Skip to content

hyperscale_proof.md

Latest commit

 

History

History
65 lines (45 loc) · 1.79 KB

hyperscale_proof.md

File metadata and controls

65 lines (45 loc) · 1.79 KB

Hyperscale Seeded-Affine Proof

examples/hyperscale_affine.rs demonstrates a non-constant sum-check certificate over domains far larger than sextillion scale.

The default run proves and verifies a seeded affine multilinear polynomial over 2^4096 Boolean points. That is roughly 1e1233 evaluations. The verifier does not enumerate the domain; it replays 4096 linear sum-check rounds.

Public Polynomial

The polynomial is:

f(x_0, ..., x_{n-1}) = c + a_0*x_0 + ... + a_{n-1}*x_{n-1}

c and the coefficients a_i are derived deterministically from:

  • the public seed,
  • the field modulus,
  • the number of variables,
  • the domain tag power_house:v1:seeded-affine.

The seed is not a secret. It is the compact public description of the structured computation being verified.

Claimed Sum

For an affine multilinear polynomial over {0,1}^n:

sum_x f(x) = 2^n*c + 2^(n-1)*sum_i a_i

All arithmetic is performed modulo the finite field.

Verifier Work

The verifier checks:

  1. the claimed sum matches the public seed-derived coefficients,
  2. each round polynomial satisfies g_i(0) + g_i(1) = running_claim,
  3. each round polynomial matches the affine closed form after previous Fiat-Shamir challenges are fixed,
  4. the final folded value equals the affine evaluation at the verifier's challenge point.

This is an O(n) certificate for this structured family. It is not claiming to verify an arbitrary 2^4096-entry table without a commitment or polynomial oracle. The point is precise: once the computation has a compact algebraic description, power_house can verify claims over domains that are physically impossible to enumerate.

Run

cargo run --example hyperscale_affine

For a faster CI-sized run:

cargo run --example hyperscale_affine -- 1024