TFPT scientific source excerpt
Original repository path: documents/articles--2026-08-30--mmst_charged_scaling_limit_en/sections/005-subsection-the-neutral-net-and-its-index.tex
Original file SHA-256: e088b0132a5a17823222866a4cef0f2665317b1a2e65039cb307232c1bcc5171
Inclusive original lines: 331-349
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000331 | \paragraph{Round-7 microscopic twist boundary (2026-09-05).}
000332 | The repository checker \texttt{v1033\_charged\_disorder.py} constructs
000333 | order-four charged corners in the actual QWZ matter Fock space only after
000334 | adding a local four-level flux register to the seam Hamiltonian.
000335 | An onsite scalar matter gauge transformation alone cannot change its
000336 | Wilson holonomy. The eight-channel quarter twist has charge
000337 | $q=(1/4)^8$, hence $h=\lVert q\rVert^2/2=1/4$, not the required
000338 | $h_\lambda=1$. Every same-phase integer dressing with norm squared two
000339 | has odd fermion parity. The $D_5$ half-twist and $A_3$ inverse-quarter
000340 | description additionally requires its diagonal-$U(1)$ quotient and
000341 | cocycle/GSO identification; it is not automatically the same microscopic
000342 | eight-channel collar. The source's forward seam $i^r$ fixes the Bloch
000343 | shift to $k=(2\pi n-r\pi/2)/N$ in the stated convention.
000344 | Finite sharp-string energy and nonlocal smooth-twist scaling are
000345 | diagnostics, not a conformal-weight or support-preserving FE-GEN proof.
000346 | Thus the construction supplies actual corners in an enlarged model,
000347 | not the missing MMST upper inclusion. Complete definitions, proofs and
000348 | typed regressions are in the round-7 supplement of
000349 | \texttt{tfpt\_research\_contracts}.