The Return of the Lemma: Launchpads, corridor obstructions, and the shape of a counterexample

We refine the frontier formulation of Gilbreath’s Conjecture by proving a new local obstruction. Although the conjecture still reduces to showing that the {0,2}-frontier never reaches position 4, we show that the most direct minimal erosion corridor from the initial frontier-8 row is impossible. In particular, any pure minimal 8 → 7 → 6 → 5 → 4 collapse would force a zero-block in positions 4–7 of the launchpad row, whereas Row 2 has twos there. Thus one natural route to failure is eliminated by proof, and any remaining counterexample must arise through a more complicated frontier dynamic. This companion note reframes the earlier local-bound reduction in terms of frontier dynamics and the {0,2} basin. For correspondence and updates: BMorgan007(at)protonmail.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-03-21
DOI
https://doi.org/10.5281/zenodo.19144967
Primary Topic
Advanced Differential Equations and Dynamical Systems
Type
article
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article

The Return of the Lemma: Launchpads, corridor obstructions, and the shape of a counterexample

Blair Morgan
Zenodo (CERN European Organization for Nuclear Research)
Advanced Differential Equations and Dynamical Systems
article

The Return of the Lemma: Launchpads, corridor obstructions, and the shape of a counterexample

Blair Morgan
article en

Abstract

We refine the frontier formulation of Gilbreath’s Conjecture by proving a new local obstruction. Although the conjecture still reduces to showing that the {0,2}-frontier never reaches position 4, we show that the most direct minimal erosion corridor from the initial frontier-8 row is impossible. In particular, any pure minimal 8 → 7 → 6 → 5 → 4 collapse would force a zero-block in positions 4–7 of the launchpad row, whereas Row 2 has twos there. Thus one natural route to failure is eliminated by proof, and any remaining counterexample must arise through a more complicated frontier dynamic. This companion note reframes the earlier local-bound reduction in terms of frontier dynamics and the {0,2} basin. For correspondence and updates: BMorgan007(at)protonmail.com

Zenodo (CERN European Organization for Nuclear Research)
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Advanced Differential Equations and Dynamical Systems
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