RefacteOriginal research
Original research by Henry Shin, with readable explanations, source editions, publication details, and corrections.
I look for working representations that expose the constraints controlling a problem: finite incidence structures, graphs, explicit equations, and matrix methods. The Taiko obstruction shows this practice in a group-theoretic construction problem.
My essay on AI and research strategy argues for developing it further in the diagnosis and repair of sparse numerical representations. The Refacte approach connects these questions to the worked mathematics on the site.
A group-ring construction becomes a finite incidence problem. Follow the representation, the obstruction, and the return to the original question.
Under consideration at Groups, Geometry, and Dynamics.
A global obstruction to the Garg–Mineyev triple-girth route to zero-divisor and unit counterexamples in group rings over F₂, proved through incidence geometry.
Research on permutation modules, finite generation, and tensor-triangular geometry.
Representation spheres give multigraded section rings for permutation modules. This paper proves a finite-module theorem over arbitrary commutative Noetherian bases and uses the doubled regular representation to construct an explicit Noetherian model for the tensor-triangular geometry of permutation complexes.
Finite additive relations, growth exponents, and integer models.
Determines the growth exponent of the number of possible h-fold sumset sizes for fixed-size integer sets, together with sharp bounds for integer models preserving finite additive relations. Also proves the formula conjectured in OEIS A227589 for minimal labelings of identical four-sided dice that maximize the number of distinct sums.
Earlier work in geometric analysis, with its correction linked alongside the article.
Advances in Mathematics 372 (2020), 107303
Curvature estimates for four-dimensional gradient Ricci soliton singularity models, using geometric analysis and topological arguments.
Preprints in algebraic and extremal combinatorics, number theory, and arithmetic geometry.
Exchange identities and symmetry for the area-zero and area-one slices of the valley Delta generating function.
Berge cycles of every length from a Hamiltonian Berge cycle and one additional edge, in the stated large-order uniformity regime.
Rational maps from Hilbert-90 descent: cancellation, torsion, and characteristic-zero monodromy.
Trace distributions on cosets in cubic norm-one tori, including singular fibers and local branch geometry.
Geometry at infinity of polynomial fiber products, rational lifts, and their arithmetic counting behavior.
Further preprints on Ricci flow and partial differential equations.
Formation of FIK singularities under Ricci flow and the local parameters governing their first-order asymptotic behavior.
Local damping mass, resolvent bounds, and decay, including spectral asymptotics near logarithmic damping wells.
The Tensorgami archive also preserves research records alongside dated editions and source packages.