# kaal:claim:3125827-037

**Claim.** Under the worst case model with no admission safeguards and no other users paying fees, a malicious group must invest at minimum twice the total sem tokens of the system to reach 50% voting power in the validation pool, because half of every fee it pays mints tokens for the existing good faith experts.

**Type.** empirical  **Support.** evidenced

**Holds when.**

- no safeguards on joining as an expert
- no other users adding fees
- continuous micro payment strategy, which is the attacker's optimum

**Source quote.**

> Consequently the malicious group would need to invest an absolute minimum of 2g8 , that is, double the total sem tokens of the system to gain 50% power in the system in order to outvote the rest of the good-faith experts in the validation pool.

**From.** Craig Calcaterra, Wulf A. Kaal, *Secure Proof of Stake Protocol* (2018), A.1 The price to purchase 51% of the sem tokens, page 31

**Cite as.** Craig Calcaterra, Wulf A. Kaal, Secure Proof of Stake Protocol (2018). SSRN: https://ssrn.com/abstract=3125827

**Verify.** sha256 of source PDF `598d9bd95e4af7a0a35328677c6bfc069f69f2e32c30c720b3a0be98a23a40cb` at https://raw.githubusercontent.com/wulfkaal/Academic-Papers/main/papers/pdf/Calcaterra%20and%20Kaal%20-%202018%20-%20Secure%20Proof%20of%20Stake%20Protocol.pdf

**Topics.** consensus-and-security, tokenomics

**Keywords.** attack-cost, 51-percent-attack, formal-proof, token-minting, sem-tokens

**Related claims.**

- supports: https://wulfkaal.github.io/claims/3125822-022
- extends: https://wulfkaal.github.io/claims/3125822-019

**Canonical form.** This markdown file is the canonical hashed representation of the claim. Its sha256 is the content hash used for attestation.