What question did this study set out to answer?

The research aims to establish the Poset Algebra A(P) and explore its algebraic properties generated by Bender-Knuth toggles.

March 27, 2026Open Access

The Poset Algebra: Obstruction Hierarchy of Bender-Knuth Toggles on Finite Posets

Key Points

The research aims to establish the Poset Algebra A(P) and explore its algebraic properties generated by Bender-Knuth toggles.
Development of Poset Algebra and universal functor definitions.
Characterization of the braid relation using V-shape analysis.
Exploration of obstruction cohomology with quantized eigenvalues and spectral hierarchy.
Implementation of ladder.rs computational engine for high-performance benchmarking.
Identification of a universal relation D(D-2)(D+2)=0 within the algebra.
Characterization of the braid relation through V-shape identification.
Demonstration of parameter-free mass predictions in physical observables.
Achieved a 765x speedup benchmark using the ladder.rs computational engine.

Abstract

Four papers and computational engine establishing the Poset Algebra A(P) — a new algebraic family generated by Bender-Knuth toggles on linear extensions, with universal relation D(D-2)(D+2)=0. Contains: (1) V-shape characterization of the braid relation, (2) Poset Algebra definition and universal functor, (3) obstruction cohomology with quantized eigenvalues and spectral hierarchy, (4) physical observables including parameter-free mass predictions. Includes ladder.rs computational engine with 765x benchmark speedup.

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