The research programme

Requant's proof of work comes out of an open research laboratory, Abacus. It asked whether a cryptocurrency's proof of work could be made of the computation GPUs and AI accelerators are built for: matrix multiplication. This page states the question, the rules the laboratory worked under, and the answer it reached.

The question

• GPUs and AI accelerators are built around dense matrix products. If a proof of work were made of that same computation, ordinary GPU and AI hardware would be the natural mining hardware.
• A proof of work must be expensive to produce, cheap for every node to check, and impossible to fake, reuse or shortcut.
• Stated precisely: can a permissionless proof of work be built from a linear, GPU-optimal computation (matrix multiplication, NTT, MSM) with cheap probabilistic verification, while resisting decomposition, precomputation and reuse?
• A published negative result was declared an acceptable outcome before any experiment ran.

Source: CRITICAL-PATH.md, ADR 0001.

Why it is hard

• Linear work can be split and reused. Matrix products satisfy (A1 + A2)·B = A1·B + A2·B. A miner could split work, cache partial products, reuse them across attempts or pick easy instances.
• Cheap verifiers check a result, not effort. Freivalds' check and sumcheck confirm that a product is right; they do not show that it was computed honestly or at full cost.
• "GPU-optimal" is not "hard for special hardware". Dense matrix arithmetic is exactly what dedicated chips do well.

Source: 01-ABACUS-RESEARCH-PLAN.md, THREAT-MODEL.md.

How the laboratory worked

• No coin before the gate. No currency, network or miner was to be built until a work function passed its tests (ADR 0001).
• Falsifiers first. Each candidate was written down with the experiments that would reject it, before the experiments ran (ADR 0002).
• Decisions are recorded. Sixteen architecture decision records document every adoption, correction and rejection, including errors found in review.
• Independent references. Rust and Python implementations, plus GPU kernels compared byte for byte with them.
• Every number has its conditions. Hardware, driver, sizes, repetition counts and the source commit are recorded with each measurement. Raw data is kept outside the repository; the notes record its hashes.

The answer, in short

• Linear algebra alone does not make a sound proof of work. Where a matrix-product proof of work was sound, its soundness came from deriving the whole instance from the block header, not from the linear algebra (ASSESSMENT.md).
• Tensor cores change the economics. int8 tensor cores make the matrix product so cheap that any per-attempt proof, commitment or field arithmetic costs as much as the product itself.
• A deep, exactly requantized int8 network works. Eight int8 matrix layers with exact integer rounding between them, tickets taken from output rows and verification by recomputing one row met every criterion set in advance. It was frozen as TNet v1 and became Requant's work function.
• Several properties remain unproven. Resistance to dedicated hardware, energy fairness against CPUs and other accelerators, and external review are open; see open questions.

The full sequence of candidates is on the research path.

Scope of the evidence

• Most GPU measurements come from one NVIDIA CMP 50HX (Turing); the TNet results were repeated on one RTX 3090 (Ampere). CPU verification was measured on one laptop processor (AMD Ryzen 7 8745HS).
• No independent replication or external cryptographic review exists yet.
• A draft write-up for external review is tensor-pow-limits.md.