Spin-orbital mixing in the topological ladder of the two-dimensional metal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>PtTe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

We visualize the topological ladder and band inversions in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>PtTe</a:mi><a:mn>2</a:mn></a:msub></a:math> using spin-polarized photoemission spectroscopy augmented by three-dimensional momentum imaging. This approach enables the detection of spin polarization in dispersive bands and provides access to topological properties beyond the reach of conventional methods. Extensive mapping of spin-momentum space reveals distinct topological surface states, including a surface Dirac cone at a binding energy <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:msub><b:mi>E</b:mi><b:mi>B</b:mi></b:msub><b:mo>∼</b:mo><b:mn>2.3</b:mn><b:mspace width="0.16em"/><b:mi>eV</b:mi></b:mrow></b:math> and additional states at <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>E</d:mi><d:mi>B</d:mi></d:msub><d:mo>∼</d:mo><d:mn>1.6</d:mn><d:mspace width="0.16em"/><d:mi>eV</d:mi></d:mrow><d:mo>,</d:mo><d:mo> </d:mo><d:mrow><d:msub><d:mi>E</d:mi><d:mi>B</d:mi></d:msub><d:mo>∼</d:mo><d:mn>1.0</d:mn><d:mspace width="0.16em"/><d:mi>eV</d:mi></d:mrow></d:math>, and near the Fermi level. The electronic structure analysis demonstrates strong hybridization between Pt and Te atomic orbitals, confirming the nontrivial topology of these surface states. Furthermore, by comparison to one-step model photoemission calculations, we identify a robust correlation between the initial-state and measured spin polarizations while revealing asymmetries in specific experimental spin textures. These asymmetries, absent in the initial states due to symmetry constraints, arise from the breaking of time-reversal symmetry during the photoemission process, emphasizing the crucial influence of symmetries on experimental signatures of topology. A phase analysis of ladder states in real space suggests a route to probe them using photoemission, paving the way towards spectroscopic access to the quantum geometric tensor.