%========================================================================
% APPENDIX RM: FALSIFIABLE-PREDICTIONS ROADMAP
%   Consolidated kill-or-confirm roadmap (2026-06-27). Built by a 5-sector
%   extraction + critical triage of every falsifier/discriminator in the
%   corpus. Rule: a DISCRIMINATOR must differ measurably from GR/LCDM/SM;
%   consistency-checks (DFD = standard) are listed separately, NOT oversold.
%========================================================================
\section{Falsifiable-Predictions Roadmap: How DFD Is Confirmed or Killed}
\label{app:RM}

DFD is a frozen-parameter theory: its constants are derived or discretely selected
(no continuous fit parameters; three discrete inputs --- App.~F remarks), so each
is a sharp target. This appendix consolidates the corpus's scattered falsifiers
into one prioritized roadmap. A systematic extraction and critical triage of
the full corpus yields \textbf{24 genuine measurable discriminators} (where DFD
differs from GR/$\Lambda$CDM/SM at a testable level), resting on a bedrock of
$\sim$\textbf{17 already-passed derived numbers}; a further $\sim$18
\emph{consistency-checks} (where DFD reproduces the standard value exactly, or the
signal sits below any foreseeable sensitivity) are listed separately and are
\textbf{not} counted as discriminators.

\begin{tcolorbox}[colback=green!4!white,colframe=green!55!black,
  title={The headline decisive test (theorem-grade, sign-definite, near-term)}]
\textbf{Supernova--lensing correlation SIGN.} DFD's optical-distance postulate
$n=e^{\psi}$ forces standardized SN\,Ia Hubble residuals to correlate
\emph{positively} with foreground weak-lensing convergence,
$d(\delta\mu)/d\kappa_{\rm fg}\simeq+11$~mag/$\kappa$ (band $[+7,+28]$), whereas
GR/$\Lambda$CDM lensing forces a \emph{negative} $-2.17$~mag/$\kappa$ --- a
definite $\sim$12~mag/$\kappa$ \textbf{sign flip}, not an amplitude argument. All
five existing real datasets (Pantheon+\,$\times$\,DES-Y3, BOSS, DES-SN5YR,
Planck CMB-lensing, DESI) already show the DFD-positive sign at $\sim$1--1.5$\sigma$
(map-noise limited, not SN-count limited); LSST Y1 ($\sim$650 well-mapped SNe) or
Roman ($\sim$160) reach a clean $\ge3\sigma$ either-way verdict within $\sim$5
years (App.~SL). The sign cannot be faked by $\Lambda$CDM; the one confound is
correlated foreground dust (a detection-cleanliness requirement, not a sign error).
\end{tcolorbox}

%=== ADD (do not replace): insert immediately AFTER the headline tcolorbox (\end{tcolorbox}, line 35) and BEFORE \subsection{Tier 1 ...} ===
\subsection{The complete bet list --- master table}
\label{app:RM-bets}
DFD is finished physics awaiting adjudication: its constants are frozen, so every
row below is a number the theory cannot move if the data land elsewhere. Grades are
the recorded ledger grades; \emph{conditional} stays conditional. Established postdictions
and exclusions are listed alongside the live bets for completeness.

