This report refines the concepts of idealized block generation and idealized network assumptions within blockchain and DAG-based consensus protocols. It formalizes the process in which network delay is absent, block production eligibility is determined by a public-coin/Bernoulli process, and block referencing is strictly limited to previously unreferenced blocks. The goal is to clarify the theoretical underpinnings and consensus implications of these idealizations.
In the idealized network model, there is no network delay or message latency. All validators observe the same global view of the system state at the beginning of each round. This assumption abstracts away real-world networking complexities such as asynchronous message delivery, propagation delays, or partitioning. The absence of delay ensures that all validators make decisions based on identical information, which is crucial for theoretical analysis of consensus safety and liveness. This model is often used as a baseline for protocol design and analysis before introducing more realistic network conditions.
Block generation proceeds in discrete rounds (or slots). In each round, a randomized process determines which validators are eligible to produce blocks. The randomization is modeled as an ideal public-coin process, often formalized as a Bernoulli process: each validator independently flips a public, unbiased coin to decide eligibility. This process is assumed to be perfectly fair, unpredictable, and unmanipulable, sidestepping the subtle issues of practical randomness generation (e.g., VRFs or randomness beacons). The result is that in every round, each validator has an independent, equal probability of being selected as a block producer.
All validators determined to be eligible in a round independently produce a block. Each block contains a set of transactions and references to previous blocks. There is no leader election or centralized coordination; all eligible validators act simultaneously and autonomously.
A core rule in this idealized model is that each newly produced block may reference only previous blocks that have not yet been referenced by any other block. In other words, a block can only reference blocks that are "tips"—blocks that have not yet appeared as a reference in any subsequent block. This rule ensures that:
To maximize the connectivity and consensus power of each new block, the protocol prescribes that each block references as many independent unreferenced blocks as possible. This set of blocks forms a maximal antichain: a largest possible collection of blocks within a sliding reference window such that no two blocks in the set are reachable from one another. Referencing the maximal antichain ensures that the new block "votes" for the greatest number of independent recent blocks, accelerating consensus convergence and making it more difficult for adversaries to build conflicting histories[[2]](https://www.notion.so/New-Cryptarchia-202261aa09df8026b31ad5e09c1a3fbb?pvs=53).
The combination of idealized network and block generation assumptions greatly simplifies the analysis of protocol safety (no conflicting histories are finalized) and liveness (honest blocks are eventually finalized). The maximal antichain referencing rule amplifies the influence of honest majority blocks and helps ensure that honest nodes rapidly converge on a single history, resisting adversarial attempts to split or delay consensus[[2]](https://www.notion.so/New-Cryptarchia-202261aa09df8026b31ad5e09c1a3fbb?pvs=53).