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In a network of mining pools that secure Bitcoin-like blockchains, it is known that a self-interested mining pool can dishonestly siphon off another pool’s mining rewards by executing a block withholding (BWH) attack. In this paper, we show that a BWH attack is always unprofitable for an initial startup period which is at least one difficulty retarget interval (approximately 14 days for Bitcoin). Furthermore, we prove that the payback period to recoup this initial startup cost is always at least as long as the initial unprofitable startup interval, and we show numerically that it can be substantially longer. Thus, the decision of whether or not to execute a BWH attack is not a dominant strategy, and the so called Miner’s Dilemma is not in fact a dilemma.
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On the generic behavior of the spectral norm
Our main result is that for any closed symplectic manifold, the spectral norm of the iterates of a Hamiltonian diffeomorphism is locally uniformly bounded away from zero C-infinity generically.
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- PAR ID:
- 10535784
- Publisher / Repository:
- Mathematical Sciences Publishers
- Date Published:
- Journal Name:
- Pacific Journal of Mathematics
- Volume:
- 328
- Issue:
- 1
- ISSN:
- 0030-8730
- Page Range / eLocation ID:
- 119 to 135
- Subject(s) / Keyword(s):
- Spectral norm periodic points Hamiltonian diffeomorphisms Floer homology
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.2140/pjm.2024.328.119
