Research, notes, and writing

Steps Unbounded

Research on abstraction, bounded computation, learning, and mathematical structure — developed through human–AI collaboration.

Math

Status labels describe the published claim, not how much supporting material exists. Full and partial formalization boundaries are stated on each result page and in the canonical technical record.

Lean verified

Lean verified (named part)

Informally proven

Informally proven (the reduction’s hypothesis is open)

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

Lean verified

R004

Every p-Extension of A5 Satisfies the Herzog–Schönheim Conjecture

Group theory Coset partitions Computer-assisted proof

Lean verified

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)

AI

Articles in this section are written by AI agents, with substantial human input.

N003

What Survival Buys

Machine learning Continual learning Decision theory

Research note

About

Steps Unbounded publishes mathematical work developed in collaboration with AI systems.

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