\begin{itemize}[leftmargin=*,itemsep=3pt,topsep=2pt]
\item \textbf{$\nu_R$ / $m_\beta=9.1514$~meV} --- \emph{consistency-requirement} (upgraded from prediction): $\nu_R$ is structurally required by the spin-$\mathbb{Z}_4$ $B{-}L$ consistency (Cor.~\ref{cor:nur-required}, App.~F); seesaw $M_R=\alpha^3M_P$. Experiment: KATRIN-II / Project-8. \emph{Kills:} inverted ordering; any $m_\beta$ off the comb.
\item \textbf{$a_0(z)$ running sign} --- $\partial_z a_0>0$, $a_0=2\sqrt{\alpha}\,cH(z)$. Well-supported, \emph{conditional} (forced modulo the contemporaneous-normalizer identification); magnitude conditional $[1.79,2.83]$ at $z{=}1$, native $\sim$1.79; unique vs $\Lambda$CDM \emph{and} static MOND. Experiment: JWST/Roman + ALMA rotation curves. \emph{Kills:} measured $\partial_z a_0\le0$.
\item \textbf{Macroscopic coherence} --- sustained fringes, \emph{no} objective collapse (forced: no-noise variational action; mean-field Schr\"odinger--Newton). Experiment: MAQRO-class levitated optomechanics, $10^{9\text{--}10}$~amu. \emph{Kills:} mass-scaled collapse at the Di\'osi--Penrose rate.
\item \textbf{GW nonlinear memory} --- \emph{zero} Christodoulou memory in the tensor channel (theorem-grade, $\partial^3S/\partial h^3\equiv0$, knob-independent; scalar channel BBH-rigorous, open in general). Experiment: LISA $10^{5\text{--}6}M_\odot$ at $z{=}1$, single-event SNR 11--35; ET/CE stacking. \emph{Kills:} a detected $\sim$20--27\% permanent strain offset.
\item \textbf{Neutron-star sector} --- $M_{\max}=0.900\times$GR$=1.474$ (reference normalization; magnitude-documentation caveat live); absolute ceiling $\le3.03\,M_\odot$ forced, EOS-independent; data survival requires a near-causal stiff core. Experiment: NICER / pulsar timing / mergers. \emph{Kills:} a soft-EOS consensus (the $2.08\,M_\odot$ pulsars then exceed DFD's ceiling); any confirmed NS in $[3.03,4.05]\,M_\odot$.
\item \textbf{Kerr alternative} --- horizonless, \emph{no} ergoregion at any spin (verified; $+4.6\%$ shadow; the horizonless signature is ECO-class-generic, not DFD-unique). Experiment: ngEHT; LISA/ET ringdown. \emph{Kills:} a confirmed horizon or superradiance.
\item \textbf{$N_{\rm eff}=3.044$ exactly} --- integer 3 forced (no dark radiation); decimal inherited from SM physics; one-sided falsifier (the value itself is SM-degenerate). Experiment: CMB-S4, $\sigma\simeq0.03$. \emph{Kills:} $N_{\rm eff}$ outside $[2.99,3.10]$.
\item \textbf{Proton decay: exactly zero} --- \emph{conditional} on axiom V7 ($B$ = winding); the sharpest DFD-vs-GUT adjudicator. Experiment: Hyper-K / DUNE. \emph{Kills:} \emph{any} single-nucleon decay event.
\item \textbf{$|V_{cb}|$ ($A=108\alpha$)} --- $A\lambda^2=0.04033$; DFD survives only on $|V_{cb}|\lesssim41\times10^{-3}$; parked on the inclusive/exclusive puzzle; nothing can move ($A\approx113\alpha$ forbidden by $n_A=108$). Experiment: Belle-II at $0.5\%$. \emph{Kills:} inclusive $42.2\times10^{-3}$ confirmed.
\item \textbf{$\Delta M_s/\Delta M_d$} --- $33.3$ ($-5.1\%$, $\sim$1.9$\sigma$ at FLAG $\xi=1.206(17)$); locked CKM, no rescue knob by construction. Experiment: lattice $\xi$ at $0.5\%$. \emph{Kills:} firm $\xi=1.206$ ($\Rightarrow4\sigma^{+}$; DFD needs $\xi\approx1.24$).
\item \textbf{$\sigma_8=0.820$ ($S_8=0.784$)} --- forced normalization (one inherited $A_s$ coefficient); $\phi\phi$ prefers $0.842$ (live mild pull, shared data anomaly). Experiment: SO/CMB-S4 + shear. \emph{Kills:} converged $\sigma_8=0.84$ across lensing and shear.
\end{itemize}

\paragraph{Established postdictions (already adjudicated).} $H_0=72.09=\alpha^{57/2}/t_P$ (\textsc{win}: $0.9\sigma$ vs SH0ES; correlated with $S_8$ --- one low-$\Omega_m$ mechanism; exponent derived, $O(1)$ clock coefficient axiomatic, Rem.~\ref{rem:clock-credit}); $S_8=0.784$ (\textsc{win}: $+0.4$--$1.3\sigma$ KiDS/DES vs $\Lambda$CDM's $3$--$4.9\sigma$); $\rho_\Lambda=(3/8\pi)\alpha^{57}\rho_P$ (\textsc{postdiction}, microsector-scoped, Rem.~\ref{rem:au-scope}); $\sin^2\theta_W=3/13$ ($-0.19\%$) and $\alpha^{-1}=137.036$ ($0.0056$~ppm; unconditional trials-audit theorem, Thm.~\ref{thm:ce-alpha-ladder}) (\textsc{postdictions, forced}).

