TFPT scientific source excerpt
Original repository path: documents/tfpt_research_contracts/sections/015-source.tex
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Inclusive original lines: 340-364
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000340 | derivative-filtered wall block
000341 | (\texttt{CHIRAL4D.MIRROR.DFILTER.BLOCK.01};
000342 | \veri{v1023\_\allowbreak derivative\_\allowbreak filtered\_\allowbreak wall.py}; no parent
000343 | marker move).}
000344 | For
000345 | \[
000346 |  H_{\rm df}=\Delta b^\dagger b+
000347 |  \lambda\bigl(b+gD_{\rm GW}p\bigr)^\dagger
000348 |               \bigl(b+gD_{\rm GW}p\bigr)
000349 | \]
000350 | each singular-value sector is the exact $2{\times}2$ block with determinant
000351 | $\lambda g^2\Delta s^2$.  It preserves $\ker D_{\rm GW}$ on the physical summand,
000352 | the adiabatically mirror-continuated high branch is at least $\Delta+\lambda$, and
000353 | \(
000354 |  \mu_-(s)=\lambda g^2\Delta(\Delta+\lambda)^{-1}s^2+O(s^4).
000355 | \)
000356 | The finite covariance and SVD-reduction defects are
000357 | $2.408{\times}10^{-15}$ and $1.776{\times}10^{-15}$.  This is only a finite
000358 | quasi-free block lemma.  For $s\ne0$ the bare $b$ subspace is not invariant and has
000359 | low-band weight, so no bare-mirror response gap is proved; the low branch has
000360 | $z=2$, not a Weyl cone.  No canonical DET16/DET32 realization, interacting parent,
000361 | admissibility/quasilocality theorem, measure/anomaly/index control, universality or
000362 | $3{+}1$D continuum limit follows.  The derivative-filtered witness therefore does
000363 | not upgrade \texttt{CHIRAL4D.MIRROR.DET16.01}~\mC,
000364 | \texttt{CHIRAL4D.NOMIRROR.01}~\mO, T4, or TOE.