TFPT scientific source excerpt
Original repository path: documents/tfpt_research_contracts/sections/015-source.tex
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000235 | \section*{Research Contract --- \texttt{CHIRAL4D.NOMIRROR.01} (the chiral 4D lattice matter theorem)}
000236 | \addcontentsline{toc}{section}{Research Contract: CHIRAL4D.NOMIRROR.01}
000237 | % =====================================================================
000238 | \noindent\emph{Typing.} A research contract \mO\ (ledger row \texttt{CHIRAL4D.NOMIRROR.01}:
000239 | Open, research contract), \emph{not} a claim.  Step (4) of the firewall route ordering: chirality
000240 | and mirror decoupling must be proven \emph{in the same 4D model} that
000241 | \texttt{QFT4D.OS.RECON.01} constructs --- the seam's $c_-{=}8$ and Chern/inflow structure are a
000242 | boundary-\emph{anomaly} signal, not yet 4D matter.
000243 | 
000244 | \par\smallskip\noindent\textbf{Target theorem.}  An explicit chiral lattice operator
000245 | (Ginsparg--Wilson/overlap type) for the TFPT representation content with proofs of:
000246 | \textbf{(C1)}~a local, gauge-invariant fermion measure; \textbf{(C2)}~perturbative \emph{and}
000247 | global anomaly freedom; \textbf{(C3)}~no Witten $SU(2)$ anomaly; \textbf{(C4)}~no mirror
000248 | generation in the physical spectrum (the mirror decouples with a mass that survives the
000249 | continuum limit); \textbf{(C5)}~the correct index and charges (the TFPT charge lattice,
000250 | generation count $\Nfam$); \textbf{(C6)}~a stable continuum limit compatible with the
000251 | \texttt{QFT4D.OS.RECON.01} package.
000252 | 
000253 | \par\smallskip\noindent\textbf{Calibration (state of the art, honestly).}  The strongest
000254 | comparable theorem is Mastropietro's construction (\texttt{arXiv:2303.02790}): a \emph{weakly
000255 | coupled} 4D $U(1)$ chiral gauge theory with a \emph{massive} gauge field.  The TFPT target ---
000256 | chiral $SU(3){\times}SU(2){\times}U(1)$ with three generations, massless nonabelian gauge
000257 | fields, EWSB and confinement downstream --- is far stronger; the gap between the two is the
000258 | honest measure of this contract's difficulty.  \emph{Kill tests:} the mirror fails to decouple
000259 | (kill test (3) of \texttt{WOIT.OS.TWISTOR.01} at lattice level); a Witten anomaly obstructs the
000260 | carrier $SU(2)$; every gauge-invariant measure for the TFPT content is provably nonlocal.
000261 | \emph{Consistency note (ledger wins):} the celestial-branch scope fence above honestly lists
000262 | interacting RP, mirror decoupling, the internal $SU(2)$, both helicities, local matter fields,
000263 | EWSB and confinement as \emph{not} closed; the contradictory ``zero open internal mechanisms''
000264 | phrase in \texttt{docs/OPEN\_PROBLEMS.md} is corrected in the same change that registers this
000265 | contract (that phrase was a certification statement about a \emph{different}, narrower residual
000266 | matrix and had drifted into an overclaim).  Status: \texttt{CHIRAL4D.NOMIRROR.01} \mO.