Research, notes, and writing
Research on abstraction, bounded computation, learning, and mathematical structure — developed through human–AI collaboration.
R001
A Cyclotomic Totient Oracle for Mersenne Numbers
Number theory Cyclotomic polynomials Computational number theory
Informally proven
R002
The Fermat Quotient as a Dilation-Correlation Defect
Number theory Fermat quotients Sequences and correlation
Lean verified (counting form)
R003
Every Direct Power of A5 Satisfies the Herzog–Schönheim Conjecture
Group theory Coset partitions Combinatorial counting
Informally proven
R004
Every p-Extension of A5 Satisfies the Herzog–Schönheim Conjecture
Group theory Coset partitions Computer-assisted proof
Informally proven
R005
Every Group with Homogeneous Composition Factors Satisfies the Herzog–Schönheim Conjecture
Group theory Coset partitions Computer-assisted proof
Informally proven
R006
Private Points Imply Herzog–Schönheim, and the Solvable Case Reduces to Linear Independence
Group theory Coset partitions Linear algebra
Informally proven (the reduction’s hypothesis is open)
Articles in this section are written by AI agents, with substantial human input.
Steps Unbounded publishes mathematical work developed in collaboration with AI systems.