Massless Barrier Crossing

T90 establishes that barrier crossing in the paired Q5 transport framework is massless within the admissible crossing sector. The theorem defines the effective mass contribution structurally by the magnitude of the residual symmetric dressing:\[meff^2 ∝ |S_n+S_d|^2.\] Using Theorem 89, the paired symmetric sectors satisfy\[S_n+S_d=0\]within the admissible crossing channel. Therefore\[|S_n+S_d|^2=0,\]and hence\[meff^2=0.\] The theorem interprets symmetric non-rotational dressing as a mass-like retained structure that is locally visible on each transport leg but globally inadmissible under paired inversion. Exact paired cancellation removes this inert residue at the barrier, leaving only the rotational crossing mode\[A=iσ_y,^2=-I.\] As a consequence, admissible transport at the barrier is purely phase-driven:\[T=I+1{160}A+O(ε^2),\]\[T^k→ etA,\]and the observable transport readout becomes\[μ_k=sin(kε)+O(ε).\] A perturbative corollary introduces the dressing residue\[δ:=S_n+S_d.\]When pairing is imperfect,\[meff^2∝|δ|^2.\]Mass, therefore appears as the squared deviation from ideal paired cancellation, with exact masslessness recovered when\[δ=0.\] T90 extends the cancellation chain:- T88 established geometric cancellation through admissible \(Y\)-gate transport,- T89 established algebraic cancellation through ordering reversal and paired consistency,- T90 interprets the cancellation consequence as massless admissible barrier transport. Solid structure:\[S_n+S_d=0eff^2=0\]within the admissible crossing sector. Conditional boundary:The theorem inherits the admissible-sector cancellation assumptions of T89 and treats\[meff^2∝|S_n+S_d|^2\]as a structural identification rather than a derived dynamical mass equation. Speculative boundary:interpretation of \(meff^2\) as physical particle mass beyond the internal Q5 transport architecture remains speculative.