TFPT scientific source excerpt
Original repository path: documents/tfpt_1_architecture_e8/sections/001-source.tex
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000067 | \begin{keybox}[Foundational postulates --- the two genuine axioms (hardenable, not derivable)]
000068 | Everything downstream is a theorem \emph{given} two structural inputs that are not reduced further and
000069 | are honestly flagged as the theory's axioms:
000070 | \begin{description}[leftmargin=2.2em,style=nextline]
000071 |   \item[\textnormal{(P1) Boundary kernel.}] A single oriented seam $\Sigma$ carries a primitive,
000072 |   reflection-positive boundary kernel with unit winding $[u_\Sigma]=1$; its self-linking normalisation
000073 |   fixes $\cthree=1/(8\pi)$. \emph{Status:} primitive postulate. \emph{Organizing identity (2026-08-06,
000074 |   markers unchanged):} the closed normalization $I\cdot\beta_{\rm angle}\cdot\cthree=4\cdot2\pi\cdot
000075 |   \tfrac1{8\pi}=1$ holds exactly with the Jones index $I=4=|\mu_4|$ a $\cthree$-free theorem and
000076 |   $\beta_{\rm angle}=2\pi$ independently measured --- the identity \emph{explains} the value, it does
000077 |   not derive it; the open bridge is the even modular-response normalization
000078 |   (\texttt{P1.INDEX.KMS.01} \mO, \veri{v813\_p1\_index\_kms.py}). \emph{Hardenable by:} the Calder\'on
000079 |   projector / determinant-character chain (the P1 hardening) and the Lean carrier-rigidity development
000080 |   (\texttt{TfptCarrier.*}, boundary-polarization and Calder\'on interfaces).