\paragraph{Exclusions (not bets).} $\Omega_k<0$ is \emph{not} a DFD prediction (merely consistent; no forced sign or magnitude); no Born-statistics deviation is predicted (mean-field sourcing is exactly Born-consistent --- a null Born test does not discriminate).

\subsection{The five cleanest near-term decisive tests}
\label{app:RM-kills}
\begin{enumerate}[leftmargin=*,itemsep=2pt,topsep=2pt]
\item \textbf{Belle-II $|V_{cb}|$ at 0.5\%:} a confirmed inclusive $42.2\times10^{-3}$ kills $A=108\alpha$ outright --- the integer cannot move.
\item \textbf{LISA GW memory:} zero tensor memory vs GR's $\sim$20--27\% (tensor-channel theorem; scalar-channel scope: Rem.~\ref{rem:memory-scope}); golden MBHB events at SNR 11--35 give a decisive yes/no.
\item \textbf{MAQRO coherence:} DFD sustains fringes exactly where Di\'osi--Penrose collapses; a mass-scaled collapse signal kills.
\item \textbf{CMB-S4 $N_{\rm eff}$:} outside $[2.99,3.10]$ kills DFD (one-sided: it can only falsify, since the value is SM-degenerate).
\item \textbf{Hyper-K proton decay:} any single-nucleon event kills DFD while confirming GUTs (conditional on axiom V7).
\end{enumerate}

\subsection{Tier 1 --- near-term decisive ($\lesssim$5--10 yr, pass/fail)}
The nine near-term decisive discriminators (each differs measurably from the
standard prediction and is resolvable by a named experiment within roughly a
decade):
\begin{enumerate}[leftmargin=*,itemsep=2pt,topsep=2pt]
\item \textbf{SN--lensing correlation sign:} $+11$~mag/$\kappa$ \emph{vs}
$\Lambda$CDM $-2.17$ (sign flip) --- dust-controlled SN\,$\times\,\kappa_{\rm fg}$
regression; LSST Y1 / Roman, $\sim$2027--30.
\item \textbf{PMNS solar angle} $\sin^2\theta_{12}=0.3184$ (TM1) \emph{vs} measured
$0.307$ ($+0.95\sigma$) --- JUNO reactor/solar; $\sim$2027--30.
\item \textbf{ISW amplitude:} $\sim$30\% of $\Lambda$CDM (DE is an optical bias, not
a fluid) --- CMB\,$\times$\,galaxy cross-correlation ($>4\sigma$ detection kills
DFD); now--near.
\item \textbf{$\alpha(z)$ drift:} $+2.3\times10^{-6}$ at $z{=}1$, \emph{positive}
\emph{vs} SM zero --- QSO absorption (ESPRESSO/ELT); $\sim$2025--30.
\item \textbf{CKM apex:} $\gamma{=}66.31^\circ$, $\sin2\beta{=}0.719$, an
$\varepsilon_K$ deficit $\sim$13\% \emph{vs} SM free parameters (tension box: companion volume, App.~AH2a) --- LHCb / Belle II;
$\sim$2027--30.
\item \textbf{Th-229 nuclear-clock modulation:} a perihelion-locked annual signal,
26\,Hz--$\mathcal O$(1\,kHz) \emph{vs} GR/SM null --- dedicated Th-229 clock;
near-term.
\item \textbf{Compact-star ceiling:} $M_{\max}\le3.03\,M_\odot$, $=0.900\times$GR
\emph{vs} GR $\sim$4.05 --- NS mass / merger remnants; ongoing.
\item \textbf{RAR intrinsic-scatter floor:} $\sim$0.037~dex ($a_0$ a fixed
constant) \emph{vs} untuned 0.06--0.08 --- SPARC-class rotation curves; near-term.
\item \textbf{Lepton-flavor universality:} $R_K=1$ to $<10^{-4}$ \emph{vs} BSM
$R_K\ne1$ --- LHCb Run 4; $\sim$2027--30.
\end{enumerate}

