research_claim.md

Research Claim Standard

Power-House must not call a result "the first in history" merely because its implicit domain is extremely large. Classical sum-check, GKR, Spartan, Jolt, STARKs, and multilinear polynomial commitments already verify computations whose expanded representations are infeasible to materialize.

Relevant prior art includes:

• Justin Thaler, Proofs, Arguments, and Zero-Knowledge: https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.html
• A Time-Space Tradeoff for the Sumcheck Prover: https://eprint.iacr.org/2024/524
• Spartan: https://github.com/microsoft/Spartan
• Jolt: https://eprint.iacr.org/2023/1217
• LiLAC multilinear polynomial commitments: https://eprint.iacr.org/2024/1943
• Recent sub-linear GKR work: https://eprint.iacr.org/2025/717

Current Established Result

Power-House has a reproducible public engineering artifact:

A Rust/Python reproducible, one-million-round deterministic sum-check transcript for a separately stored, hash-bound sparse multilinear polynomial over a one-million-variable Boolean domain, with a stable 16 MB certificate and no hypercube allocation.

This is an engineering result, not an established world-first claim. The v1 verifier reads the complete workload and recomputes the exact expected transcript. The represented sum also has a closed form. These facts prevent a succinct-verification or novel-protocol claim. See Security Model and Prior-Art Review.

Historical Claim Gates

The project may use a world-first or historical claim only after all gates are complete:

1. Protocol specification
   Publish the polynomial derivation, transcript, binary certificate format, field assumptions, complexity analysis, and security limitations.

2. Immutable artifact
   Publish source, certificate, manifest, checksums, compiler version, hardware details, and exact commands in a timestamped release or archival DOI.

3. Independent implementation
   Obtain verification by an implementation authored by an unaffiliated team. The bundled Python verifier is useful cross-language conformance evidence but is not an independent external audit.

4. Prior-art comparison
   Compare the result directly against sum-check, sparse-dense sum-check, GKR, Spartan, Jolt, Scribe, and multilinear commitment systems. Domain size alone is not a valid comparison metric.

5. External reproduction
   At least two unaffiliated parties must reproduce the certificate digest and publish machine details and timings.

6. Cryptographic scope
   The PHSMv1/PHCPv1 workflow binds public external data with BLAKE2b-256. For a general or succinct verifiable-computation claim, replace full workload replay with a reviewed multilinear polynomial commitment and an opening proof for an externally supplied computation or witness. A standard one-repetition sum-check at the published million-round field parameters has only about 9.97 bits under the classical n/|F| bound.

7. Public review
   Publish a technical preprint and obtain specialist review or a formal audit.

Claim Levels

• Allowed now: "Power-House deterministically replays a separately stored, hash-bound sparse polynomial transcript over a one-million-variable Boolean domain through a million-round reproducible certificate."
• Allowed after external reproduction: "Power-House publishes an independently reproduced million-round sparse sum-check artifact."
• Allowed after novelty review: A narrowly worded "first" claim matching exactly what the literature review and audit establish.
• Not currently allowed: "Quantum computers were previously required" or "first system to verify computations beyond sextillion scale."