arxiv: 2605.05193 · v1 · submitted 2026-05-06 · 🧮 math.PR · cs.AI· math.AP· math.CA· math.FA

Recognition: unknown

Grokability in five inequalities

Paata Ivanisvili , Xinyuan Xie

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:10 UTC · model grok-4.3

classification 🧮 math.PR cs.AImath.APmath.CAmath.FA

keywords inequalitiesGaussian perimeterHamming cubeautoconvolutionSidon setsSzarek inequalitymathematical discovery

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The pith

Grok suggested five inequalities that the authors verified as improvements over prior results in Gaussian geometry and discrete analysis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reports five discoveries made in collaboration with Grok, each an inequality that the authors proved after the suggestion. These consist of a better lower bound for the largest Gaussian perimeter among convex sets in R to the n, sharper L two to L one moment comparisons on the Hamming cube, a stronger autoconvolution inequality, improved bounds on the largest g-Sidon sets up to n, and an optimal balanced Szarek inequality. The work shows that the AI can generate conjectures which, when checked, yield new mathematical facts. Readers might care as it provides concrete examples of AI contributing to inequality research in a verifiable way.

Core claim

The authors claim to have verified five inequalities proposed by Grok: an improved lower bound on the maximal Gaussian perimeter of convex sets in R^n, sharper L_2-L_1 moment comparison inequalities on the Hamming cube, a strengthened autoconvolution inequality, improved asymptotic bounds on the size of the largest g-Sidon sets in {1,...,n}, and an optimal balanced Szarek's inequality.

What carries the argument

The five Grok-proposed inequalities that serve as the specific advancements in their fields after verification.

If this is right

Convex sets achieve higher minimal Gaussian perimeters than earlier estimates allowed.
Moment comparisons on the hypercube become sharper in the L2 versus L1 regime.
The autoconvolution inequality is strengthened beyond its previous form.
g-Sidon sets have their maximal size bounded more precisely for large n.
The balanced Szarek inequality now holds with the optimal constant.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method of AI conjecture generation followed by proof could be tested in additional branches of mathematics.
It remains to be seen how many such suggestions turn out to be both correct and new.
This division of labor between suggestion and verification may become a standard tool for researchers.

Load-bearing premise

The suggestions made by Grok during the collaboration are accurate inequalities that had not been established before the authors' work.

What would settle it

A single counterexample to any claimed inequality or the discovery of a prior proof of one of them would invalidate the report of new discoveries.

read the original abstract

In this note, we report five mathematical discoveries made in collaboration with Grok, all of which have been subsequently verified by the authors. These include an improved lower bound on the maximal Gaussian perimeter of convex sets in $\mathbb{R}^n$, sharper $L_2$-$L_1$ moment comparison inequalities on the Hamming cube $\{-1,1\}^n$, a strengthened autoconvolution inequality, improved asymptotic bounds on the size of the largest $g$-Sidon sets in $\{1,\dots,n\}$, and an optimal balanced Szarek's inequality.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This short note lists five inequalities the authors say Grok suggested and they verified, but supplies no proofs or literature checks so the claims rest on their word alone.

read the letter

The one thing to know is that this paper is a short announcement of five inequalities the authors say they discovered by working with Grok and then verified on their own. The new parts are the specific bounds they list: an improved lower bound on maximal Gaussian perimeter for convex sets, sharper L2 to L1 moment inequalities on the cube, a strengthened autoconvolution inequality, better asymptotic bounds for g-Sidon sets, and an optimal balanced version of Szarek's inequality. If these turn out to be correct and original, they represent modest progress in those areas of probability and combinatorics. The authors handle the AI part responsibly by stating that they verified the results themselves. That is the right standard. The soft spots are clear. The note gives no proofs, no sketches, and no detailed comparison to existing literature. A reader cannot check the derivations or see why these are improvements over what was known. The verification is internal, with no machine-checked code or independent checks mentioned. This makes the central claim rest on trust rather than evidence in the paper. For a specialist in one of those five topics, the paper might be worth a quick look to see if the stated inequality matches what they know, but most readers will need the full proofs to get anything out of it. It is not a paper that stands alone. I would bring this to a reading group only if we were talking about AI-assisted math research. I would not cite the inequalities without seeing the proofs. It deserves peer review because the topic of AI in math discovery is timely and the claims are specific enough that referees could usefully ask for the details and check the literature search.

Referee Report

1 major / 0 minor

Summary. The manuscript reports five inequalities discovered via collaboration with Grok and verified by the authors: an improved lower bound on the maximal Gaussian perimeter of convex sets in R^n, sharper L2-L1 moment comparisons on the Hamming cube, a strengthened autoconvolution inequality, improved asymptotic bounds on g-Sidon sets in {1,...,n}, and an optimal balanced Szarek inequality.

Significance. If rigorously correct and novel, these would constitute incremental advances in geometric probability, discrete Fourier analysis, additive combinatorics, and functional inequalities. The note format and emphasis on AI collaboration limit assessment of their technical depth or broader impact.

major comments (1)

[Abstract] Abstract: the central claim that the five results are verified discoveries is unsupported because the manuscript contains no explicit statements of the inequalities, no proof sketches, no error bounds, and no verification steps for any of the five items. This directly prevents evaluation of correctness or novelty.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review and the opportunity to clarify our manuscript. We address the single major comment below and commit to a substantial revision that incorporates explicit details for each result.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the five results are verified discoveries is unsupported because the manuscript contains no explicit statements of the inequalities, no proof sketches, no error bounds, and no verification steps for any of the five items. This directly prevents evaluation of correctness or novelty.

Authors: We agree that the current manuscript is too concise and does not contain the explicit statements, comparisons, or verification details needed for independent assessment. The note was written to highlight the AI-collaboration aspect, but this came at the expense of technical content. In the revised version we will add a dedicated section for each of the five inequalities. Each section will state the precise inequality (including the improved constants or bounds), compare it to the best previously known result, and describe the verification performed by the authors (analytical proofs where available, or rigorous numerical checks with explicit error bounds otherwise). This will directly support the claim of verified discoveries and enable evaluation of novelty and correctness. revision: yes

Circularity Check

0 steps flagged

No circularity: paper reports externally verified inequalities without self-referential derivations

full rationale

The manuscript states that five inequalities were suggested by Grok and then rigorously verified by the authors. No derivation chains, parameter fittings, or first-principles steps are exhibited that reduce to the paper's own inputs by construction. There are no self-citations invoked as load-bearing uniqueness theorems, no ansatzes smuggled via prior work, and no renaming of known results presented as new organization. The central claims rest on the authors' verification (external to any internal fitting loop), making the note self-contained against the listed circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, ad-hoc axioms, or invented entities are mentioned in the abstract; the work rests on standard axioms of real analysis and probability theory.

pith-pipeline@v0.9.0 · 5388 in / 1009 out tokens · 68556 ms · 2026-05-08T16:10:12.514878+00:00 · methodology

discussion (0)

Reference graph

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