Science in the Open
Multiscalar Intelligence is a research driven company, and we publish what we find. We believe open science is how a field advances: proofs, benchmarks, code and results released where anyone can check them, including the results that did not go our way. Our contributions begin with the foundations the rest of our work depends on, mathematics, mechanism design and economics, and extend to the multi-agent systems built on top of them.
We are opening a community of top tier researchers and engineers to collaborate on scientific work. If you would like to be part of it, write to hello@multiscalar.ai with your research interests and CV.
Six More Erdős Problems, in Five Days
Found by GPT-5.6 under the Multiscalar research prompt
Erdős problem 690 took months of harness engineering. These six took five days, and almost all of the work went into the prompt. Each one states exactly what a full proof has to establish, names the traps, and sends adversarial agents at every candidate argument. We attempted about thirteen problems, so a little under half worked out. Every proof is posted on the erdosproblems.com forum for public attack, and the prompt that produced it is published next to it.
- 390 An exact asymptotic for the least largest factor of a factorisation of n! Number Theory
- 486 A sieve whose survivors have no logarithmic density Number Theory
- 536 Sets with no three equal pairwise least common multiples have density zero Combinatorics
- 788 The trade-off function is a square root, up to no(1) Additive Combinatorics
- 1002 Rotation discrepancy converges to a Cauchy law Equidistribution
- 1038 The exact infimum of a polynomial sublevel set Approximation Theory
Proposed solutions, published for attack rather than certified. Source, prompts and Lean formalisations are at github.com/ShouqiaoW/erdos.
A Complete Answer to Erdős Problem 690
Discovered by the Multiscalar Fields System
We prove that the natural density dk(p), of integers whose k-th smallest prime divisor is p, is not unimodal for every k ≥ 4, completing Erdős' classification. The proof was discovered by the Multiscalar Fields System with limited human interaction.
Read the proof →Neural Compression of Satellite Imagery
Discovered by Multiscalar Dynamo
A Sentinel-2 earth-observation tile compressed by our learned codec with no visible loss. Drag the slider across rate points. Even at the highest ratio, the reconstruction stays visually identical to the original.