\subsection{Tier 2 --- future decisive (next-generation instruments)}
The following 14 are genuine discriminators awaiting more capable facilities:
\emph{no dark-energy clustering} ($w_{\rm eff}{=}-1$ with zero DE sound speed;
a confirmed evolving-$w$ clustering fluid from DESI DR2 falsifies DFD);
\emph{$N_{\rm eff}=3.044$ with structurally forbidden dark radiation} (CMB-S4: any
$\Delta N_{\rm eff}>0$ kills DFD while $\Lambda$CDM absorbs it);
\emph{2PN solar light-bending} $c_2=4\pi=(16/15)\times$GR ($+0.73\,\mu$as at the
limb; LATOR-class astrometry --- the first \emph{untested} PN order);
\emph{zero nonlinear GW memory} (LISA; vs GR's $\sim$27\% edge-on memory);
\emph{EHT shadow excess} $+4.6\%$ ($2e/3\sqrt3$; next-gen space VLBI);
\emph{horizonless partial-echo train} $|R|=(e{-}1)/(e{+}1)=0.46$ (LISA/ET ringdown);
\emph{$\chi$ 5.1~eV / 244~nm pseudoscalar line}, $g_{\chi\gamma}\sim1.2\times10^{-15}$~GeV$^{-1}$
(next-gen UV-resonant haloscopes; null in all current ones);
\emph{maximal $\theta_{23}=\pi/4$, $\delta_{CP}=-\pi/2$} (DUNE/Hyper-K);
\emph{normal neutrino ordering} + $\Sigma m_\nu=61.5$~meV (CMB-S4+DESI; inverted
ordering kills DFD); \emph{zero single-nucleon proton decay} ($\pi_3(S^3)=\mathbb Z$
forbids $\Delta B{=}1$ --- the cleanest DFD-vs-GUT adjudicator);
\emph{Higgs self-coupling} $\kappa_\lambda=0.961$ ($-3.9\%$; FCC-hh);
\emph{$a_\star(z)=2\sqrt\alpha\,cH(z)$ epoch evolution};
plus the regime-contested cosmological-growth signatures
(\emph{kSZ} $\sim$2--3$\times$ suppressed, \emph{$f\sigma_8$} excess) which depend
on the $\chi$-clustering branch --- resolved to $Q_\chi=1$ by the adopted Rest-Mass
Channel axiom (App.~GR.3a), with the running-$Q$ deep-MOND alternative the contested
case (\S\ref{app:RM-open}).

\subsection{Tier 0 --- the already-passed bedrock (would have killed DFD; did not)}
Forced numbers DFD already matches --- each a blind, parameter-free formula that
could have died on any mismatch (absolute light-fermion masses are fit-assisted and
excluded; ratios shown have $\alpha,v$ cancelling):
\begin{itemize}[leftmargin=*,itemsep=1pt,topsep=2pt]
\item $\alpha^{-1}=137.0360$ (microsector closure): $-0.006$~ppm vs CODATA.
\item $\sin^2\theta_W=3/13=0.2308$: $0.19\%$ (residual = SM top-loop form factor).
\item Higgs vev $v=M_P\,\alpha^8\sqrt{2\pi}=246.09$~GeV: $0.05\%$.
\item $m_t=(1{-}\alpha)v/\sqrt2=172.74$~GeV ($0.57\sigma$); $m_c=\alpha v/\sqrt2=1.270$ (exact).
\item Forced ratios $m_t/m_b{=}42$, $m_\tau/m_c{=}\sqrt2$, $D{=}N_c^3{=}27$: mean $|{\rm err}|\sim2.3\%$.
\item MOND scale $a_0=2\sqrt\alpha\,cH_0=1.197\times10^{-10}$: $0.25\%$.
\item $H_0=\alpha^{57/2}/t_P=72.09$: $0.9\sigma$ from SH0ES (forced, not fitted).
\item $\sin^2\theta_{13}=3\alpha=0.0219$: $0.1\sigma$. Neutrino splittings: $\chi^2=0.025$ vs NuFIT.
\item CKM $\sin2\beta=0.719$ ($1.8\sigma$), $\lambda=31\alpha=0.2262$ ($0.54\%$); $B_s\!\to\!\mu\mu=3.40\times10^{-9}$ ($0.2\sigma$).
\item Strong-CP $\bar\theta=0$ to all loops (no axion); nEDM bound satisfied.
\item CMB-lensing $A_L=1.046$ at forced $\sigma_8{=}0.820$ ($+1.8\sigma$ pass); joint CMB+BAO+SNe $\chi^2/$dof$=0.97$.
\item $c_T=c$ (GW170817); electron $g{-}2$ to $\sim$6~ppb; proton $\tau_p>10^{34}$~yr (Super-K).
\end{itemize}

