A research laboratory of Metriq Foundation
Mathematics, intelligent systems, and computational methods. An open record of the work.
Explore the researchProgram for Research in
Intelligent Systems and Methods
14 candidate proofs to unsolved math problems.
29 current publications.
Open research record.
One count per current, publicly released manuscript that explicitly presents a candidate resolution of a mathematical open question. Partial-progress papers, research reports, technical notes, publication holds, withdrawn work, and duplicate versions are excluded. The website catalog contains 29 records; 14 meet this rule.
Candidate preprint / v1.3
An Explicit Cantorval Achievement Set with Convergent Consecutive-Term Ratio
An explicit base-4 construction presented as a candidate affirmative solution to the Second Jones Problem.
Not peer reviewed. See the record for scope and status.
Candidate preprint / v1.3
An Achievable Cantorval with Full-Dimensional Boundary
A variable-base construction examining whether an achievable Cantorval can have a boundary of Hausdorff dimension one.
Not peer reviewed. See the record for scope and status.
Candidate preprint / v1.4
Every Infinite Achievement Set Is a Sum of Two Achievement Sets of Hausdorff Dimension Zero
A candidate decomposition of infinite achievement sets into a Minkowski sum of two zero-dimensional achievement sets.
Not peer reviewed. See the record for scope and status.
Candidate preprint / v1.2
An Achievable Cantorval with Zero-Dimensional Boundary
A factorial mixed-radix construction examining achievable Cantorvals with zero-dimensional boundary.
Not peer reviewed. See the record for scope and status.
Publication hold / v1.2
A Note on the Literal Formulation of Problem 13 for Fast Achievement-Set Sumsets
An interpretation note on Problem 13. Publication remains on hold pending clarification of the source authors’ intended formulation.
Awaiting source-author clarification.
Candidate preprint / v2.2
Finite Certificates for Three Unresolved Cardinal-Function Ranges
Three exact finite subset-sum certificates, with Cantor-set extensions and reproducible verification materials.
Not peer reviewed. See the record for scope and status.
Candidate preprint / v1.2
Endpoint Walks Evaluate the Complete Homogeneous Symmetric Norms of Path Graphs
A candidate identity connecting endpoint walks on path graphs with complete homogeneous symmetric norms.
Not peer reviewed. See the record for scope and status.
Candidate preprint / v1.1
A Bessel-Factorization Proof of Mathar's Recurrence for Type-ace Lattice Walks
A candidate proof of Mathar’s recurrence for Type-ace lattice walks, accompanied by exact verification materials.
Not peer reviewed. See the record for scope and status.
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This collection reflects the 2026-09-12 catalog: 29 current records across four research programs. Publication status stays with every record.
Canonical catalogMetriq PRISM Laboratory brings mathematical reasoning and computational methods to difficult problems. We develop ideas, examine their limits, and share the work that others can build on.
Part of Metriq FoundationBring us a problem worth solving. We’ll start with the question, agree on a useful scope, and identify the research needed to move it forward.
Prefer email? prism@metriq.org
Email a short outline of your problem, what you have already tried, and what a useful result would look like.
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