Hexagon

Submitted works

math.QA — Quantum Algebra

A Uniform Calculation of Weight-Preserving Infinitesimal Braid Deformations in Type D

Contributed by Hangang Wang

Over $\mathbb Q(q)$ , for every $n\ge4$ , we calculate the full space of classical-weight-preserving solutions of the linearized braid equation at the standard type- $D_n$ vector braiding. Its dimension is $(n+1)(n+2)/2$ . A coordinate slice for scalar and parameter variations, diagonal vector-basis changes, and alternating twists reduces the upper bound to a homogeneous vanishing problem. Outer-pair coefficients eliminate the zero-weight block through a recurrence closed by the two central weights. We also give a functorial formal local parametrization over local Artin algebras. The explicit integrable family belongs to earlier multiparameter constructions; an exact parameter dictionary is provided. No bibliographic priority claim is made for the full tangent-space exhaustion. The proof is uniform in $n$ ; finite-rank computations are diagnostics.

Primarily AI-generated textHuman understanding: some partsYang–Baxter equationexact computationformal deformationsinfinitesimal braid deformationsquantum groupstype D

Oct 27, 2026PDF ↗View work →

hexagon:2610.00561v1

math.MG — Metric Geometry

Volume Computation and Comparison for Four-Dimensional Bodies of Constant Width

Contributed by Hangang Wang

We compute and compare the volumes of explicit four-dimensional bodies of constant width one. The original five-entry comparison consists of the simplex-symmetric projection body $U_4$ , the canonical raised Meissner pair, the canonical raise of $U_3$ , the body $B_5$ , and $M_4$ . We combine exact geometric formulas, numerical integration, interval enclosures and inscribed rational polytopes to obtain a certified strict ordering of their volumes. We also compare $U_4$ with the direct four-dimensional AMO peabody. The two raised Meissner bodies are proved noncongruent but exactly equal in volume. An introductory account explains why different constructions benefit from different computational methods, and distinguishes approximate volume estimates from inequalities certified by exact or outward-rounded arithmetic.

Primarily human-written textHuman understanding: all partsBodies of constant widthcertified comparisonfour-dimensional volumeinterval arithmetic

Oct 26, 2026PDF ↗View work →