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Papers · 01—02

Research papers

Two connected manuscripts on the geometry of Damascus violation sets.

Cover of Geometry, Escape, and Phase Transitions in Violation Sets for the Generalized Damascus Inequality

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Independent Research · Paper II · 2026

Geometry, Escape, and Phase Transitions in Violation Sets for the Generalized Damascus Inequality

Brandon Deonarine · Working manuscript · Website edition v6.9

A structural classification of higher-dimensional Damascus violation sets, their boundedness, separation, exponent dynamics, and asymptotic geometry.

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Scope

Extends the Damascus inequality program into higher dimensions, locating sharp transitions in escape, nesting, topology, and continuous-exponent behavior. Finite lower-cell inclusions are established with deterministic exact rational Bernstein subdivision.

Cover of Nested Violation Sets for the Generalized Damascus Inequality

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Independent Research · Paper I · 2026

Nested Violation Sets for the Generalized Damascus Inequality

Brandon Deonarine · Submitted manuscript · Technical checks in progress · Not peer reviewed

An elementary proof of the nestedness conjecture for the generalized Damascus inequality, with reproducibility checks and a Lean 4 formalization.

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Addresses the nestedness conjecture proposed by Chanatip Sujsuntinukul and Christophe Chesneau, establishing the following stronger result.

Result

\begin{gathered} x,y,z>0,\qquad xyz=1,\\[0.45em] S_n(x,y,z)>0 \Longrightarrow S_{n+1}(x,y,z)>S_n(x,y,z)>0 \end{gathered}

Proof & verification Original conjecture

Materials

The repository includes the compiled manuscript, reproducibility checks, exact symbolic and rational verification, and a Lean 4 formalization.

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Research papers

Geometry, Escape, and Phase Transitions in Violation Sets for the Generalized Damascus Inequality

Nested Violation Sets for the Generalized Damascus Inequality