TFPT scientific source excerpt
Original repository path: documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/007-subsection-bosonic-relative-index-and-higgs-selection.tex
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Inclusive original lines: 185-204
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000185 | \[
000186 | \dim E_+=2.
000187 | \]
000188 | Equivalently, the unique seam-even light bosonic zero mode fills one complex weak doublet and no
000189 | larger positive carrier block is retained.
000190 | \end{corollary}
000191 | 
000192 | \begin{proof}
000193 | By \TFPTxref{thm:callias-higgs-selection}, the light seam-even bosonic zero mode lies in the weak block
000194 | \[
000195 | \Phi\in\Gamma(E_2)\cong (1,2)_{1/2},
000196 | \]
000197 | and the compact index identifies its zero-mode space with
000198 | \[
000199 | H^0(S^2,\mathcal O(1))\cong\mathbb C^2.
000200 | \]
000201 | Hence the retained positive carrier block is exactly two-dimensional.
000202 | \end{proof}
000203 | 
000204 | This is the sharp form of the Higgs claim used here. The issue is not whether a Higgs doublet can