Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Research
erdos_1150/: Source notes and audits of claimed flatness proofs for Littlewood polynomials, written before the release's disproof.
erdos_1171/: Reconstruction of the conditional proof of the finite-color relation for omega_1 squared under Martin's axiom; the ZFC question stays open.
erdos_1219/: Author-recorded reconstruction of Shelah's Canonization Lemma 1.1, Theorem 1.2 and Corollary 1.3, which prove Problem 1219; the status is unchanged.
erdos_1221/: Source-proof reconstructions for the de Bruijn–Erdős consecutive-gap constants: the 1949 bounds, the fixed-r ratio improvement, the balanced-stick upper bound and the claimed 2026 resolution, each with the reading of the problem it addresses; the problem stays open.
erdos_132/: Source notes on published work on rare distances in planar point sets; both questions are open.
erdos_15/: Author-recorded reconstruction of Tao's conditional convergence proof under the uniform prime tuples conjecture; the unconditional question remains open.
erdos_156/: The cubic-root problem, its counting lower bound, and the Ruzsa benchmark.
erdos_18/: Author-recorded reconstructions of the proved factorial bounds and of the claimed (log log n)^2 construction for Problem 18; all three questions keep their recorded status.
erdos_25/: Paper summaries and source comparisons for Problem 25 on the density of integers avoiding one residue class per modulus.
erdos_354/: Author-recorded reconstructions of the 2026 source proofs on Problem 354: the Yu--Chen strong-completeness argument for base two and the Fan and Geneson results bearing on the second question.
erdos_416/: Reconstructions of the 2026 doubling-law argument for the count of distinct totient values and of the fixed-scale cluster-interval argument; the asymptotic formula remains open.
erdos_49/: Source-proof reconstruction of the Pollack--Pomerance--Treviño bound M(x) = o(x) for nondecreasing totient sets, the clause of Problem 49 it settles, and the clauses that remain open.
erdos_501/: Author-recorded reconstructions of the two 2026 consistency proofs behind the independence of the first question: the random-real argument and the measure-extension argument.
erdos_617/: Source notes for multicolor independent-set bounds; the unrestricted case remains open.
erdos_644/: Source notes on seven-edge transversal bounds; both unrestricted assertions remain open.
erdos_699/: A reading guide to the common-prime problem: the statement, its sources, and Van Doorn and Rocca's argument.
erdos_774/: Source notes, the finite-block reduction and exact checks of published examples for Problem 774.
erdos_809/: The seven-cycle argument and Lean formalization of the full k≥3 threshold, recorded as claim L17 and accepted at tier 2 on 2026-09-25 for its audited Lean sources and statement.
erdos_864/: Published bounds and source notes for the one-exception Sidon problem.
erdos_939/: Reconstruction of the binomial construction of r-powerful sums of r-2 coprime r-powerful numbers for r at least 6; r=4 and finiteness at r=5 remain open.
erdos_940/: Paper summaries and source comparisons for Problem 940 on sums of r-powerful numbers.
erdos_963/: Paper summaries and source comparisons for Problem 963 on the largest dissociated subset of a finite set of reals.
leads/: Research approaches, unresolved verification tasks, and attack plans linked to their exact targets, source results, dependencies, and obstacles.
methods/: Reusable mathematical arguments, their assumptions and limits, and links to the source results and problems where they apply.
Reconstructions of published proofs, source notes, and reading guides record the checks behind the established results on problem pages. These notes retain the shape their work needs, following the wiki's naming policy and update-lint cycle.
The research leads organize proposed connections and unresolved verification tasks around exact targets, source results, dependencies, and obstacles. They retain stable identities as the work grows. Each retained argument states its assumptions, deductions, and remaining gaps, with the evidence needed to assess it.