Fork Rate-Based Analysis of the Longest Chain Growth Time Interval of a PoW Blockchain
Bibliographic record
Abstract
Nakamoto's consensus protocol, which is well known for its resistance to sybil attacks by using PoW (Proof of Work), enables us to build public blockchains, such as Bitcoin. In this protocol, miners seek to extend the longest chain by solving blockhash-based cryptographic puzzles and the required time is probabilistically determined. Therefore, the distribution of the time interval affects security, performance and applications which utilize the block height information. Some researchers assumed that the time follows an exponential distribution but this assumption requires that the blockchain network is fully synchronized. To overcome this unreal scenario, the bounded delay model, in which there is an upper bound for block propagation delay on the network, was proposed. However, it is difficult to calculate the upper bound without observing delay and bandwidth on real-world network links. To solve this problem, we proposed another method to analyze the distribution of the longest chain growth time interval by using the observed fork rate. We derived a closed-form lower bound for the CDF (Cumulative Distribution Function) of the time to update the global block height. We also obtained the Pearson distance which can be used as the metric to judge whether the network is approximately synchronous or not. Finally, we conducted network simulations for comparing our lower bound with the lower bound that is based on the bounded delay model. In numerical examples, we show how the block size affects these lower bounds.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".