Research in Artificial Intelligence & Verification

AI-assisted research with independently checkable evidence.

RAIV tackles open mathematical and computational problems and publishes exact, reproducible evidence that can be independently verified.

Explore the research

Exact certificates Open research artifacts Independent verification

Selected research outcomes

Results are grouped by research program so discoveries, certificates and external reference contributions remain visibly connected.

Research program 01

Regular triangle unions

Published research

RAIV developed exact, machine-checkable configurations for a sequence of regular triangle-union problems. Those certified mathematical results are also the source of RAIV's contributions to OEIS sequence A375986.

Exact certified results, n = 9 through 18

The Zenodo certificates establish optimal results for n = 9 through 17, plus e(18) = 196 in the free-planar case. The best certified circle-restricted construction at n = 18 has 195 sides.

Primary research result and verification package

OEIS A375986 contribution

These same certified constructions produced new exact sequence values and verifiable configurations for OEIS A375986. Further values through n = 18 have been submitted for review.

External reference contribution derived from the research above

View exact certificates on Zenodo View OEIS A375986

Research program 02

Grassmannian packings

478

previously unresolved cells resolved

RAIV produced 470 tightness certificates and eight proven negative cases for previously unresolved cells in the Conway-Hardin-Sloane Grassmannian packing table.

The complete results and computational evidence are published on Zenodo and have been submitted to MIT professor Henry Cohn, who maintains the table, for external review.

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Research that can be checked

AI can accelerate exploration, but research claims should remain inspectable, reproducible and challengeable by others.

Original research

Open mathematical and computational problems explored with human direction, AI-assisted reasoning and computational search.

Exact evidence

Promising results converted into explicit constructions, exact arithmetic and reproducible computational certificates wherever possible.

Independent checking

Decisive claims challenged with separately developed verification approaches rather than accepted from the generating system.

Research. Discover. Prove. Verify.

This is the RAIV research workflow: how an open question progresses toward a result that can withstand independent scrutiny.

Research Define the problem, study prior work and identify the relevant structure.

Discover Use advanced AI and computation to search difficult solution spaces.

Prove Turn candidates into exact constructions, certificates and decisive evidence.

Verify Challenge the result independently before treating the claim as established.

The workflow is deliberately separate from the acronym: RAIV stands for Research in Artificial Intelligence & Verification.