What question did this study set out to answer?

This research aims to establish a four-divisor bound for a specific divisor window in relation to Erdős Problem 887.

June 13, 2026Open Access

The Eventual Four-Divisor Bound for Erdős Problem 887: Root-band Reconstruction and a K5 Interval-Overload Obstruction

Key Points

This research aims to establish a four-divisor bound for a specific divisor window in relation to Erdős Problem 887.
Proved the eventual four-divisor bound for the fourth-root near-root divisor window.
Used an external reconstruction reduction to relate five-divisor violations to a K5 survivor.
Demonstrated an internal obstruction to show the non-existence of canonical interval-overload data.
Establishes that for a fixed constant C > 0, there exists a threshold N(C) for which specific divisor conditions hold.
Shows that the interval (sqrt(n), sqrt(n) + C n^(1/4)) contains at most four divisors for all n >= N(C).

Abstract

This record contains a preprint manuscript presenting a proof of Erdős Problem 887. The manuscript proves an eventual four-divisor bound for the fourth-root near-root divisor window. For each fixed constant C > 0, it proves that there is a threshold N (C) such that the interval (sqrt (n), sqrt (n) + C n^ (1/4) ) contains at most four divisors of n for all n >= N (C). The proof is organized around two reductions. The external reconstruction reduction turns an unbounded sequence of five-divisor violations into a normalized legal five-endpoint K5 survivor carrying a canonical interval-overload datum. The internal obstruction proves that no such canonical interval-overload datum exists. A companion Lean 4 formalization is archived separately and mirrors the theorem-source architecture of the manuscript.

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