Numbers. Relationships. Structure.
An independent research project exploring how the natural numbers fit together—and what those relationships can help us prove.
Current research / 01
Robin’s inequality places a precise limit on the sum of a number’s divisors. It holds for every whole number greater than 5,040 if and only if the Riemann Hypothesis is true.
We study how often that limit could fail, and build formally checked tools for investigating it.
A quantitative counting argument connecting estimates for zeta zeros, a centered Mertens identity and prime-support patterns. The manuscript is open for scrutiny. The shell/profile construction and canonical finite certification are separate follow-ups; the full analytic theorem remains outside that formalization.
25 October / Finite certification
For every real cutoff y in [100000, 102000], the actual canonical N(y) is greater than 5040 and strictly satisfies Robin’s inequality. A reusable generator and kernel checker certify complete events, exact ties and a compensated margin budget. This does not describe every integer in that numerical interval or prove a global sign result.
Read the result and its limits →The consolidated research also includes a completed finite prime-support certificate and the closed Plimpton E1–E3 experiments, including their negative findings. Explore the research and its evidence →
How the project works
Explore factorization, divisibility, residues and graphs in finite sets of integers. Use the pictures to formulate precise questions.
Check proposed patterns against reproducible computations, comparison cases and counterexamples.
State the assumptions, prove what follows, and identify what remains unresolved. Invite independent scrutiny.
An invitation to look closely
We welcome checks of individual arguments, missing hypotheses and references to earlier results. You do not need to review an entire manuscript to contribute.
