TFPT scientific source excerpt
Original repository path: documents/tfpt_research_contracts/sections/017-source.tex
Original file SHA-256: 492599a0d20043a5589ca610ce7e1ebceffb8de043eae8eb406e4469d3e4be83
Inclusive original lines: 153-191
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
Conversation metadata and personal execution details are omitted where indicated.

000153 | \section*{Research Contract --- \texttt{TFPT4D.LATTICE.ACTION.01} (the explicit finite 4D lattice action and its seven finite gates)}
000154 | \addcontentsline{toc}{section}{Research Contract: TFPT4D.LATTICE.ACTION.01}
000155 | % =====================================================================
000156 | \noindent\emph{Typing.} A research contract \mO\ (ledger row \texttt{TFPT4D.LATTICE.ACTION.01});
000157 | route step (2) of the \texttt{DIMENSION.UPLIFT.FIREWALL.01} ordering made concrete --- the
000158 | single object on which nearly all open 4D questions become simultaneously testable.
000159 | \textbf{Demand.}  Exhibit one fully explicit finite family of 4D Euclidean lattice theories
000160 | \[
000161 | \mathcal Z_a[J]=\int\mathcal DU\,\mathcal D\psi\,\mathcal D\Phi\;
000162 | e^{-S_a[U,\psi,\Phi]+J\mathcal O},
000163 | \qquad
000164 | S_a=S_{\rm Wilson}[U]+\bar\psi\,D_{\rm GW}[U,\Phi]\,\psi+S_\Phi[U,\Phi]+S_{\rm seam/top},
000165 | \]
000166 | where $U$ are the fundamental holonomies (TFPT fixes representation content, charge lattice,
000167 | coupling relations and boundary conditions), $D_{\rm GW}$ is a Ginsparg--Wilson/overlap operator
000168 | for the TFPT chiral representation content (the \texttt{CHIRAL4D.NOMIRROR.01} operator), $\Phi$
000169 | is the \emph{only} allowed relevant scalar/link-mixing sector (EWSB downstream), and
000170 | $S_{\rm seam/top}$ is the boundary/topological module transporting the seam data into the bulk
000171 | --- first at finite lattice spacing $a$, deliberately \emph{without} continuum claims.
000172 | \textbf{Finite gates} (all machine-checkable at finite size; the promotion criteria for any
000173 | candidate): \textbf{(T1)}~exact gauge invariance; \textbf{(T2)}~a positive transfer matrix (RP
000174 | at finite $a$); \textbf{(T3)}~the seam boundary restriction reproduces the TFPT seam data
000175 | \emph{exactly}; \textbf{(T4)}~anomaly bookkeeping including the global $SU(2)$ anomaly;
000176 | \textbf{(T5)}~the index/generation count; \textbf{(T6)}~the mirror spectrum separated;
000177 | \textbf{(T7)}~at least one \emph{nonvanishing} connected four-point function.
000178 | \textbf{Kill tests.}  No local reflection-positive action with the correct seam restriction
000179 | exists (master route dead); every candidate is generalized-free (T7 unreachable); a hidden
000180 | freely tunable dimensionless parameter is required (the strong parameter-freeness claim is
000181 | refuted); the uniform twistor flat direction shifts \emph{normalized} observables rather than
000182 | only the vacuum normalization of $\mathcal Z$ (a genuine undetermined modulus).
000183 | \textbf{Relation.}  The continuum limit is the separate contract \texttt{QFT4D.OS.RECON.01};
000184 | the unitary dilation is \texttt{DYN.UNITARY.DILATION.01}; $d=4$ is typed by
000185 | \texttt{DIMENSION.SELECTOR.4D.01} \mC; the generating-functional collapse is
000186 | \texttt{FTRANSFER.GENERATING.01}.  Chiral lattice state of the art is calibrated in
000187 | \texttt{CHIRAL4D.NOMIRROR.01} (L\"uscher's exactly gauge-invariant abelian construction,
000188 | arXiv:hep-lat/9811032; the nonabelian anomaly analysis, arXiv:hep-lat/9904009; reflection
000189 | positivity proven for \emph{free} overlap fermions, Kikukawa--Usui arXiv:1005.3751 --- none of
000190 | this is the interacting chiral Standard Model).  Nothing in the corpus closes any gate.
000191 | Status: \texttt{TFPT4D.LATTICE.ACTION.01} \mO.