TFPT scientific source excerpt
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000001 | \section*{Research Contract --- \texttt{GRAV.SPIN2.EMERGENCE.01} (massless transversal spin-2 from the same spectral determinant)}
000002 | \addcontentsline{toc}{section}{Research Contract: GRAV.SPIN2.EMERGENCE.01}
000003 | % =====================================================================
000004 | \noindent\emph{Typing.} A research contract \mO\ (ledger row \texttt{GRAV.SPIN2.EMERGENCE.01}),
000005 | registered 2026-08-28 from review wave~3.  \textbf{Demand.}  From the
000006 | \emph{same} spectral determinant that carries the gauge fixpoints, a massless transversal
000007 | spin-2 pole with two helicities, universal $T_{\mu\nu}$ coupling, diffeomorphism Ward identities,
000008 | and positive Hessian / reflection-positive transfer.  \textbf{Relation.}  The
000009 | entanglement-equilibrium Einstein equation (\vref{v358}/\vref{v359}) stays a
000010 | \emph{downstream / conditional} readout --- it presupposes a local QFT and can never be cited as
000011 | producing one; \texttt{GRAV.NONCIRCULAR.01} is \emph{binding} (BW/CHM uses remain
000012 | assumption-declared).  \textbf{Kill tests.}  A massive or longitudinal extra mode; non-universal
000013 | coupling; failed diffeomorphism Ward; negative Hessian / RP violation on the spin-2 sector.
000014 | Status: \texttt{GRAV.SPIN2.EMERGENCE.01} \mO.
000015 | 
000016 | \par\smallskip\noindent\textbf{Executed update (2026-08-28, completeness wave): quadratic
000017 | witnesses, with the local truncation's ghost typed
000018 | (\veri{v997\_\allowbreak spin2\_\allowbreak smg\_\allowbreak witnesses.py}; the contract stays \mO).}
000019 | Exact Barnes--Rivers decomposition of the quadratic spectral action: $R{+}R^2$ is \emph{clean}
000020 | (one massless TT pole, two helicities, scalaron at $M_{\mathrm{scal}}$ exact).  The local $a_4$
000021 | Weyl$^2$ truncation \emph{necessarily} carries an opposite-residue spin-2 ghost --- typed.
000022 | The contract's content is pinned on the untruncated form factor $a(\Box)=e^{-\Box/M^2}$.
000023 | Einstein equation stays downstream/conditional; \texttt{GRAV.NONCIRCULAR.01} remains binding.
000024 | Display marker stays \mO.
000025 | 
000026 | \par\smallskip\noindent\textbf{Executed update (2026-08-29, review wave 4): quadratic Hamiltonian
000027 | half executed
000028 | (\veri{v1000\_\allowbreak spin2\_\allowbreak sk\_\allowbreak witnesses.py}; the contract stays \mO).}
000029 | Positivity exact; $2$ TT helicities at all $5852$ nonzero momenta ($N=6..12$);
000030 | $\omega=|q|$ with $q_i=2\sin(k_i/2)$ and axis expansion $\omega=k-k^3/24$ exact.
000031 | Must-fail: a mass term gaps TT; a wrong-sign kinetic term yields two negative directions.
000032 | Spectral-action Hessian identification, nonlinear Ward and universal coupling stay \mO.
000033 | Display marker stays \mO.
000034 | 
000035 | \par\smallskip\noindent\textbf{WAVE-6 firewall (2026-08-30): \texttt{GRAV.WEINBERG.WITTEN.01}
000036 | registered \mO; this contract's display stays \mO.}
000037 | The Weinberg--Witten theorem is the binding firewall \emph{before any spin-2 marker move}:
000038 | the microscopic Hamiltonian family must \emph{not} possess a fundamental Lorentz-covariant
000039 | local conserved $T_{\mu\nu}$; Lorentz symmetry, diffeomorphism Ward identities and the
000040 | spin-2 mode must emerge in the \emph{same} IR limit.  Cross-link only (this row does not
000041 | list \texttt{GRAV.WEINBERG.WITTEN.01} as a dependency --- that would cycle).
000042 | 
000043 | \par\smallskip\noindent\textbf{Executed update (2026-08-30, evening TOE-gate wave): interacting
000044 | TT half-step
000045 | (\veri{v1012\_\allowbreak toe\_\allowbreak gate\_\allowbreak witnesses.py}; the contract stays \mO).}
000046 | Conserved interaction-complete lattice stress $\sim10^{-15}$; TT spectral positivity exact;
000047 | sum rules $\sim10^{-15}$; the dominant positive-$Z$ pole persists under $\phi^4$ (gapped, as
000048 | expected for massive generic matter); $Z$ trend $k_1$ suppressed $0.958$ / $k_2$ enhanced $1.033$;
000049 | free-limit analytic match.  Missing: TFPT content, $k\to0$ volume scaling, Ward identities.
000050 | Display marker stays \mO.
000051 | 
000052 | \par\smallskip\noindent\textbf{Executed update (2026-09-05, round-3 integration):
000053 | gapped-parent/TT boundary
000054 | (\texttt{GRAV.PARENT.GAP.NO\_GO.01};
000055 | \veri{v1024\_\allowbreak parent\_\allowbreak internal\_\allowbreak boundaries.py}; no parent
000056 | marker move).}
000057 | A uniform full-parent gap $\Delta>0$ excludes a massless pole with
000058 | $\omega(k_{\min})\to0$.  Away from $k=0$ the symmetric-traceless target has five
000059 | pointwise components and the transverse-traceless projector has rank two, but its
000060 | direction-dependent $k\to0$ limit prevents an exact strictly finite-range direct TT
000061 | projector.  A viable escape therefore requires a critical physical sequence together
000062 | with local tensor gauge constraints whose Ward identities generate the TT sector only
000063 | in the infrared.  The finite representation count is not a derived TFPT stress
000064 | operator, and no massless pole, universal coupling, diffeomorphism Ward identity or
000065 | gravitational continuum theorem is constructed.  \texttt{GRAV.SPIN2.EMERGENCE.01},
000066 | T7 and TOE remain \mO.
000067 | 
000068 | % =====================================================================