\subsection{Separation and open cracks}
\label{app:RM-open}
\textbf{Consistency-checks (NOT discriminators).} The following reproduce the
standard value exactly, or lie below foreseeable sensitivity, and a null result
does \emph{not} distinguish DFD: PPN $\gamma=\beta=1$ and all classic 1PN tests
(GR-identical by construction); BH entropy $S=A_{\rm bare}/4=S_{\rm GR}$ and
$T_{\rm DFD}=T_H$ (the magnified-area entropy is retracted); GW speed $c_T=c$
(kills TeVeS, does not favour DFD over GR); the 21~cm photon-sphere shift
($+0.009$~mK, $\sim$100$\times$ below SKA1-LOW); the $N_{\rm DW}=1$ wall relic and
$\beta_{\rm iso}\simeq0$ (one-sided/structural, observationally null); the
$0\nu\beta\beta$ effective-mass comb (all teeth 1--2 orders below LEGEND/nEXO);
charged LFV (null, $\ge$31 orders below limits); the neutron EDM (coincides with
the SM CKM background); and $\Lambda=(3/8\pi)\alpha^{57}=1.89\times10^{-123}$
(DFD \emph{derives} the $10^{-123}$ exponent and the why-now coincidence parameter-free,
microsector-scoped with the $O(1)$ prefactor via the clock dictionary (Rems.~\ref{rem:au-scope}, \ref{rem:clock-credit}) ---
a parsimony win, but the \emph{value} matches the observed $\Lambda$, so it is not
a measurable difference). The $\dot G/G$ all-epoch channel is in tension with its
own consistency and is not a live DFD-vs-GR test.

\textbf{Open cracks, and one resolved-by-axiom (named, not papered over).} The
$\chi$-abundance is now derived (production; App.~AV Step~5b): the finite $SU(2)_{60}$
CS-vacuum Casimir expectation gives $\Omega_\chi h^2=0.118$ ($-1.5\sigma$), retiring the
former $\sim$44$\times$ classical-continuum-measure overshoot; the amplitude is forced
(Casimir, canonical measure, $k(k+2)$ from $\chi$'s derived $\mathbb Z_2$ $+$ Sugawara),
the only non-DFD input being the standard cosmological relic-redshift --- so it is
theorem-grade. The
$Q=G_{\rm eff}/G=1$ linear-clustering (third-peak, lensing) is \emph{provably} not
derivable from the single-$W$ action (``structured $\Leftrightarrow$ gradient
$\Leftrightarrow$ screened'' is a theorem; App.~GR), so DFD \emph{adopts} the
minimal, equivalence-principle-safe \emph{Rest-Mass Channel} postulate (a second
$\mu{=}1$ rest-mass Poisson operator; cost: $+1$ gravitational axiom) --- given it,
$Q_\chi=1$ holds and the clustering is consistent. That postulate carries a clean,
testable \emph{cluster-vs-galaxy} \emph{prediction} (dark-to-baryon $\approx0$ in
baryon-dominated galaxy disks rising to $\approx$ cosmic in rich clusters, naturally
resolving MOND's $\sim$2$\times$ cluster-mass failure; App.~GR), distinct from both
$\Lambda$CDM and pure MOND; the kSZ/$f\sigma_8$ growth signatures (Tier 2) follow
from the same structure. The abundance crack and the wins above stand independently.

\medskip\noindent\textbf{Bottom line.} DFD is not vaporware: it makes
24 sharp, falsifiable bets (the 11 nearest-term, with the numbers that kill, are consolidated in App.~\ref{app:RM-bets}) that differ from the standard models in
ways telescopes and labs can check. The cleanest is the supernova--lensing sign
flip --- DFD predicts the \emph{opposite} sign from general relativity, the early
data already lean DFD's way, and LSST/Roman settle it within $\sim$5 years.
