is far greater than any potential reward from attempting to propagate an invalid block. This dynamic reinforces the security of Bitcoin’s consensus mechanism, ensuring that miners act honestly and continue to extend the longest chain of valid blocks.

Nodes must choose an honest path…

Psychological Manipulation of Full Node Operators

BTC Core’s narrative that full nodes are vital participants in consensus plays into psychological manipulation tactics (Balakrishnan et al., 2019; Book et al., 2015; Harrison et al., 2018). Full node operators, misled into believing they have influence, become emotionally and intellectually invested in running nodes, reinforcing their perception of value. This psychological manipulation is compounded by social pressure and herd mentality, where full node operators feel part of a collective action to secure the network, despite their irrelevance to consensus.

Psychological Investment: Believing in Full Node Importance

Full node operators may continue running nodes despite evidence of their irrelevance because of psychological investment (Camerer, 1997). When individuals invest time, effort, and resources into an activity, they are more likely to overestimate the value of that activity. This cognitive bias keeps full node operators entrenched in their belief that they are contributing to network security, even when their participation has no impact.

• P16: ∀x (Node(x) ∧ Investment(Time(x) ∧ Resources(x)) → OverestimateInfluence(x)) Translation: For all entities x, if x is a full node and invests time and resources, then x will overestimate its influence.

This predicate captures the psychological mechanism that leads full node operators to overestimate their importance. The more they invest in running nodes, the harder it becomes for them to accept that their actions do not influence consensus.

Social Influence and Herd Mentality

BTC Core also capitalises on social influence and herd mentality (Baddeley, 2010). Full node operators, seeing others running nodes and believing in the importance of decentralisation, may feel social pressure to follow the same path. The narrative of collective security and decentralisation encourages operators to act not based on the protocol’s actual requirements but on the perceived value of full node participation.

• P17: ∀x (Node(x) ∧ SocialInfluence(Majority(x)) → Follow(Majority(x))) Translation: For all entities x, if x is a full node and perceives social influence from the majority, then x will follow the majority.

This predicate demonstrates how social factors drive full node participation. The perception that running a full node contributes to a collective good encourages individuals to continue participating, even though their actions have no real impact on network governance.

Formal Conclusion: Full Nodes’ Irrelevance and BTC Core’s Manipulation

In this extended analysis, it has been demonstrated that full nodes are passive participants in Bitcoin’s network, playing no role in voting, consensus, or block selection. The only true form of voting in Bitcoin is done through proof-of-work, where miners automatically extend the longest chain of valid, honest blocks. Any attempt by miners to follow a dishonest chain would require changing the protocol and convincing the majority of economic actors to adopt the new rules—an event that is both economically and socially improbable without overwhelming manipulation.

BTC Core’s manipulation of full node operators relies on asymmetric information, false signalling, and psychological tactics. By convincing full node operators that they are essential to network governance, BTC Core creates a false narrative that reinforces the operators’ emotional and intellectual investment in running nodes. This illusion is further supported by social pressures and herding behaviour, where operators follow the perceived majority, even though their participation has no impact on consensus.

Ultimately, Bitcoin’s consensus and security are maintained by miners, whose costly signalling through proof-of-work ensures that only honest participants can afford to extend the blockchain. The small-world network structure of Bitcoin further cements miners’ central role, as they receive transactions and blocks before full nodes, rendering the latter irrelevant to consensus.

Consequently, it is proven that full nodes are passive entities that contribute neither to network governance nor security. BTC Core’s narrative is a manipulation designed to centralise control while giving full node operators a false sense of participation. The true power and security of the Bitcoin network lie in the hands of the miners, whose actions through proof-of-work are the only meaningful form of voting.

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