3.Results

This section records problems π∈Π\pi \in \Pi for which the pipeline Φ\Phi has been executed, along with the current verification status of each candidate proof. Entries are updated as work progresses.

The project is in its initial phase. All entries below represent active investigations, not completed proofs.

π728\pi_{728}Sum-free sets in finite abelian groups

2026-04

In Progress

Investigating upper bounds on the maximum size of sum-free subsets of arbitrary finite abelian groups. GPT-5.4 Pro produced a Fourier-analytic argument; Opus 4.6 applied the container method. Synthesis identified a gap in the Fourier approach and is refining the container bound.

π105\pi_{105}Covering systems with distinct moduli

2026-04

In Progress

Attacking the minimum modulus conjecture for covering systems. Opus 4.6 identified a promising family of constructions via Chinese Remainder Theorem residues. Formalization pending.

π210\pi_{210}Chromatic number of distance graphs

2026-04

In Progress

Seeking improved bounds on the chromatic number of the unit distance graph in the plane. GPT-5.4 Pro applied a Ramsey-type argument; Opus 4.6 used a probabilistic coloring. The synthesized bound is under verification.

Additional problems will be documented here as Φ\Phi is applied to new instances.