WARPfold : Wrongfield ARithmetic for Protostar folding

Inspired by range-check trick from recent Latticefold paper we construct elliptic-curve based IVC capable of simulating non-native arithmetic efficiently. We explain the general principle (which can be applied to both Protostar and Hypernova), and describe the Wrongfield ARithmetic for Protostar folding in details. Our construction supports circuits over mutilple non-native fields simultaneously and allows interfacing between them using range-checked elements. WARPfold can be used to warp between different proof systems and construct folding schemes over curves not admitting a dual partner (such as BLS12-381)

Power circuits: a new arithmetization for GKR-styled sumcheck

Goldwasser-Kalai-Rothblum protocol (GKR) for layered circuits is a sumcheck-based argument of knowledge for layered circuits, running in $\sim 2\mu \ell$ amount of rounds, where $\ell$ is the amount of layers and $\mu$ is the average layer logsize. For a layer $i$ of size $2^{\mu_i}$ the main work consists of running a sumcheck protocol of the form $$\underset{x,y}{\sum} \text{Add}_i(x,y,z)(f(x)+f(y)) + \text{Mul}_i(x,y,z)f(x)f(y)$$ over a $2^{2\mu_i}$-dimensional cube, where $\text{Add}_i(x,y,z)$ and $\text{Mul}_i(x,y,z)$ are (typically relatively sparse) polynomials called wiring predicates . We present a different approach, based on the (trivial) observation that multiplication can be expressed through linear operations and squaring. This leads to the different wiring, which is marginally more efficient even in a worst-case scenario, and decreases the amount of communication $\sim 2 \times$ in the case where wiring predicates are sparse

Reverie: an end-to-end accumulation scheme from Cyclefold

Recent advances in SNARK recursion and incrementally-verifiable computation are vast, but most of the efforts seem to be focused on a particular design goal - proving the result of a large computation known completely in advance. There are other possible applications, requiring different design tradeoffs. Particularly interesting direction is a case with a swarm of collaborating provers, communicating over a peer-to-peer network - which requires to also optimize the amount of data exchanged between the participants of the swarm. One notable such application is Ethereum\u27s consensus, which requires to aggregate millions of signatures of individual validators. In this technical note, we propose an informal notion of an end-to-end IVC scheme, which means that the amount of data that the prover needs exchange with the previous prover to continue the computation is small. We explore the existing design space from this point of view, and suggest an approach to constructing such a scheme by combining the PlonK proof systemwith the recent Cyclefold construction

Networks uncover hidden lexical borrowing in Indo-European language evolution

Language evolution is traditionally described in terms of family trees with ancestral languages splitting into descendent languages. However, it has long been recognized that language evolution also entails horizontal components, most commonly through lexical borrowing. For example, the English language was heavily influenced by Old Norse and Old French; eight per cent of its basic vocabulary is borrowed. Borrowing is a distinctly non-tree-like process—akin to horizontal gene transfer in genome evolution—that cannot be recovered by phylogenetic trees. Here, we infer the frequency of hidden borrowing among 2346 cognates (etymologically related words) of basic vocabulary distributed across 84 Indo-European languages. The dataset includes 124 (5%) known borrowings. Applying the uniformitarian principle to inventory dynamics in past and present basic vocabularies, we find that 1373 (61%) of the cognates have been affected by borrowing during their history. Our approach correctly identified 117 (94%) known borrowings. Reconstructed phylogenetic networks that capture both vertical and horizontal components of evolutionary history reveal that, on average, eight per cent of the words of basic vocabulary in each Indo-European language were involved in borrowing during evolution. Basic vocabulary is often assumed to be relatively resistant to borrowing. Our results indicate that the impact of borrowing is far more widespread than previously thought