Toward a holographic realization of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> -flavor QCD phase structure

We present a fully backreacted Einstein-Maxwell-Dilaton–flavor model with dynamical light and strange sectors, calibrated to lattice QCD using a machine-learning–assisted spectral method. The model reproduces the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> -flavor equation of state and chiral dynamics with quantitative accuracy, and maps the Columbia plot with a tricritical point at <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msubsup> <c:mrow> <c:mi>m</c:mi> </c:mrow> <c:mrow> <c:mi>s</c:mi> </c:mrow> <c:mrow> <c:mi>tri</c:mi> </c:mrow> </c:msubsup> <c:mo>≃</c:mo> <c:mn>21</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>MeV</c:mi> </c:mrow> </c:math> and a critical mass <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>m</e:mi> <e:mi>c</e:mi> </e:msub> <e:mo>≃</e:mo> <e:mn>0.785</e:mn> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>MeV</e:mi> </e:math> , consistent with lattice results. At finite density, it yields a crossover-to-first-order transition and predicts a critical endpoint at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>T</g:mi> <g:mi>C</g:mi> </g:msub> <g:mo>=</g:mo> <g:mn>75.4</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>MeV</g:mi> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>μ</i:mi> <i:mi>C</i:mi> </i:msub> <i:mo>=</i:mo> <i:mn>768</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>MeV</i:mi> </i:math> , within the reach of heavy-ion experiments. These findings establish a unified holographic framework for the QCD phase structure across quark masses and baryon density, providing the first consistent and quantitative description of both deconfinement and chiral transitions within a single holographic model.