Current papers

Problem papers

The #243 short paper leads with irrationality under the cubic rate $a_n^2/a_{n+1}=1+3/n+o(n^{-3})$ for strictly increasing positive integer sequences. Its bounded-increment criterion for an eventual Sylvester tail is a second result; the unrestricted problem remains open. The #1049 short paper proves a rational-base sufficient region using Zudilin’s forms after cyclotomic cancellation and denominator accounting. Its region contains $31/4$, which is outside the earlier Bundschuh–Väänänen sufficient region; $3/2$ remains open.

Reading the eight together

One cross-problem paper develops the mathematics that arises from reading the programmes together. For $c>0$ and integers $d\ge 1$, it considers entire functions $f(z)=\sum _{n\ge 1}{e}_n{z}^n/n!$ with nonnegative integer $e_n$ eventually bounded by $n^c$ and, for each fixed positive integer $q$, eventually divisible by $q$. The set of derivative-value vectors at $1$ has Hausdorff dimension $min(c,d)$ and contains an open set exactly when $c>d$. This result has an ordinary proof with the formal ingredients identified separately. The paper also contains the capacity and congruence criterion, Lambert-subsum results, exact computations and method limits.

Reading Eight Erdős Problems Together (source).

Follow the argument into its evidence

Read the assumptions of the result you want to use, then the proof. The longer record gives the surrounding working context, including routes that failed, finite experiments and open obligations. If you cannot reconstruct a step or find its source, that is useful feedback through Contributing.

Some results are checked in Lean; others are ordinary mathematical arguments or applications of cited external theorems. Each paper states the boundary for its own claims. Results and limits gives the result beside what remains open, and the source map connects the paper to supporting declarations. Lean files are proof authority only for the exact declarations they check; docs/claims.json records the selected public claim interfaces.

The full-text index provides generated Markdown versions for browsing. The PDFs and .tex files above are the authored manuscripts. The older joint #249/#257 paper is retained for provenance; it is not the entry point for either problem.

Project papers

Start with A Repository-Based System for Research and Publication (source). This is the main systems paper: it follows a result from its mathematical argument through formal support, written explanation, review and contribution.

Two earlier papers are retained as historical background. Their account is superseded by the main paper; their observations and cross-references belong to the revisions they describe.

For current use, follow the reading guide, agent instructions or Contributing.

For the repository layout, sources of truth, build path, and release infrastructure, see docs/ARCHITECTURE.md.

Sources and earlier manuscripts

The manuscript layer (the .tex sources and rendered PDFs) is licensed CC-BY-4.0; see REUSE.toml at the repository root.