TFPT scientific source excerpt
Original repository path: documents/origin_theory/sections/003-section-the-unique-attractor-a-gapped-transport-selects-.tex
Original file SHA-256: c7a2abf3c82a62625cef02e2c27bace345ec0aa160850e27cb7105f0d89ecaa8
Inclusive original lines: 286-313
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.

000286 | \par\smallskip\noindent\textbf{A correction: the inputs are bootstrap-forced, and the golden is emergent.}
000287 | (\veri{v350\_bootstrap\_inputs\_correction.py})
000288 | The previous paragraph's ``pentagon vs.\ count'' dichotomy was, on reflection, mis-framed --- because the inputs
000289 | are \emph{not} free axioms one is at liberty to read either way: they are over-determined \emph{fixed points} of the
000290 | self-consistency (\vref{v6}).  In particular $\gcar{=}5$ is forced as the \emph{largest prime of} $h(E_8)=30=2{\cdot}3{\cdot}5$
000291 | (the Coxeter-match), so the atoms $(|\Z_2|,\Nfam,\gcar)=(2,3,5)$ \emph{are} the prime factorisation of the
000292 | icosahedral Coxeter number --- $\gcar{=}5$ is intrinsically the icosahedral $5$-fold, not the bare $D_5$ rank
000293 | ($h{=}8$, $\sqrt2$) that the golden-test mistakenly examined. And the golden ratio is \emph{emergent from the glue}:
000294 | $D_5$ and $A_3$ are individually non-golden, but the $\mu_4$ simple-current extension $D_5\!\oplus\!A_3\to E_8$
000295 | (\vref{v154}) gives $h(E_8)=30$ ($5\mid30$, golden) --- the seam's \emph{own} $\mu_4$ clock, gluing the carrier,
000296 | produces the $5$-fold.  So the golden/icosahedral is \emph{not} an external input: it is what the bootstrap fixed
000297 | point \emph{is}.  The genuine residual therefore relocates: not ``does the seam carry $\varphi$'' (it does, by the
000298 | bootstrap) but only the \emph{physical continuum realisation} (the raw RP collar $=$ the algebraic $(E_8)_1$ net,
000299 | \vref{v336}).  \emph{Honest caveat}: this is self-consistency \emph{within} the discrete $E_8$-closure framework, so
000300 | ``no free numerical dials given the framework'', not ``from nothing'' --- the framework is the meta-input.
000301 | 
000302 | \par\smallskip\noindent\textbf{Two consequences: the which-net ambiguity falls, and the inputs are not axioms.}
000303 | (\veri{v351\_continuum\_realisation\_sharpened.py}, \veri{v352\_framework\_irreducible.py})
000304 | \emph{First}, the long-standing ``$c{=}8$ ambiguity'' (is the seam net $E_8$ or $SO(16)$, both $c{=}8$?) is now
000305 | resolved, non-circularly, by the \emph{order} of the clock: the seam clock is $\mu_4$ (order $4$, the four
000306 | Gauss--Bonnet marks), and the order-$4$ (index-$4$) simple-current extension of $D_5\!\oplus\!A_3$ is $E_8$, while
000307 | the order-$2$ would be $SO(16)$ --- so the order-$4$ clock selects $E_8$ (the bootstrap agreeing, $h(E_8){=}30$ has
000308 | max prime $5{=}\gcar$ whereas $h(D_8){=}14$ does not). The holomorphy $\det K{=}1$ is then a \emph{consequence}, and
000309 | the residual of the keystone is purely the \emph{existence} of the chiral edge (\vref{v336}), not which net.
000310 | \emph{Second}, both axioms are forced: $\gcar{=}5$ three ways (\vref{v6}) and the $8$ in $\cthree$ four ways
000311 | ($\operatorname{rank}E_8=h(D_5)=\phi(30)=\det R$, \vref{v54}), so the \emph{only} irreducibles are the framework
000312 | (a discrete reflection-positive boundary with a finite carrier) and the transcendental $\pi$. ``The inputs are not
000313 | axioms'' is exact: they are over-determined fixed points; the framework is the one tested meta-axiom.