Kirti Singh | Searcharxiv

arXiv2025

Is mathematics like a game?

We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are inferential. The pure side of mathematics is essentially formalist, where we propose that truth is not carried by theorems corresponding to whatever independent reality and arrived at through proof, but is defined by correctness of rule-following (and as such is objective given these rules). Goedel's theorems, which are often seen as a threat to formalist philosophies of mathematics, actually strengthen our concept of truth. The applied side of mathematics arises from two practices: first, the dual nature of axiomatization as taking from heuristic practices like physics and informal mathematics whilst giving proofs and logical analysis; and second, the ability of using the inferential role of theorems to make surrogative inferences about natural phenomena. Our framework is pluralist, combining various (non-referential) philosophies of mathematics.

math.HO↗

arXiv2025

4-Swap: Achieving Grief-Free and Bribery-Safe Atomic Swaps Using Four Transactions

Cross-chain asset exchange is crucial for blockchain interoperability. Existing solutions rely on trusted third parties and risk asset loss, or use decentralized alternatives like atomic swaps, which suffer from grief attacks. Griefing occurs when a party prematurely exits, locking the counterparty's assets until a timelock expires. Hedged Atomic Swaps mitigate griefing by introducing a penalty premium; however, they increase the number of transactions from four (as in Tier Nolan's swap) to six, which in turn introduces new griefing risks. Grief-Free (GF) Swap reduces this to five transactions by consolidating assets and premiums on a single chain. However, no existing protocol achieves grief-free asset exchange in just four transactions. This paper presents 4-Swap, the first cross-chain atomic swap protocol that is both grief-free and bribery-safe, while completing asset exchange in just four transactions. By combining the griefing premium and principal into a single transaction per chain, 4-Swap reduces on-chain transactions, leading to faster execution compared to previous grief-free solutions. It is fully compatible with Bitcoin and operates without the need for any new opcodes. A game-theoretic analysis shows that rational participants have no incentive to deviate from the protocol, ensuring robust compliance and security.

cs.CR↗