My journey as a researcher began with a PhD in applied math for the automotive & aeronautic industries! . Every day now, I'm amazed by the parallels between solving physics problems and building eth future. Blockchain draws from so many fields — an often underappreciated fact!.

New reference blog post from @class_lambda (super comprehensive and covers all the necessary stuffs about multilinear polynomials). Multilinear Polynomials: Survival Kit.

RT @drakefjustin: Ethereum Foundation Protocol will host a Reddit AMA on Aug 29 at 2pm UTC. questions can be submitted now :). https://t.co….

Hash based folding schemes by @kleptographic.

11/11 Why does this matter? . A tighter soundness proof (thanks to the proximity gap) means each query is more effective at catching fraud. This allows us to achieve high security with fewer queries, directly leading to smaller proof sizes and faster verification in STARKs.

10/11 By applying this logic at each recursive step, the proximity gap guarantees that if the final, tiny function is a low-degree polynomial, the initial, massive one must have been very close to one. This secures the entire protocol from the bottom up.

9/11 The "All-In" case forces a strong structural property called correlated agreement. It means the prover's original even and odd component functions must themselves be close to low-degree polynomials. The low-degree property is thereby propagated backward one step.

8/11 This "All-In or All-Out" property is super important. If the verifier sees that the combined function is close to a low-degree polynomial, the theorem implies the "All-In" case must be true.

7/11 The theorem dictates that such a line of functions must be either . - "All-In" (all functions on the line are close to the code) or .- "All-Out" (almost no functions are). A middle ground, where a significant fraction are close, is mathematically impossible.

6/11 This is precisely the attack vector that the Proximity Gap Theorem for Reed-Solomon codes eliminates. It addresses the properties of the entire line of possible functions the prover could have formed, not just the single one that was checked.

5/11 Here's the potential vulnerability: A malicious prover could craft two functions (even/odd parts) that are both far from low-degree, but hope their specific random combination appears close to a low-degree polynomial for the verifier's chosen random challenge.

4/11 The security analysis relies on soundness: proving that a dishonest prover, starting with a function that is far from any low-degree polynomial, will be caught. The core of the proof works backward, from the final small function to the initial large one.

3/11 FRI works through recursion. In each round, the prover "folds" a function into a smaller one. This is done by splitting the function into even and odd components and combining them with a random challenge z from the verifier, halving the domain size at each step.

2/11 First, a quick refresher: . The FRI protocol is a low-degree test. A prover claims a large dataset is the evaluation of a low-degree polynomial (a Reed-Solomon codeword), and a verifier needs to check this by sampling only a few points.

1/11 [Proximity prize] Why “proximity gap” matters for FRI (the low-degree test inside STARKs)? . It turns the folding check into a robust detector, which means smaller proofs and faster verification for the same security. Thread ↓.

RT @0xJaehaerys:

Link of the book (seems like there can be certificate error with the one originally shared):

WIP zkEVM book from EF’s zkEVM team for Ethereum engineers/researchers has been published recently: (repo: . It explains what we’re building, why, and how. Feedback welcome, under active construction.

15/ In short:. RISC-V is no longer just a hardware ISA: it’s becoming the backbone of zkVMs. Ethereum must decide: keep EVM as the core forever, or embrace RISC-V for (maybe) a simpler, faster, more interoperable future.

14/ Still, momentum is clear:. - Most zkVMs are already RISC-V based. - Ethereum research is aligning toward zk-friendly, minimal execution. - Enshrining RISC-V could unify prover and execution models, bringing efficiency and simplicity.

13/ Concerns remain:. - Should Ethereum commit to a single ISA, or preserve diversity?. - Is proving efficiency a premature optimization given fast-moving research?. - How to standardize host interfaces, syscalls, and precompiles in a zkVM world?.