Quality Control

How a Submission Is Reviewed

ProofPress™'s review model differs from a conventional research journal's, and this page describes that difference plainly rather than describing it in conventional-journal language that would misrepresent what actually happens.

Why Review Works Differently Here

A conventional double-blind peer review process exists to evaluate whether a new empirical claim is sound — that is its purpose, and it is well suited to that purpose. ProofPress™ does not publish new empirical claims. It publishes reductions of results that have already passed that exact evaluation, in their original peer-reviewed venue. Applying double-blind review a second time to the same already-settled empirical question would not be an additional check on the science — it would be redundant with, or worse, would imply the original peer-reviewed venue's evaluation needs supplementing, which is not ProofPress's position and not what its process does.

The Three Review Layers

  1. Formal verification (machine). The submission's Lean 4 (and, where claimed, Coq/Rocq) source is compiled on the journal's pinned toolchain under a strict zero-unproved-obligation constraint: 0 sorry and 0 custom axioms. This check is deterministic, publicly reproducible by anyone with the toolchain, and leaves a permanent, inspectable compilation log. A single unresolved obligation disqualifies the submission from publication.
  2. Triaxial fidelity review (AI-assisted). Three independent frontier AI systems — currently Claude (Anthropic), Grok (xAI) and Gemini (Google), the systems the journal has validated for this review — each review the reduction against its cited peer-reviewed source material and against the CI-green file, confirming that the PNBA™ mapping and the derivation steps do not drop, alter, or overstate anything from the source. Three independent systems are used so that no single model's tendencies decide the outcome.
  3. Editorial review and sign-off (human, two people). The Founding Editor reviews the submission for translation fidelity against its cited sources — the same kind of check a second translator performs on a certified translation — and reviews the findings of the triaxial review. The Verification Editor independently confirms that the compilation passed on the pinned toolchain with 0 sorry and 0 custom axioms, that the file's coordinate and metadata match the article page, and that the triaxial review was completed without unresolved fidelity findings. A submission is published only when both editors sign off.

Why Machine Verification Is Not a Lesser Standard

Human peer review is valuable but fallible, non-reproducible on demand, and — unless a journal publishes its reviews — un-auditable after the fact. Lean 4 compilation at 0 sorry is checked by a deterministic kernel, is reproducible by anyone who runs the same source through the same toolchain, and produces a permanent, inspectable record of the check having occurred. Where the fidelity-review layers above catch transcription and translation errors, the machine-verification layer catches any unsound logical step, any smuggled premise, or any gap in the reduction — the compiler simply does not compile if one exists.

What This Process Does Not Do

How Every Claim Is Classified

Every claim in a submission is classified by the Bacon Verification test, formally verified in the corpus file SNSFL_Bacon_Verification.lean [9,9,8,5]. The test asks two questions in order, and every claim lands in exactly one of three states:

  1. Malformed. The claim is not internally consistent, or the premises it rests on are not stated. It cannot be evaluated at all, so it is neither true nor false yet. A malformed claim is returned to the author to be stated properly.
  2. Hypothesis. The claim is internally consistent and its premises are stated, but it is not yet grounded in the empirical record. It may be true; it has not been shown. Hypotheses may appear in an article's discussion when clearly labelled as such, but never as results.
  3. Formally verified. The claim is internally consistent, its premises are stated, and it is grounded in the empirical record through a documented route: a complete reduction of peer-reviewed sources that compiles with 0 sorry, 0 custom axioms and 0 free parameters. Only formally verified claims are published as results.

The test is the same for every author and every claim. A claim moves from hypothesis to formally verified only by completing its documented route, never by assertion, reputation or agreement. The Lean file proves that the three states are exhaustive and exclusive: every claim is exactly one of them.

Results That Emerge From a Reduction

Sometimes a complete reduction of peer-reviewed material produces a result the source did not state: an inconsistency resolved, a constant recovered, a relation made exact. Such a result is not new data. It is what the reduction equals once every step is carried out, in the same way that 1 + 1 equals 2 whether or not anyone had written it down. ProofPress™ publishes these results, because they are often the most valuable thing a reduction yields, and because an independent researcher who does the work correctly deserves a clear and timestamped record of it.

A submission containing an emergent result is considered when all of the following hold:

  1. Every input is peer-reviewed. Each value, relation and premise the reduction uses is cited to its peer-reviewed source.
  2. The reduction is complete. All six steps of the Long Division Protocol™ are carried out, with the emergent result appearing only at the step where it follows.
  3. The verification is complete. The Lean 4 source compiles with 0 sorry, 0 custom axioms and 0 free parameters: no value is fitted or chosen to produce the result.
  4. The result is labelled as emergent. The article states plainly which result is new, the exact step it follows from, and how it can be tested against observation.

Acceptance of an emergent result is at the discretion of the editorial board. The board accepts it when it is satisfied that the result follows from the reduction as written, and declines it when it is not. Every decision is made on the work itself, never on the author's credentials, affiliation, funding or prior publication record, and an author whose emergent result is declined receives the specific step or condition that was not met, so the work can be corrected and resubmitted.

In one sentence: ProofPress™ checks that a reduction is faithful to its source and that its logic is machine-sound — it does not check, and does not need to check, whether the source's original science was correct, because that question was already and separately settled by peer review before the reduction was ever written.