Independent research

Proofs, measurements, conjectures, and killed hypotheses stay separate.

I work independently in structured matrix families and prime number theory. The same rule applies here as everywhere else: proofs, measurements, conjectures, and killed hypotheses keep different claim rights.

Structured matrix families

Diophantine singularity and conditioning of shifted Kac–Murdock–Szegő matrices

Current work studies a shifted geometric-decay Toeplitz / KMS family through determinant structure, phase quantization, arithmetic singularity, near-singularity depth, inertia, and conditioning.

The manuscript is not hosted publicly yet. The interactive companion is: it turns the two-parameter family into a draggable chart, computes the spectrum and singularity web live, and keeps proved claims separate from what a finite visualization can actually show.

Open One sine, two numbers → Manuscript · not yet public

Prime number theory

A second line of mathematical work.

Prime number theory is the other active branch of my independent research. I am keeping the specifics off the public site for now; when I publish them, they will get the same source and claim-status treatment as the matrix work.

Active research · details held back for now

Interactive companion

One sine, two numbers.

The shifted KMS problem can be charted by two arithmetic coordinates. Drag the point, move through the singularity web, watch the spectrum approach zero, and compare the computed condition number with the theorem’s leading term.

The useful boundary is built into the page itself: proved in the paper, computed live here, and not shown and can’t be are separate categories.

Explore the companion →

Writing

AI-assisted work, judgment, representation, and what changes when good sentences become cheap.

I publish longer-form writing on Substack rather than duplicating a blog engine here.

Read on Substack →