TFPT scientific source excerpt
Original repository path: documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/004-subsection-absolute-spectral-planck-closure.tex
Original file SHA-256: 669d088bea83eef25cfd9960905893cc57d2827c7b4d7558c5aa7b408b85581a
Inclusive original lines: 26-49
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.

000026 | \end{figure}
000027 | 
000028 | \begin{theorem}[Geometric Hodge quantization and relative spectral gravity branch]
000029 | \label{thm:gravity-cosmology-closure}
000030 | The same geometric closure sector defines the canonical spectral gravity branch
000031 | \[
000032 | \Gamma_{\mathrm{grav}}
000033 | :=
000034 | -6\chigeo^2\mathcal E_D+\Gamma_D^{(4)}.
000035 | \]
000036 | On admissible geometric fluctuations, let
000037 | \[
000038 | Q_{\mathrm{geo}}
000039 | \]
000040 | denote the geometric BRST/Hodge differential that quotients diffeomorphism and local-frame gauge
000041 | directions, and set
000042 | \[
000043 | P_{\mathrm{phys}}^{\mathrm{grav}}
000044 | :=
000045 | \Pi_{\ker\Delta_{\mathrm{tot}}},
000046 | \qquad
000047 | \Delta_{\mathrm{tot}}
000048 | :=
000049 | \{Q_{\mathrm{adm}}+Q_{\mathrm{geo}},(Q_{\mathrm{adm}}+Q_{\mathrm{geo}})^\dagger\}.